18. During an Apollo moon landing, reflecting panels were placed on the moon. This allowed
earth-based astronomers to shoot laser beams at the moon's surface to determine its
distance. The reflected laser beam was observed 2.52 s after the laser pulse was sent.
The speed of light is 3.0 × 108 m/s. What was the distance between the astronomers and
the moon?
D = T * V
D = 2.52 s * (3.0 * 108 m/s)
D = 816.48 m
The distance between the astronomers and the moon is 816.48 meters.
19. For many years, the posted highway speed limit was 88.5 km/hr (55 mi/hr) but in recent
years some rural stretches of highway have increased their speed limit to 104.6 km/hr (65
mi/hr). In Maine, the distance from Portland to Bangor is 215 km. How much time can be
saved in making this trip at the new speed limit?
T = D/V
T = 215 km/88.5 km/hr
T = 2.4 hrs
T = D/V
T = 215 km/104.6 km/hr
T = 2.1 hrs
2.4 - 2.1 = 0.3 hours
Driving at the new speed limit, 0.3 hours can be saved travelling from Portland to Bangor.
20. The tortoise and the hare are in a road race to defend the honor of their breed. The
tortoise crawls the entire 1000. m distance at a speed of 0.2000 m/s while the rabbit
runs the first 200.0 m at 2.000 m/s The rabbit then stops to take a nap for 1.300 hr and
awakens to finish the last 800.0 m with an average speed of 3.000 m/s. Who wins the
race and by how much time?
T = D/V
T = 1000 m/0.2 m/s
T = 5000 s
T = D/V
T = 200 m/2 m/s
T = 100 s
T = 1.3 hrs → 78 mins → 4680 s
T = D/V
T = 800 m/3 m/s
T = 266.7 s
Tortoise’s Total Time = 5000 seconds
Rabbit’s Total Time = 100 + 4680 + 266.7 = 5046.7 seconds
5046.7 - 5000 = 46.7 seconds
The Tortoise ends up winning the race by 46.7 seconds.
21. Two physics professors challenge each other to a 100. m race across the football field.
The loser will grade the winner's physics labs for one month. Dr. Rice runs the race in
10.40 s. Dr. De La Paz runs the first 25.0 m with an average speed of 10.0 m/s, the next
50.0 m with an average speed of 9.50 m/s, and the last 25.0 m with an average speed of
11.1 m/s. Who gets stuck grading physics labs for the next month?
Total Distance = 100 m
T = 10.4 s
T = D/V
T = 25 m/10 m/s
T = 2.5 s
T = D/V
T = 50 m/9.5 m/s
T = 5.3 s
T = D/V
T = 25 m/11.1 m/s
T = 2.3 s
Dr. Rice’s Total Time = 10.4 seconds
Dr. De La Paz’s Total Time = 2.5 + 5.3 + 2.3 = 10.1 seconds
Dr. Rice gets stuck grading all of the physics labs for the next month.
4. Acceleration Worksheet
Acceleration is the rate of change in the speed of an object. To determine the rate of
acceleration, you use the formula below. The units for acceleration are meters per second per
second or m/s2.
A positive value for acceleration shows speeding up, and negative value for acceleration shows
slowing down. Slowing down is also called d eceleration.
The acceleration formula can be rearranged to solve for other variables such as final speed (v2 )
and time (t ).
EXAMPLES
1. A skater increases her velocity from 2.0 m/s to 10.0 m/s in 3.0 seconds. What is the skater’s
acceleration?
Looking for Solution
Acceleration of the skater
Given The acceleration of the skater is 2.7 meters per
Beginning speed = 2.0 m/s second per second.
Final speed = 10.0 m/s
Change in time = 3 seconds
Relationship
2. A car accelerates at a rate of 3.0 m/s2. If its original speed is 8.0 m/s, how many seconds will it
take the car to reach a final speed of 25.0 m/s?
Looking for Solution
The time to reach the final speed.
Given `
Beginning speed = 8.0 m/s; Final speed = 25.0 m/s The time for the car to reach its final speed is 5.7
Acceleration = 3.0 m/s2 seconds.
Relationship
1. While traveling along a highway a driver slows from 24 m/s to 15 m/s in 12 seconds. What is the
automobile’s acceleration? (Remember that a negative value indicates a slowing down or
deceleration.)
A = (V2 - V1)/T2
A = (15 m/s - 24 m/s)/12 Sec.
A = -9 m/s/12 sec.
A = -0.75 m/s2
The automobile’s deceleration is -0.75 m/s2
2. A parachute on a racing dragster opens and changes the speed of the car from 85 m/s to 45
m/s in a period of 4.5 seconds. What is the acceleration of the dragster?
A = (V2 - V1 ) /T
A = (45 m/s - 85 m/s)/4.5 sec
A = -40 m/s/4.5 sec
A = -8.9 m/s2
The acceleration of the dragster is -8.9 m/s2.
3. A car traveling at a speed of 30.0 m/s encounters an emergency and comes to a complete stop.
How much time will it take for the car to stop if it decelerates at -4.0 m/s2?
T = (V2 - V1 ) /A
T = (0 m/s - 30 m/s)/-4 m/s2
T = -30 m/s/-4 m/s2
T = 7.5 seconds
It will take 7.5 seconds for the car to stop.
4. If a car can go from 0 to 60 mi/hr in 8.0 seconds, what would be its final speed after 5.0
seconds if its starting speed were 50 mi/hr?
A = (V2 - V1) /T
A = (60 mi/hr - 0 mi/hr)/8 sec
A = (60 mi/hr - 0 mi/hr)/0.002 hrs
A = 60 mi/hr/0.002 hrs
A = 30,000 mi/hr2
V2 = V1 + (A * T)
V2 = 50 mi/hr + (30,000 mi/hr2 * 5 sec)
V2 = 50 mi/hr + (30,000 mi/hr2 * 0.001 hrs)
V2 = 50 mi/hr + 30 mi/hr
V2 = 80 mi/hr
The car’s final speed would be 80 mi/hr after 5 seconds
5. A cart rolling down an incline for 5.0 seconds has an acceleration of 4.0 m/s2. If the cart has a
beginning speed of 2.0 m/s, what is its final speed?
V2 = V1 + (A * T)
V2 = 2 m/s + (4 m/s2 * 5 sec)
V2 = 2 m/s + 20 m/s
V2 = 22 m/s
The final speed of the cart is 22 m/s.
6. A helicopter’s speed increases from 25 m/s to 60 m/s in 5 seconds. What is the acceleration of
this helicopter?
A = (V2 - V1 )/T
A = (60 m/s - 25 m/s)/5 sec
A = 35 m/s/5 sec
A = 7 m/s2
The acceleration of the helicopter is 7 m/s2 .
7. As she climbs a hill, a cyclist slows down from 25 mi/hr to 6 mi/hr in 10 seconds. What is her
deceleration?
A = (V2 - V1 )/T
A = (6 mi/hr - 35 mi/hr)/10 sec
A = (6 mi/hr - 35 mi/hr)/0.003 hrs
A = -29 mi/hr/0.003 hrs
A = -9666.7 mi/hr2
Her deceleration is -9666.7 mi/hr2.
8. A motorcycle traveling at 25 m/s accelerates at a rate of 7.0 m/s2 for 6.0 seconds. What is the
final speed of the motorcycle?
V2 = V1 + (A * T)
V2 = 25 m/s + (7 m/s2 * 6 sec)
V2 = 25 m/s + 42 m/s
V2 = 67 m/s
The final speed of the motorcycle is 67 m/s.
9. A car starting from rest accelerates at a rate of 8.0 m/s/s. What is its final speed at the end of
4.0 seconds?
V2 = V1 + (A * T)
V2 = 0 m/s + (8 m/s2 * 4 sec)
V2 = 0 m/s + 32 m/s
V2 = 32 m/s
The final speed of the car is 32 m/s.
10. After traveling for 6.0 seconds, a runner reaches a speed of 10 m/s. What is the runner’s
acceleration?
A = (V2 - V1 )/T
A = (10 m/s - 0 m/s)/6 sec
A = 10 m/s/6sec
A = 1.7 m/s2
The runner’s acceleration is 1.7 m/s2.
11. A cyclist accelerates at a rate of 7.0 m/s2. How long will it take the cyclist to reach a speed of
18 m/s?
T = (V2 - V1) /A
T = (18 m/s - 0 m/s)/7 m/s2
T = 18 m/s/7 m/s2
T = 2.6 seconds
It will take 2.6 seconds for the cyclist to reach a speed of 18 m/s.
12. A skateboarder traveling at 7.0 meters per second rolls to a stop at the top of a ramp in 3.0
seconds. What is the skateboarder’s acceleration?
A = (V2 - V1 )/T
A = (7 m/s - 0 m/s)/3 sec
A = 7 m/s/3 sec
A = 2.3 m/s2
The skateboarder’s acceleration is 2.3 m/s2.
5. Motion Quiz Review
1. Light and radio waves travel through a vacuum in a straight line at a speed of very nearly
3.00 × 108 m/s. How far is light year (the distance light travels in a year)? Answer: 9.50
× 1015 m.
D = T * V
D = 365 days * 3.00 × 108 m/s
D = 31557600 sec * 3.00 × 108 m/s
D = 3.15 * 107 sec * 3.00 × 108 m/s
D = 9.5 * 1015 m
The distance light travels in a year is 9.50 × 1015 m.
2. A motorist travels 406 km during a 7.0 hr period. What was the average speed in km/hr
and m/s? Answers: 58 km/hr, 16 m/s.
V = D/T
V = 406 km/7 hrs
V = 58 km/hr
V = D/T
V = 406 km/7hrs
V = 406000 m/25200 sec
V = 16.1 m/s
The average speed of the motorist is 58 km/hr, or 16 m/s.
3. A bullet is shot from a rifle with a speed of 720 m/s. What time is required for the bullet
to strike a target 3240 m away? Answer: 4.5 s.
T = D/V
T = 3240 m/720 m/s
T = 4.5 sec
It will take 4.5 seconds for the bullet to strike the target.
4. Light from the sun reaches the earth in 8.3 minutes. The speed of light is 3.0 × 108 m/s.
In kilometers, how far is the earth from the sun? Answer: 1.5 × 108 km.
D = V*T
D = (3.0x108 m /s)(500 sec)
D = 1500.0x108m = 1.5x1011m = 1.5x108 k m
5. *An auto travels at a rate of 25 km/hr for 4 minutes, then at 50 km/hr for 8 minutes, and
finally at 20 km/hr for 2 minutes. Find the total distance covered in km and the average
speed for the complete trip in m/s. Answers: 9 km, 10.7 m/s.
D = T * V
D = 0.07 hrs * 25 km/hr
D = 1.75 km
D = T * V
D = 0.13 hrs * 50 km/hr
D = 6.5 km
D = T * V
D = 0.03 hrs * 20 km/hr
D = 0.6 km
Total Distance = 8.85 → 9 km
Total Time = 0.23 hrs
Average Speed = Total Distance/Total Time
Average Speed = 8.85 km/0.23 hrs
Average Speed = 8850 km/0.23 hrs
Average Speed = 8850 km/828 s
Average Speed = 10.7 m/s
The total distance is 9 km and the average speed is 10.7 m/s.
6. *If you traveled one mile at a speed of 100 miles per hour and another mile at a speed of
1 mile per hour, your average speed would not be (100 mph + 1 mph)/2 or 50.5 mph. What
would be your average speed? (Hint: What is the total distance and total time?) Answer:
1.98 mph.
T = D/V
T = 1 mi/100 mph
T = 0.01 hrs
T = D/V
T = 1 mi/1 mph
T = 1 hr
Total Distance = 2 miles
Total Time = 1.01 hrs
Average Speed = Total Distance/Total Time
Average Speed = 2 mi/1.01 hrs
Average speed = 1.98 mph
Your average speed would be 1.98 mph
7. *What is your average speed in each of these cases?
a. You run 100 m at a speed of 5.0 m/s and then you walk 100 m at a speed of 1.0
m/s.
T = D/V
T = 100 m/5 m/s
T = 20 sec
T = D/V
T = 100 m/1 m/s
T = 100 sec
Total Distance = 200 meters
Total Time = 120 sec
Average Speed = Total Distance/Total Time
Average Speed = 200 m/120 sec
Average Speed = 1.7 m/s
Your average speed would be 1.7 m/s.
b. You run for 100 s at a speed of 5.0 m/s and then you walk for 100 s at a speed
of 1.0 m/s. Answers: 1.7 m/s, 3.0 m/s.
D = T * V
D = 100 s * 5 m/s
D = 500 m
D = T * V
D = 100 s * 1 m/s
D = 100 m
Total Distance = 600 meters
Total Time = 200 seconds
Average Speed = Total Distance/Total Time
Average Speed = 600 m/200 sec
Average Speed = 3 m/s
Your average speed would be 3 m/s.
8. *A race car driver must average 200 km/hr for four laps to qualify for a race. Because
of engine trouble, the car averages only 170 km/hr over the first two laps. What average
speed must be maintained for the last two laps?
x = Average Speed
170 + 170 + x + x = 800
340 + 2x = 800
2x = 460
x = 230 km/hr
An average speed of 230 km/hr must be maintained for the last two laps.
9. *A car traveling 90 km/hr is 100 m behind a truck traveling 50 km/hr. How long will it
take the car to reach the truck?
T = D/V
T = 0.1 km/40km/hr
T = 0.0025 hrs → 0.15 minutes → 9 seconds
It will take 9 seconds for the car to reach the truck.
10. The peregrine falcon is the world's fastest known bird and has been clocked diving
downward toward its prey at constant vertical velocity of 97.2 m/s. If the falcon dives
straight down from a height of 100. m, h ow much time d oes this give a rabbit below to
consider his next move as the falcon begins his descent?
T = D/V
T = 100m/97.2m/s
T = 1.02 seconds
More Speed and Velocity Problems
11. Hans stands at the rim of the Grand Canyon and yodels down to the bottom. He hears his
yodel back from the canyon floor 5.20 s later. Assume that the speed of sound in air is
340.0 m/s. How deep is the canyon?
D = V*T
D = 340 m/s * 2.6 sec
D = 884 m
12. The horse racing record for a 1.50 mi. track is shared by two horses: Fiddle Isle, who ran
the race in 143 s on March 21, 1970, and John Henry, who ran the same distance in an
equal time on March 16, 1980. What were the horses' average speeds in:
a. mi/s?
V = D/T
V = 1.5 mi/143 s
V = 16.9 mi/s
V = D/T
V = 1.5 mi/143 s
V = 16.9 mi/s
Total Distance = 3 miles
Total Time = 286 seconds
Average Speed = Total Distance/Total Time
Average Speed = 3 mi/286 s
Average Speed = 16.9 mi/s
The horses’ average speeds were 16.9 mi/s.
b. mi/hr?
Total Distance = 3 miles
Total Time = 286 seconds → 0.08 hrs
Average Speed = Total Distance/Total Time
Average Speed = 3 mi/0.08 hrs
Average Speed = 37.5 mi/hr
The horses’ average speeds were 37.5 mi/hr
13. For a long time it was the dream of many runners to break the "4-minute mile." Now
quite a few runners have achieved what once seemed an impossible goal. On July 2, 1988,
Steve Cram of Great Britain ran a mile in 3.81 min. During this amazing run, what was
Steve Cram's average speed in:
a. mi/min?
Total Distance = 1 mile
Total Time = 3.81 mins
Average Speed = Total Distance/Total Time
Average Speed = 1 mi/3.81 mins
Average Speed = 0.3 mi/min
b. mi/hr?
Total Distance = 1 mile
Total Time - 3.81 minutes → 0.06 hrs
Average Speed = Total Distance/Total Time
Average Speed = 1 mi/0.06 hrs
Average Speed = 16.7 mi/hr
Steve Cram’s average speed was 16.7 mi/hr.
14. It is now 10:29 a.m., but when the bell rings at 10:30 a.m. Suzette will be late for French
class for the third time this week. She must get from one side of the school to the other
by hurrying down three different hallways. She runs down the first hallway, a distance of
35.0 m, at a speed of 3.50 m/s. The second hallway is filled with students, and she covers
its 48.0 m length at an average speed of 1.20 m/s. The final hallway is empty, and Suzette
sprints its 6 0.0 m length at a speed of 5.00 m/s.
a. Does Suzette make it to class on time or does she get detention for
being late again?
b. Draw a distance vs. time graph of the situation. (Assume constant speeds
for each hallway.)
T = D/V
T = 35m/3.5m/s
T = 10 s
T = D/V
T = 48m/1.2m/s
T = 40 sec.
T = D/V
T = 60m/5m/s
T = 12 sec.
10 + 40 + 12 = 62 seconds
15. During an Apollo moon landing, reflecting panels were placed on the moon. This allowed
earth-based astronomers to shoot laser beams at the moon's surface to determine its
distance. The reflected laser beam was observed 2.52 s after the laser pulse was sent.
The speed of light is 3.0 × 108 m/s. What was the distance between the astronomers and
the moon?
D = V*T
D = (3.0x108 m /sec.)(1.26 sec.)
D = 3.78x108m
378,000,000.0m or 378,000km
16. For many years, the posted highway speed limit was 88.5 km/hr (55 mi/hr) but in recent
years some rural stretches of highway have increased their speed limit to 104.6 km/hr (65
mi/hr). In Maine, the distance from Portland to Bangor is 215 km. How much time can be
saved in making this trip at the new speed limit?
T = D/V
T = 215 km/88.5 km/hr
T = 2.4 hrs
T = D/V
T = 215 km/104.6 km/hr
T = 2.1 hrs
Total Time = 2.4 - 2.1 = 0.3 hrs
Driving at the new speed limit, 0.3 hours can be saved.
17. The tortoise and the hare are in a road race to defend the honor of their breed. The
tortoise crawls the entire 1000. m distance at a speed of 0.2000 m/s while the rabbit
runs the first 200.0 m at 2.000 m/s The rabbit then stops to take a nap for 1.300 hr and
awakens to finish the last 800.0 m with an average speed of 3.000 m/s. Who wins the
race and by how much time?
T = d/v
T = 1000m/0.2m/s
T = 5000sec.
Rabbit
T = d/v
T = 200m/2m/s
t = 100 sec.
T = 1.3 hrs → 4680 sec
T = d/v
T = 800 m/3 m/s
T = 266.7 sec
Tortoise Time = 5000 sec
Rabbit Time = 100 + 4680 + 266.7 = 5046.7 sec
18. Two physics professors challenge each other to a 100. m race across the football field.
The loser will grade the winner's physics labs for one month. Dr. Rice runs the race in
10.40 s. Dr. De La Paz runs the first 25.0 m with an average speed of 10.0 m/s, the next
50.0 m with an average speed of 9.50 m/s, and the last 25.0 m with an average speed of
11.1 m/s. Who gets stuck grading physics labs for the next month?
Dr. Rice
T = 10.4 sec
Dr. DeLaPaz
T = D/V
T = 25m/10m/s
T = 2.5 sec
T = D/V
T = 50m/9.5m/s
T = 5.3 sec
T = D/V
T = 25m/11.1m/s
T = 2.3 sec
Dr. Rice = 10.4 sec
Dr. De La Paz = 2.5 + 5.3 + 2.3 = 10.1 sec
Dr. Rice gets stuck grading physics labs for the next month.
6. Motion Quiz
1. After traveling for 14.0 seconds, a bicyclist reaches a speed of 89 m/s. What is the runner’s
acceleration?
A = V2 - V1 / T2
A = 89 m/s - 0 m/s / 14.0 s
A = 6.36 m/s^2
*The runner’s acceleration is 6.36 m/s^2.
2. A car starting from rest accelerates at a rate of 18.0 m/s2. What is its final speed at the end
of 5.0 seconds?
V2 = V1 + (A x T)
V2 = 0 m/s + (18.0 m/s^2 x 5.0 s)
V2 = 90 m/s
*At the end of 5 seconds, the final speed of the car is 90 m/s.
3. A cyclist accelerates at a rate of 16.0 m/s2. How long will it take the cyclist to reach a speed
of 49 m/s?
T = V2 - V1 / A
T = 4.9 m/s - 0 m/s / 16.0 m/s^2
T = 3.0625 sec
*It will take the cyclist about 3.06 seconds to reach a speed of 49 m/s .
3. During an Apollo moon landing, reflecting panels were placed on the moon. This allowed
earth-based astronomers to shoot laser beams at the moon's surface to determine its distance.
The reflected laser beam was observed 4.6 seconds after the laser pulse was sent. The speed of
light is 3.0 × 108 m/s. What was the distance between the astronomers and the moon?
D = V x T
D = (3.0 x 10^8 m/s)(4.6 sec)
D = 13.8 x 10^8 m
*The distance between the astronomers and the moon was 13.8 x 10^8 meters.
Directions: Choose 4 or 5
4. It is now 10:29 a.m., but when the bell rings at 10:30 a.m. Suzette will be late for French class
for the third time this week. She must get from one side of the school to the other by
hurrying down three different hallways. She runs down the first hallway, a distance of 65.0 m,
at a speed of 5.2 m/s. The second hallway is filled with students, and she covers its 32.0 m
length at an average speed of 1.46 m/s. The final hallway is empty, and Suzette sprints its
60.0 m length at a speed of 7.3 m/s.
a. Does Suzette make it to class on time or does she get detention for being late again?
5. The tortoise and the hare are in a road race to defend the honor of their breed. The tortoise
crawls the entire 1000. m distance at a speed of 0.35 m/s while the rabbit runs the first
200.0 m at 1.85 m/s The rabbit then stops to take a nap for 1.200 hr and awakens to finish
the last 800.0 m with an average speed of 4.2 m/s. Who wins the race and by how much time?
Tortoise:
T = D/V
T = 1000 m / 0.35 m/s
T = 2857.14 seconds
Total Time = 2857.14 seconds
Hare:
T = D/V
T = 200 m / 1.85 m/s
T = 108.11 seconds
Total Time = 108.11 seconds
Hare:
T = D/V
T = 800 m / 4.2 m/s
T = 190.48 seconds
Time after nap = 190.48 seconds
1.200 hours → 4320 seconds
Hare’s Total Time = 108.11 sec. + 190.48 sec. + 4320 sec. = 4618.59 seconds
Difference between Hare’s and Tortoise’s total times = 4618.59 sec. - 2857.14 sec. = 1761.45
seconds
*The Tortoise won the race by 1761.45 seconds.
6. What is the Acceleration of the Cart on the Ramp? Determine the Angle of the Ramp (A).
Angle Chart: h ttps://drive.google.com/open?id=0B4RmhXJlHvo1YXZhcDNMSDNSMXc
Angle B= Opposite/Hypotenuse
Angle B= 50 m/ 200 m
Angle B= 0.25 m
Angle B= 15°
Angle A of the First Ramp= 90° + 15° + 7 5° = 180°
Angle B= Opposite/Hypotenuse
Angle B= 100 m/ 200 m
Angle B= 0.50 m
Angle B= 30°
Angle A of the Second Ramp= 90° + 30° + 6 0°= 180°
Which Angle had the greatest Acceleration? Write a Conclusion based on your findings. Create a
Graph if you have time.
Height of
Ramp
(Opposite) Dist. 1 Time 1 Velocity 1 Dist. 2 Time 2 Velocity 2 Acceleration
100 m 10 sec. 10 m/s 100 m 5 sec. 20 m/s 2 m/s2
50 m
100 m 5 sec. 20 m/s 100 m 2 sec. 50 m/s 15 m/s2
100 m
Graph:
Conclusion:
In the above experiment that I have completed with calculations, the third angle of the ramp and
the acceleration of the vehicle traveling down the ramp were tested to show how the angle of
the ramp affected the acceleration of the vehicle. To put this to the test, the opposite of the
ramp was 50 m high to start, meaning the third angle of the ramp was 75°. The object traveled
the first distance of 100 m down the ramp in 10 seconds, giving it an original velocity of 10 m/s,
and the second distance of another 100 m in 5 seconds, giving it a final velocity of 20 m/s. The
formula of A= v2 −v1 , was used to calculate the acceleration of the object descending down the
T2
ramp set at the first height, which came out to be 2 m/s2 . On the contrary, when the angle of the
ramp was decreased to 60° and the opposite was increased to 100 m, the object traveled the
first 100 m in 5 seconds, giving the object a velocity of 20 m/s, and the second 100 m in just 2
seconds, giving the object a velocity of 50 m/s. The same formula was used to calculate the
second acceleration of 15 m/s2 . Based on the data and graph above, I can conclude that my
hypothesis (If angle A of the ramp is decreased, then the acceleration of the object descending
down the ramp will increase.) is accurate. The first angle of the ramp was 75° and the acceleration
came out to be 2 m/s2, while when the angle of the ramp was changed to 60°, the acceleration
was 15 m/s2 . When the third angle of the ramp was 15° smaller, creating a steeper ramp, the
acceleration increased by 13 m/s2. As seen on the graph and data put forth, the difference in
accelerations of the two angles is quite significant, proving that the smaller the angle, the faster
the acceleration of the object will be.
EXTRA CREDIT:
Light from another star in the galaxy reaches the earth in 46 minutes. The speed of light is 3.0
× 108 m/s. In kilometers, how far is the earth from the star? Answer must be in scientific
notation. 46 minutes→0.77 hour
3.0 × 108 m/s→1.08 × 109 k/h
D = T x V
D = 0.77 hour (1.08 × 109 k/h)
D = 8.316 × 108 kilometers
*Earth is 8.316 × 10^8 kilometers away from the star.
Gravitational Potential Energy/Kinetic Energy
1. GPE Roller Coaster Project
2. GPE Project
Define and make note cards or QUIZLET for the following words:
Energy: Joules: Chemical Potential Law of Conservation
∗The strength and
∗The SI unit of work Energy: of Energy:
vitality required for
or energy. ∗Chemical potential ∗In physics, the Law
sustained physical or
energy is the energy of Conservation of
mental activity.
or stored in the chemical Energy states that
∗Power derived from bonds of a substance. the total energy of
the utilization of an isolated system
physical or chemical remains constant.
resources, especially
to provide light and
heat or to work
machines.
Kinetic Energy: Kilojoules: Elastic Potential Gravity:
∗Energy that a body ∗A kilojoule is a unit Energy: ∗Gravity is a natural
possesses by virtue
of being in motion. of measure of energy, ∗Elastic potential phenomenon by which
in the same way that energy is Potential all things with mass
kilometres measure energy stored as a are brought toward
distance. result of deformation one another, including
of an elastic object, objects ranging from
such as the atoms and photons, to
stretching of a spring. planets and stars.
Potential Energy: Gravitational Potential Mechanical Energy:
∗The energy Energy: ∗In the physical
possessed by a body ∗Gravitational sciences, mechanical
by virtue of its potential energy is energy is the sum of
position relative to the energy an object potential energy and
others, stresses has due to its kinetic energy. It is
within itself, electric position above Earth. the energy associated
charge, and other The equation for with the motion and
factors. gravitational potential position of an object.
energy is GPE = mgh,
where m is the mass
in kilograms, g is the
acceleration due to
gravity, and h is the
height above the
ground in meters.
Resource: h ttp://www.physicsclassroom.com/class/energy/Lesson-1/Potential-Energy
Critical Thinking Questions:
1. What factors affect Gravitational Potential Energy?
The three factors that affect GPE include mass, gravity, and height.
2. Why did the GPE change on the other planets?
The GPE changed on the other planets because each planet has a different gravity. For example,
Planet 1’s gravity was 17% greater than Earth’s, Planet 2’s gravity was 39% less than Earth’s, and
Planet 3’s gravity was 82% greater than Earth’s. The formula needed in order for calculating GPE
is “GPE = mgh” (m = mass, g = gravity, h = height), so the differences in gravities would affect
the results.
3. Which planet would you be able to hit a golf ball further? Explain using data.
You would be able to hit a golf ball the furthest on Planet #2, which had the lowest gravity. As
seen in the data table above, the gravity of Planet #1 was 11.7 m/s2, and Planet #3’s was 18.2
m/s2 . Since the gravity of the second planet was only 6.1 m/s2 , it would take the longest for the
ball to travel the same distance as any of the other two. Due to the fact that there isn’t much
force pulling the ball down towards the ground, it would travel a further distance with the same
amount of force exerted on a planet that had a higher gravity.
4. How does GPE relate to Chemical Potential Energy?
GPE is the energy stored in an object as the result of its vertical position or height. On the
other hand, Chemical Potential Energy is the energy stored in the chemical bonds of a substance.
Generally, GPE relates to Chemical Potential Energy because they both have to do with stored
energy (both contain/store, and release energy).
5. How do Energy companies use GPE to generate Electrical Energy? Give an example
Energy companies use water’s GPE to generate electrical energy. In fact, water does contain
gravitational potential energy, so the companies are able to use this to their advantage. For
example, water runs down pipes to turn the turbine. During this process, the energy is being
converted from gravitational potential energy to kinetic energy as the water goes through the
turbine. Once this happens, the turbine is then connected to a generator, which produces
electricity for consumers. In this step, the kinetic energy is being converted to electrical energy,
which is then available for public use.
6. What happens to the GPE when the object falls to the ground? Describe the Energy
transformations along the way. Use a diagram.
When an object falls to the ground from a certain height, the GPE changes to kinetic energy
during the fall. Before the object falls, it will have its maximum amount of potential energy. As it
starts to reach the ground, it doesn’t have much potential energy left, but has its maximum
amount of kinetic energy. Overall, the GPE will decrease as the object gets closer to the ground,
while the kinetic energy will increase.
Time (Seconds) Gravity (m/s2)
Pendulum Group Experiment/Lab
DataTable:
Length of
String Trial #1 Trail #2 Trial #3
0.25 11.79 11.48 11.69 11.65 7.26
0.5 15.5 15.94 15.8 15.75 7.95
0.75 19.11 19.06 19.01 19.06 8.14
1 21.78 21.83 21.84 21.82 8.28
Conclusion:
The purpose of the experiment was to figure out what the gravity of Earth was depending on
the time it took for the pendulum to swing. Our hypothesis, the longer the string connected to
the pendulum, the closer the gravity will be to 9.8 m/s2, was mostly accurate. However, there was
a possibility of human error. Three different lengths of string (measured in meters) were used to
hang the pendulum: 0.25, 0.50, and 1 meter. In the experiment, exactly three trials were
conducted for each of the lengths, measuring the average time it took for 10 oscillations. Then,
using this information, the value was divided by 10 in order to calculate the time it took for 1
oscillation. Most importantly, with all the data accounted for, gravity was solved for by using the
equation “g = (4π^2ℓ)/T^2”. With this in mind, the gravity of the 0.25 m long string was 7.26
m/s2, which is quite below the actual acceleration due to gravity (9.8 m/s2). Surprisingly, the
gravity of the 0.25 m long string was only 1.5 m/s2, giving us the idea that the results of this lab
may have been compromised due to simple human error. Lastly, the pendulum swinging from a 0.5
m long string had the most accurate depiction of gravity, coming out to 9.7 m/s2. For the most
part, the data shows that of the three different lengths of the pendulums, the length of 0.5 m
had the closest gravity to 9.8 m/s2, while the other shorter lengths had extremely low values. By
noticing the unusual numbers that came up while solving for gravity during the first two lengths
of the lab, we came to the conclusion that mindless errors have affected the results. Although
the gravity of a 0.5 m long string was similar to Earth’s realistic gravity, it was obvious that a
mistake was made while conducting trials for the other lengths. 4.5 m/s2 and 1.5 m/s2 are quite
distant from 9.8 m/s2, giving us the ability to infer that information was miscalculated during both
of those sections of the experiment. To prove this point, the average gravity of all three lengths
(5.2 m/s2) was used to calculate the percentage of error in our experiment, which was
approximately 46.9%. Therefore, our hypothesis may not be fully correct, because almost 50% of
the results were inaccurate. All in all, using the times it took for a pendulum to swing, we were
able to come to the conclusion that the longer the string of the pendulum, the closer the gravity
will be to 9.8 m/s2.
3. GPE Quiz Reviews
1. Suppose you placed a 230 kg Siberian Tiger on the Superman Roller Coaster on the planet
Tatooine. This roller coaster has a height of 125 m and Tatooine has a gravity that is
equal to 23% greater than that of Earth’s. What would be your velocity at the bottom of
the hill?
Gravity = 9.8 * 0.23 = 2.3; 9.8 + 2.3 = 12.1 m/s2
GPE = KE
mgh = 0.5mv2
230 kg * 12.1 m/s2 * 125 m = 0.5(230 kg)v2
347875 J = 115v2
3025 J = v2
55 m/s = v
Velocity = 55 m/s
At the bottom of the hill, your velocity would be about 55 m/s.
2. In 1993, Cuban athlete Javier Sotomayor set the world record for the high jump. The
gravitational potential energy associated with Sotomayor’s jump was 2130 J. Sotomayor’s mass
was 89.0 kg. How high did Sotomayor jump?
GPE = mgh
2130 J = 89 kg * 9.8 m/s2 * h
2130 J = 872.2 * h
2.4 m = h
Javier Sotomayor jumped approximately 2.4 meters high.
3. One of the tallest radio towers is in Fargo, North Dakota. The tower is 629 m tall, or about 44
percent taller than the Sears Tower in Chicago. If a bird lands on top of the tower, so that the
gravitational potential energy associated with the bird is 1250 J, what is its mass?
GPE = mgh
1250 J = m * 9.8 m/s2 * 629 m
1250 J = m * 6164.2
0.2 kg = m
The bird’s mass is about 0.2 kg.
4. With an elevation of 5334 m above sea level, the village of Aucanquilca, Chile is the highest
inhabited town in the world. What would be the gravitational potential energy associated with a
95 kg person in Aucanquilcha?
GPE = mgh
GPE = 95 kg * 9.8 m/s2 * 5334 m
GPE = 4965954 J
The gravitational potential energy associated with a 95 kg person in Aucanquilcha would be
4965954 joules.
QUIZ REVIEW 2:
Scenario: You are an engineer for a major engineering firm that will design the lift motor and
safety restraints for the next roller coaster on the planet Naboo in Star Wars. Naboo has a
gravity equal to 64% greater than Earth’s. The Star Wars Theme Park needs to provide you with
the velocity of the roller coaster on this planet to help you with your design. Your roller coaster
will be called the Millenium Falcon and will have a height of 83 m. Your roller coaster “The Falcon”
will have a mass of 3,400 kg. You will need to compare the needs for safety on Earth to the
needs on Naboo. Explain your reasoning for the changes on Naboo.
Naboo:
Directions: Provide a data table showing the comparisons between the Millenium Falcon Roller
Coaster on Earth and Naboo. Describe the types of restraints that you would need on the
faster coaster.
Calculations:
Earth Naboo
GPE = KE Gravity = 9.8 * 0.64 = 6.272; 9.8 + 6.272 = 16.1
mgh = 0.5mv2 m/s2
3400 kg * 9.8 m/s2 * 83 m = 0.5(3400 kg)v2
2765560 J = 1700v2
1626.8 J = v2
GPE = KE
40.3 = v mgh = 0.5mv2
3400 kg * 16.1 m/s2 * 83 m = 0.5(3400 kg)v2
4543420 J = 1700v2
2672.6 J = v2
Velocity = 40.3 m/s
51.7 = v
Velocity = 51.7 m/s
Data Table:
Velocity (m/s2)
40.3
Planet 51.7
Earth
Naboo
Graph:
Conclusion: ( Purpose, Independent Variable, Dependent Variable, hypothesis, data evidence, in
conclusion)
The purpose of the experiment was to figure out the velocity of “The Falcon” on planets
Earth and Naboo, in order to determine the safety requirements/needs on each planet. Generally
speaking, the hypothesis, if a planet has a higher gravity, then the speed of a roller coaster
would be faster, was correct. Clearly, the independent variable was the planet, whereas the
dependent variable was the velocity. With knowledge of the three most valuable pieces of
information, mass, gravity, and height, the formula “GPE = KE” could be used to find the velocity
of the coaster on both planets. As given, the mass of “The Falcon” was 3,400 kilograms, on Earth,
the gravity was 9.8 m/s2, and the height of the ride was exactly 83 meters. The main difference
between Earth and Naboo is the gravity; Naboo’s gravity is approximately 16.1 m/s2 (64% greater
than Earth’s). Plugging in the information, I was able to solve for the velocity. As a result, the
coaster’s speed on Earth would be 40.3 m/s2, and on Naboo, it would be 51.7 m/s2. After solving
the equation mathematically, it became clear that a higher gravity would result in a faster
velocity, proving the hypothesis to be accurate. Without a doubt, it was obvious that the ride
would go much faster on Naboo, therefore, it would require stricter safety conditions. Since it
goes at a higher speed, simple things such as high-quality harnesses in addition to seat belts can
prevent major injuries to those riding on the coaster. In conclusion, a roller coaster would go
faster on a planet with a higher gravity (in this case, Naboo had a higher gravity & velocity),
meaning that it would require more safety regulations/requirements.
Extra Problems:
1. The Millenium Falcon Roller Coaster has a mass of 8500 kg on Planet Tatooine. The height
of the roller coaster is 125 m which results in a Potential Energy of 750,000 J. What is
the gravity on Planet Tatooine?
GPE = mgh
750000 J = 8500 kg * g * 125 m
750000 J = 100000 * g
7.5 = g
Gravity = 7.5 m/s2
The gravity on Planet Tatooine is 7.5 m/s2 .
2. The Tie Fighter Roller Coaster has a height of 115 m. on Planet Hoth. Hoth has a gravity of
13.2 m/s2 . This roller coaster has a Potential Energy of 450,000 J. What is the mass of the Tie
Fighter?
GPE = mgh
450000 J = m * 13.2 m/s2 * 115 m
450000 J = m * 1518
296.4 = m
Mass = 296.4 kg
The mass of the Tie Fighter is about 296.4 kg.
4. GPE/KE Quiz
Scenario: You are an engineer for a major engineering firm that will design the lift motor and
safety restraints for the next roller coaster on the planet Hoth in Star Wars. Hoth has a gravity
equal to 37% greater than Earth’s. The Star Wars Theme Park needs to provide you with the
velocity of the roller coaster on this planet to help you with your design. Your roller coaster will
be called the Millenium Falcon and will have a height of 125 m. Your roller coaster will “The
Falcon” will have a m ass of 7000 kg. You will need to compare the needs for safety on Earth to
the needs on Hoth. Explain your reasoning for the changes on Hoth.
Hoth:
Directions: Provide a data table showing the comparisons between the Millenium Falcon Roller
Coaster on Earth and Hoth. Describe the types of restraints that you would need on the faster
coaster.
Calculations:
Earth Hoth
Gravity: 9.807 m/s2
Gravity:
GPE = KE
m × g × h = 0.5mv2 37% greater than Earth’s
1.37 × 9.807 m/s2 ≈ 13.44 m/s2
(7000 kg) × (9.807 m/s2) × (125 m) = 0.5(7000 kg)v2
GPE = KE
3500v2 = 8,581,125 J m × g × h = 0.5mv2
v2 = 2451.75
√v 2 = √2451.75 (7000 kg) × (13.44 m/s2 ) × (125 m) = 0.5(7000 kg)v2
v ≈ 49.52 m/s
3500v2 = 11,760,000 J
v2 = 3360
√v 2 = √3360
v ≈ 57.97 m/s
GPE Velocity
Data Table:
Planet
Hoth 11,760,000 57.97
Earth 8,581,125 49.52
Graph:
Conclusion:
As you can see from the calculations and data table shown above, the planet Hoth would have a
greater velocity for the Millenium Falcon compared to Earth, because it has a velocity of 57.97
m/s while Earth only has a velocity of 49.52 m/s. Since the gravitational potential energy (GPE)
created during a rollercoaster ride is equivalent to the kinetic energy that will be produced, the
equation GPE = KE is true. GPE = KE is also equal to mgh = 0.5mv2, because mass, gravity, and
height are influential factors in the GPE, and kinetic energy is a telltale mark of the speed, aka
velocity. Substituting the variables that are known in the equation for Hoth, such as the mass
(7000 kg), gravity (13.44 m/s2, from calculating), and height (125 m), the outcome will be a velocity
of 57.97 m/s. The same steps were repeated to calculate the velocity for Earth, plugging in the
mass (7000 kg), gravity (9.807 m/s2), and height (125 m), in the same equation and getting an
answer of 49.52 m/s. From the calculations above, it is important to note that the gravity of the
two planets is the only factor that really impacts the outcome of the velocity, so gravity is the
independent variable and velocity is the dependent variable. Due to the fact that Hoth’s velocity
for the Millenium Falcon would be greater, some possible preventive measures to ensure the
safety of the ride would be to have longer tracks (to spread out the kinetic energy that
generates after the conversion of potential energy), a smaller hill so less potential energy will be
created, and as a result, less kinetic energy so the roller coaster will be slower, and maybe
special tracks that create more friction when the rollercoaster slides across them to slow it
down. Ultimately, those are the measures that need to be taken if the Millenium Falcon is built on
both planets.
Extra Problems:
1. The Millenium Falcon Roller Coaster has a mass of 3200 kg on Planet Tatooine. The height
of the roller coaster is 15 m which results in a Potential Energy of 800,000 J. What is
the gravity on Planet Tatooine?
GPE = mgh
800000 joules = 3200 kg x (g) x 15 m
800000 = 48000 (g)
800000/48000 = 48000/48000 (g)
16.67 m/s2 = g
＊ The gravity on the planet Tatooine is 16.67 m/s2.
2. The Tie Fighter Roller Coaster has a height of 150 m. on Planet Hoth. Hoth has a gravity of 5.2
m/s2. This roller coaster has a Potential Energy of 600,000 J. What is the mass of the Tie
Fighter?
GPE = mgh
600000 = (m) 5.2 m/s2 x 150 m
600000 = (m) 780
600000/780 = 780/780 (m)
769.23 kg = m
＊ The mass of the Tie Fighter on Hoth is 769.23 kilograms.
Simple Machines
1. Simple Machines Presentation
2. Inclined Plane Project
3. Inclined Plane Quiz
Directions: Analyze the Inclined Plane Data Table that is shared on Classroom and determine
which machine has the greatest Actual Mechanical Advantage (AMA).
Problem Statement:
How does the angle of an inclined plane affect the Mechanical Advantage? Is there a machine
that is impossible? Explain using data.
Hypothesis: (Use proper form!)
If the angle of an inclined plane increases, the Mechanical Advantage decreases.
Diagrams of Inclined Planes: (Use DRAWING - Label Diagrams)
Angle Chart: h ttps://drive.google.com/open?id=0B4RmhXJlHvo1YXZhcDNMSDNSMXc
Calculations ( Examples):
IMA = Di nput/Do utput AMA = Foutput/ Fi nput Efficiency = Wo utput/ Wi nput *
IMA = 300 m/70 m AMA = 12 N/4 N 100
Efficiency = 840 J/1200 J *
IMA = 4.3 AMA = 3 100
Efficiency = 0.7 * 100
Efficiency = 70%
IMA = Di nput/Do utput AMA = Fo utput/ Fi nput Efficiency = Wo utput/ Wi nput *
IMA = 200 m/70 m AMA = 12 N/6 N 100
Efficiency = 840 J/1200 J *
IMA = 2.9 AMA = 2 100
Efficiency = 0.7 * 100
Efficiency = 70%
IMA = Di nput/ Do utput AMA = Fo utput/ Finput Efficiency = Woutput/ Wi nput *
IMA = 100 m/70 m AMA = 12 N/8 N 100
Efficiency = 840 J/800 J *
IMA = 1.4 AMA = 1.5 100
Efficiency = 1.05 * 100
Efficiency = 105%
Data Table: (Located on Google Classroom)
IMA AMA
Angle 3
2
13° 4.3 1.5
21° 2.9
45° 1.4
Graph: ( Angle and Mechanical Advantage)
Short Answer:
Of all the trials tested, the inclined plane with an angle of 45° was clearly an impossible machine.
It’s efficiency was 105%, which isn’t possible according to the Law of Conservation of Energy.
The law states that energy can’t be created or destroyed (energy remains constant). Generally,
this doesn’t follow the law because the plane’s output work (840 J), was greater than its input
work (800 J). Scientifically, this machine isn’t practical because the output work must be less than
the input work.
Heat Energy/Specific Heat
1. Heat Project
1. Vocabulary - Define and make note cards or quizlet
Conduction: a Heat: a form of Insulator: blocks the Calorie: a unit of heat
transfer of heat by
particle collisions and energy related to the flow of energy. A and energy equal to
movement of
electrons perfect insulator does raise 1 gram of water
not exist by 1 ℃
movement of atoms
Convection: heat is Temperature: measure Second Law of Turbine: a machine
transferred by the
movement of fluids of the average kinetic Thermodynamics: when generating continuous
energy of particles in energy is transferred power by revolving
a system around fluids
from the cold object
to the hot object
Radiation: emission of Heat Engine: a device Specific Heat: the Generator: a machine
energy as for generating motive heat required to raise that converts one
electromagnetic the temperature of a form of energy to
waves or substance by a given another
degree
subatomic particles
power from heat
First Law of Conductor: An object Kinetic Energy: energy
that is generated
Thermodynamics: Heat which allows electric when an object is in
energy cannot be currents to pass
created nor through it
destroyed, but can be motion
transferred from one
location to another
and converted into
other forms of
energy
2. Provide a diagram showing molecular motion in Solids, Liquids, and gases.
*How are they different?
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(FINAL) Taruni Singanamala (Class of 2022) - Blue Science Portfolio (1)
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