EP015 TUTORIAL PART 1

PHYEP0S15ICS

TUTORIAL BOOK

SEMESTER 1
SESSION 2021/2022

(STUDENT'S EDITION)

PHYSICS UNIT
JOHORE ENGINEERING MATRICULATION COLLEGE

TUTORIAL 1 – TUTORIAL 5

1 PHYSICAL QUANTITIES AND MEASUREMENTS
2 KINEMATICS OF LINEAR MOTION
3 MOMENTUM AND IMPULSE
4 FORCES

5 WORK, ENERGY AND POWER

EP015 PHYSICS 1 1

TUTORIAL 1: PHYSICAL QUANTITIES AND MEASUREMENTS
LEARNING OUTCOMES

DIMENSIONS OF PHYSICAL QUANTITIES
1. Define dimension.
2. Determine the dimensions of derived quantities.
3. Verify the homogeneity of equations using dimensional analysis.

SCALARS AND VECTORS
4. Define scalar and vector quantities.
5. Resolve vector into two perpendicular components ( and axes).
6. Illustrate unit vectors ( iˆ, ˆj, kˆ ) in Cartesian coordinate.
7. State the physical meaning of dot (scalar) product:


A • B = AB cosθ .
8. State the physical meaning of cross (vector) product:

A × B = AB sinθnˆ .

EP015 PHYSICS 1 2

TUTORIAL 1: PHYSICAL QUANTITIES AND MEASUREMENTS

SECTION A: OBJECTIVE QUESTIONS

1. 891 000 milligrams can be written as:

A. 8.91 ×10-1 kilograms C. 8.91 ×102 kilograms

B. 8.91 ×10-2 kilograms D. 8.91 ×101 kilograms

2. The joule (J) expressed in terms of base SI units is

A. kg m s-1 C. kg m s-2

B. kg m2 s-1 D. kg m2 s-2

3. Dimension is defined as a
A. technique or method which physical quantity can be expressed in terms of
combination of basic quantities
B. technique or method which basic quantity can be expressed in terms of
combination of physical quantities
C. technique or method to determine the homogeneity of equation
D. technique or method to construct an equation

4. Which of the following is the correct dimension of k so that the equation
momentum = k x density

A. M L2 T-1 C. L4 T-1
B. M L2 T-2 D. L2 T-1

5. P and Q are two vectors. Which of the following figures will result in a scalar
product of zero?

6. M • Z means
A. Directions of vector M and vector Z is perpendicular to each other
B. Direction of vector M and vector Z is parallel to each other
C. Direction of scalar M and scalar Z is perpendicular to each other D.
D. Direction of scalar M and vector Z is parallel to each other

EP015 PHYSICS 1 3

SECTION B: SUBJECTIVE QUESTIONS
QUESTION 1

a) State FOUR basic quantities and their respective SI units.

b) The pressure of a liquid is given by P = ρgh. Calculate the pressure (in SI unit)
if the density of water, ρ is 1 g cm–3, the acceleration due to gravity, g is 10 m
s–2, and the height of water, h is 50 cm ?

[Ans: 5 × 103 Nm-2 or 5 × 103 Pa or 5 × 103 kgm-1 s-2]

QUESTION 2
a) Show that the expression v = at is dimensionally correct if in this expression v
represents velocity, a is acceleration, and t an instant of time.

b) The equation governing the rate of flow of fluid V under streamline conditions
t

through a horizontal pipe of length l and radius r is V = 4 pr 4 where p is the
t 8lη

pressure difference across the pipe and is the viscosity of the fluid. Deduce
the dimension for .

[Ans: ML-1T-1]

QUESTION 3

a) Change the following quantities into its SI unit.
i) 50 mm2
ii) 4.5 x 10-3 cm3
iii) 100 g cm-3
iv) 360 km hour-1
[Ans: i) 5.0 x 10- 5m2 ii) 4.5 x 10-9 m3 iii) 105 kg m-3 iv) 100 m s-1]

QUESTION 4

Two displacement vector A and B are shown in FIGURE 1.
Determine

a) the resultant displacement in form of unit vector?
b) magnitude and direction of the resultant displacement?

[Ans: (– 1.67i– 0.22j) km, 1.68 km, 7.5° below negative x axis]

EP015 PHYSICS 1 4

QUESTION 5
Based on Figure 2 below, calculate the resultant vector of P and Q and its direction.

y
P (35 m s-2) Q (24 m s-2)

x
FIGU0 RE 2

[Ans: 53.68 ms-2, 60.03° above positive x-axis]
QUESTION 6
Two vectors A and B respectively can be represented as follow:
A = 20 unit (directed eastwards)
B = 15 unit (directed north-westwards)
Determine A + B by resolving vectors into axes.

[Ans: 14.17 unit, 48.49° above positive x-axis]
QUESTION 7
FIGURE 3 shows how two coplanar force F1 and F2, act on point O.

FIGURE 3
a) Resolve the force along the x and y axes as well as determine the resultant

force FR.
b) Determine the direction of the resultant force FR.

[Ans: 5.15 N, 50.28° from below positive x-axis]

EP015 PHYSICS 1 5

TUTORIAL 2: KINEMATICS OF LINEAR MOTION
LEARNING OUTCOMES

LINEAR MOTION
1. Define instantaneous velocity, average velocity and uniform velocity.
2. Define instantaneous acceleration, average acceleration and uniform

acceleration.
3. Discuss the physical meaning of displacement-time, velocity-time and

acceleration-time graphs.
4. Determine the distance travelled, displacement, velocity and acceleration

from appropriate graphs.
UNIFORMLY ACCELERATED MOTION
5. Apply equations of motion with uniform acceleration:
v = u + at
s = ut + ½ at2
v² = u² + 2as
PROJECTILE MOTION
6. Describe projectile motion launched at an angle,θ as well as special cases
when θ = 0˚ and θ = 90˚ (free fall)
7. Solve problems related to projectile motion.

EP015 PHYSICS 1 6

TUTORIAL 2: KINEMATICS OF LINEAR MOTION

SECTION A: OBJECTIVE QUESTIONS
1. Mr Hassan is driving at 108 km hr-1 along a straight road suddenly sees a school

girl runs across the road 100 m ahead of his car. If his reaction time is 0.7 s and
the maximum deceleration of the car is 4.5 ms-2, determine the distance travelled
by the car before it stops.
A. the car stops immediately after seeing the girl
B. the car stops 21m after seeing the girl
C. the car stops 21m before hitting the girl
D. the car stops 21 m after hitting the girl

2. When the brakes are applied, a car reduces its velocity from 30 m s-1 to 15 m s-1
after moving 75 m. In order to stop the car completely, what is the extra distance
needed?
A. 15 m
B. 25 m
C. 30 m
D. 45 m

3. A ball is kicked horizontally with an initial velocity of 40 m s-1 from a building into
the air. If the acceleration due to gravity is 9.81 m s -2 and air resistance is negligible,
calculate the speed of the ball after 2 seconds.
A. 41 ms-1
B. 45 ms-1
C. 50 ms-1
D. 55 ms-1

4. An object is moving with a uniform acceleration of 5 m s-2. A displacement - time
graph showing the motion of this object has a gradient which
A. increases with time
B. decreases with time
C. equal 5 m s-1
D. equal 5 m s-2

EP015 PHYSICS 1 7

SECTION B: SUBJECTIVE QUESTIONS
QUESTION 1
a) State TWO differences between distance and displacement.

b) The motion of an object in a straight line is shown in the graph in FIGURE 1,
determine
i. the velocity of the object for the motions given by AB, BC and CD
ii. the total distance moved.

iii. the displacement of the motion.
iv. the average speed of the object

[Ans: 10 ms-1, 0, -20 ms -1, 80 m, 0 m, 8 ms-1]

QUESTION 2
An archer stands on a cliff elevated at 50 m high from the ground and shoots an arrow
at the angle of 30° above the horizontal with the speed of 80 ms-1.
a) How long does it fly in the air?
b) How far from the base of the cliff does the arrow fly until it hits the ground?
c) Calculate the speed of the arrow just before it hits the ground.

[Ans: 9.25 s, 641 m, 85.87 ms-1]

QUESTION 3
A projectile is launched at an angle of 30° with respect to the horizontal. The initial
velocity is 45 ms-1.
a) Determine the horizontal and vertical component of the initial velocity.
b) Calculate the maximum height of the projectile and the time taken to reach the

position
c) Calculate the horizontal displacement.

[Ans: 38.97 ms-1, 22.5 ms-1, 25.8 m, 2.29 s, 178.9 m]

EP015 PHYSICS 1 8

QUESTION 4
A projectile is shot from the edge of a cliff 125 m above ground level with an initial
speed of 65.0 ms-1 at an angle of 37° with the horizontal, as shown in FIGURE 2.

a) determine the time taken by the projectile to hit point P at ground level.
b) determine the range X of the projectile as measured from the base of the cliff. At

the instant just before the projectile hits point P.
c) the horizontal and the vertical components of its velocity.
d) the magnitude of the velocity.
e) the angle made by the velocity vector with the horizontal.
f) calculate the maximum height above the cliff top reached by the projectile.

[Ans: 10.4 s, 541 m , -63.1 ms-1, 81.7 ms-1, 50.60 below horizontal, 78.1 m]

EP015 PHYSICS 1 9

TUTORIAL 3: MOMENTUM AND IMPULSE
LEARNING OUTCOMES

MOMENTUM AND IMPULSE


1. Define momentum and impulse, J = F∆t .

2. Solve problem related to impulse and impulse-momentum theorem,

J = ∆p = mv f − mvi .

3. Use F-t graph to determine impulse.

CONSERVATION OF LINEAR MOMENTUM

4. State the principle of conservation of linear momentum.

5. Apply the principle of conservation of momentum in elastic and inelastic

collisions in 1D and 2D collisions.

6. Differentiate elastic and inelastic collisions.

7. Define and use the coefficient of restitution,

ek = − v2 − v1
u2 − u1

EP015 PHYSICS 1 10

TUTORIAL 3: MOMENTUM AND IMPULSE

SECTION A: OBJECTIVE QUESTIONS
1. Which of the following statements is true about the elastic collision between two

objects?
A. The momentum and total energy are conserved but the kinetic energy can be

converted into other forms of energy.
B. Both the momentum and total energy are conserved if and only if the mass of

the two objects is identical.
C. The kinetic energy is conserved whereas the total energy is reduced but can

be increased.
D. Momentum, kinetic energy and total energy must be conserved.

2. The purpose of an airbag or crumple zone in a car is to increase the time taken
for the driver to stop. What is the advantage of this?
A. It reduces the driver’s momentum.
B. It reduces the driver’s energy.
C. It reduces the force on the driver.
D. It reduces the energy of the impact

3. Two balls with masses of 0.4 kg and 0.6 kg respectively are thrown in such a
manner that they collide head-on. They stick together and move with common
velocity v. The initial velocity for each ball is 15 m s-1. Calculate the velocity v
A. Zero
B. - 3 m s-1
C. 6 m s-1
D. 15 m s-1

4. A tennis player returns a serve. How does the force on the ball relate to its
momentum?
A. The force is the rate of change of momentum of the ball
B. The force is the overall change of momentum multiplied by the time taken to
cause the change
C. The force is the momentum of the ball as it is hit
D. The force is the momentum of the ball leaving the racket divided by the time
taken to cause the change

EP015 PHYSICS 1 11

SECTION B: SUBJECTIVE QUESTIONS

1. Calculate the momentum of these objects:
a. an electron of mass 9.1×10–31 kg moving at 3.0×107 m s–1
b. the Earth, of mass 6.0×1024 kg and orbital speed 30 km s–1
c. a mouse of mass 100 g running at 2.3 m s–1

2. A 0.10 kg ball is thrown straight up into the air with an initial speed of 15 ms-1.
Find the momentum of the ball
a. at its maximum height and
b. halfway to its maximum height.

3. An object has a kinetic energy of 275 J and a momentum of 25.0 kg m s-1. Find
a. the speed
b. mass of the object.

4. 0.280 kg volleyball approaches a player horizontally with a speed of
15.0 m s-1. The player strikes the ball with her fist and causes the ball to move
in the opposite direction with a speed of 22.0 m s-1.
a. What impulse is delivered to the ball by the player?
b. If the player’s fist is in contact with the ball for 0.06 s, find the magnitude
of the average force exerted on the player’s fist.

5. When a force is applied to an object of mass 8 kg with an initial velocity of
15 m s-1, its velocity changes to 30 m s-1 after moving 100 m. Calculate
a. its acceleration.
b. its impulse.
c. the force applied.

6. A force, F acting on an object of mass 2.0 kg varies with time t in the way as
shown in FIGURE 1. The velocity of the object is 4.0 m s-1 before the application
of the force. Determine the velocity of the object after applying the force for 0.2s.

F(N)

100

0.2 t(s)
FIGURE 1

7. Three carts of masses 4.0 kg, 10.0 kg, and 3.0 kg move on a frictionless
horizontal track with speeds of 5.0 ms-1, 3.0 m s-1 and 4.0 m s-1 as shown in
FIGURE 2. The carts stick together after colliding.
a. Find the final velocity of the three carts.

EP015 PHYSICS 1 12

b. Does your answer require that all carts collide and stick together at the
same time?

FIGURE 2

8. A 75.0kg ice skater moving at 10.0 m s-1 crashes into a stationary skater of
equal mass. After the collision, the two skaters move as a unit at 5.00 m s-1.
Suppose the average force a skater can experience without breaking a bone is
4 500 N. If the impact time is 0.100 s, does a bone break?

9. FIGURE 3 below shows the velocities of two metal balls of mass 4.0 kg and 3.0
kg before and after collision.
a. Calculate the coefficient of restitution of the collision.
b. Determine the type of collision.

FIGURE 3

10. A 2 kg ball A moves to the right with velocity of 4 ms-1 collides with another 1 kg
ball B moving in the opposite way with velocity of 0.5 m s-1 as shown in FIGURE
4. After the collision, both balls move at 300 and 150 from the horizontal.
Calculate the final velocity of each ball after the collision. Assume the collision
is an elastic.

FIGURE 4

11. A 600 g body, P is initially at rest. A 400 g body, Q which is initially moving with
a velocity of 125 cm s-1 toward the right along the x-axis, strikes P. After the
collision, Q has a velocity of 100 cm s-1 at an angle of 370 above the x-axis in
the first quadrant. Both bodies move on a horizontal plane. Calculate:
c. The magnitude and direction of the velocity of P after the collision.
d. The loss kinetic energy during the collision.

EP015 PHYSICS 1 13

SUGGESTED ANSWERS FOR SECTION B:
1. 2.73x10-23 Ns, 1.8x1029 kgms-1, 0.23 Ns
2. 0 kgms-1, 1.1 kgms-1
3. 22 ms-1, 1.14 kg
4. -2.91 kgms-1, 48.5 N
5. 3.38 ms-2, 120 kgms-1, 27.04 N
6. 5.1 ms-1
7. 2.24 ms-1

8. 3750 N

9. 0.75
10. 1.37 ms-1, 5.28 ms-1
11. 50.01 cms-1, 53.210 below +x-axis, 0.038J

EP015 PHYSICS 1 14

TUTORIAL 4: FORCES
LEARNING OUTCOMES

BASIC OF FORCES AND FREE BODY DIAGRAM
1. Identify the forces acting on a body in different situations:

(i) weight
(ii) tension
(iii) normal force
(iv) friction
(v) external force
2. Sketch free body diagram.
3. Determine static and kinetic friction.

NEWTON’S LAWS OF MOTION
4. State Newton’s laws of motion.
5. Apply Newton’s laws of motion.

EP015 PHYSICS 1 15

TUTORIAL 4: FORCES

SECTION A: OBJECTIVE QUESTIONS

1. Three forces are acting on an object. If the object is at equilibrium, which of the
following statements is TRUE?
A. All three forces are acting at a point.
B. The forces formed a right angle triangle.
C. The resultant force is given by the hypotenuse of the triangle.
D. The resultant force is acting in the opposite direction to the forces.

2. An object will remain stationary on an inclined plane because…
A. the static frictional force is acting upward along the inclined plane.
B. the static frictional force is acting downward along the inclined plane.
C. the dynamic frictional force is acting upward along the inclined plane.
D. the dynamic frictional force is acting upward along the inclined plane.

3. If a nonzero net force is acting on an object, which of the following must we
assume regarding the object’s condition?
A. The object is at rest.
B. The object is moving with constant velocity.
C. The object is being accelerated.
D. The object is losing mass.

EP015 PHYSICS 1 16

SECTION B: SUBJECTIVE QUESTIONS

1. A 2.0 kg object is placed on a rough plane inclined at 30° with the horizontal as
shown in FIGURE 1. It is released from rest and accelerates at 4.0 m s-2.
Calculate the frictional force acting on the object.

300

FIGURE 1

2. a) State two type of frictional forces.
b)
c) A 3.0 kg cube is placed on a rough plane. The plane is then slowly tilted
until the cube starts to move from rest. This occurred when the angle of
3. inclination is 25°. Calculate the coefficient of static friction between the
cube and the rough plane.

A wooden block of mass 2.0 kg slides down with constant velocity on a

inclined rough plane of 30° from the horizontal axis.

i) Sketch a free body diagram to show forces acting on the wooden

block

ii) Calculate the kinetic frictional force between the wooden block

and the rough inclined plane. 4 kg A

rough plane

300

B FIGURE 2
1 kg

a) A 4.0 kg block A on a rough 30°inclined plane is connected to a freely
hanging 1.0 kg block B by a mass-less cable passing over the frictionless
pulley as shown in FIGURE 2 . When the objects are released from rest,
object A slides down the inclined plane with a friction force of 6.0 N.
Calculate
i) the acceleration of the objects
ii) the tension in the cable.

EP015 PHYSICS 1 17

b) Explain what is meant by
i) inertia
ii) mass
iii) weight

4. Object A and B of masses 3.5 kg and 2.0 kg respectively are connected with a
light string across a smooth pulley as shown in FIGURE 3. At t = 0, A is pulled
by 30 N force F. The coefficient of kinetic friction between block A and the table
is 0.20. Calculate
a) acceleration
b) time taken by B to move upwards by 1.0 m

F
30° A

B

FIGURE 3

5. a) Define the static equilibrium of a particle.
b) An object is moving at constant velocity on a rough surface.
i) What are the horizontal forces acting on the object?
ii) Is the object in equilibrium? Give your reason.
iii) The weight of an object W, tension T1 and tension T2 are in static
equilibrium as shown in FIGURE 4. If W = 40 N. calculate T1 and
T2.
500
T1

P T2
60O

FIGURE 4

EP015 PHYSICS 1 18

6. a) Explain why it is easy to push a moving object than to push a stationary
b) object of the same mass.
A and B are connected by a mass less cable across a frictionless pulley
are in static equilibrium as shown in FIGURE 5. The mass of A is 2.0 kg.
The coefficient of static friction between A and the inclined plane is 0.20.
Calculate the mass of B if A is about to slide down the plane.

pulley

A
B

300

FIGURE 5
7. A uniform 4 m ladder weighing 50 N rests against a smooth wall. It is inclined

60° with the horizontal. The coefficient of static friction between ladder and floor
is 0.5. How far up the ladder an 80 kg man go before the ladder slipped?

8. The system below is in equilibrium and the pulley is frictionless

Ɵ
P

C BA

200 N 300 N

(i) Draw and label a free body diagram at point P.
(ii) Write the equation for total vertical force exerted on point P
(iii) Write the equation for total horizontal force exerted on point P
(iv) Determine the angle Ɵ
(v) Find the tension in each rope
(iv) What is the mass of block C?

EP015 PHYSICS 1 19

TUTORIAL 5: WORK, ENERGY AND POWER
LEARNING OUTCOMES

WORK 
F
1. Define work done by a constant force, W = • s .

2. Apply work done by a constant force and from a force-displacement graph.

ENERGY AND CONSERVATION OF ENERGY

3. State the principle of conservation of energy.

4. Apply the principle of conservation of energy (mechanical energy and heat

energy due to friction).

5. State and apply the work energy theorem , W = ΔK.

POWER

6. Define and use average power, Pav = ∆W and instantaneous power,
∆t

P = F • v

EP015 PHYSICS 1 20

TUTORIAL 5: WORK, ENERGY AND POWER

TUTORIAL 5.1 : WORK

1. A horizontal force of 150 N is used to push a 40.0 kg packing crate a distance of 6.0m

on a rough horizontal surface. If the crate moves at constant speed, find

(a) the work done by the 150N force (900 J)

(b) the coefficient of kinetic friction between the crate and surface (0.383)

2.

A block of mass m =2.50 kg is pushed a distance d=2.20 m along a frictionless

horizontal table by a constant applied force of magnitude F=16.0 N directed at an

angle Ɵ=25.0° below the horizontal as shown in Figure below. Determine the work

done by

(a) the applied force, (31.9 J)

(b) the normal force exerted by the table, (0 J)

(c) the force of gravity, and (0 J)

(d) the net force on the block (31.9 J)

3. Starting from rest, a 5.0 kg block slides 2.50 m down a rough 30.0° incline. The

coefficient of kinetic friction between the block and the incline is µk = 0.436.

Determine

(a) the work done by the force of gravity, (61.3 J)

(b) the work done by the friction force between block and incline (-46.3 J)

(c) the work done by the normal force. (0 J)

4.

The force acting on a particle varies as in Figure below. Find the work done by the

force as the particle moves

(a) from x = 0m to x = 8.00 m, (24.0J)

(b) from x =8.00 m to x =10.0 m, (-3.0J)

(c) from x = 0m to x =10.0 m (21.0J)

EP015 PHYSICS 1 21

TUTORIAL 5.2 : ENERGY AND CONSERVATION OF ENERGY
1. A mechanic pushes a 2.50 x103 kg car from rest to a speed of v, doing 5 000 J of work

in the process. During this time, the car moves 25.0 m. Neglecting friction between car

and road, find

(a) v (2.0 ms-1)

(b) the horizontal force exerted on the car. (200 N)

2. A 7.80g bullet moving at 575 m/s penetrates a tree trunk to a depth of 5.50 cm.

(a) Use work and energy considerations to find the average frictional force that stops

the bullet. (2.34x104 N)

(b) Assuming the frictional force is constant, determine how much time elapses

between the moment the bullet enters the tree and the moment it stops moving.

(1.92x10-4s)

3.

A man pushing a crate of mass m = 92.0 kg at a speed of v = 0.850 m/s encounters a

rough horizontal surface of length, l = 0.65 m as in Figure above. If the coefficient of

kinetic friction between the crate and rough surface is 0.358 and he exerts a constant

horizontal force of 275 N on the crate, find

(a) the magnitude and direction of the net force on the crate while it is on the rough

surface, (47.8N directed opposite to the motion of the crate)

(b) the net work done on the crate while it is on the rough surface (-31J)

(c) the speed of the crate when it reaches the end of the rough surface. (0.22m/s)

4. When a 2.50kg object is hung vertically on a certain light spring described by Hooke’s

law, the spring stretches 2.76 cm.

(a) What is the force constant of the spring? (8.88x102N/m)

(b) If the 2.50kg object is removed, how far will the spring stretch if a 1.25kg block is

hung on it? (1.38cm)

EP015 PHYSICS 1 22
5.

A daredevil on a motorcycle leaves the end of a ramp with a speed of 35.0 m/s as in
Figure below. If his speed is 33.0 m/s when he reaches the peak of the path, what is
the maximum height that he reaches? Ignore friction and air resistance. (6.94m)

6.

Two blocks, A and B (with mass 50 kg and 100 kg, respectively), are connected by a

string, as shown in Figure above. The pulley is frictionless and of negligible mass. The

coefficient of kinetic friction between block A and the incline is µk =0.25. Determine

the change in the kinetic energy of block A as it moves from C to D, a distance of 20m

up the incline (and block B drops downward a distance of 20 m) if the system starts

from rest. (3.9kJ)

7.

A ball of mass m=1.80 kg is released from rest at a height h =65.0 cm above a light

vertical spring of force constant k as in Figure (a) above. The ball strikes the top of the

spring and compresses it a distance d = 9.00 cm as in Figure (b). Neglecting any

energy losses during the collision, find

(a) the speed of the ball just as it touches the spring (3.57m/s)

(b) the force constant of the spring. (3.22kN/m)

EP015 PHYSICS 1 23
8.

Two objects (m1=5 kg and m2=3kg) are connected by a light string passing over a
light, frictionless pulley as in Figure above. The 5 kg object is released from rest at a
point h=4 m above the table.
(a) Determine the speed of each object when the two pass each other. (3.13m/s)
(b) Determine the speed of each object at the moment the 5kg object hits the table.

(4.43m/s)
(c) How much higher does the 3kg object travel after the 5kg object hits the table?

(1.0m)

9. A block lying on a smooth horizontal surface has a spring constant of 60Nm-1. If the

block is stretched 4cm from equilibrium, find the work done as it passes 1 cm from the

equilibrium position. (0.051J)

TUTORIAL 5.3 : POWER

1. A horse pulls a cart of mass 20kg up a hill that has an incline of 26° with the

horizontal. It takes the horse 30s to move the cart 300m up the hill. Neglecting

friction, determine:

(a) the work done by the horse (25.8kJ)

(b) the power output of the horse (0.86W)

2. The electric motor of a model train accelerates the train from rest to 0.620 m/s in

21.0ms. The total mass of the train is 875 g. Find the average power delivered to the

train during its acceleration. (8.0W)
3. A 1.50x103kg car starts from rest and accelerates uniformly to 18.0 m/s in 12.0 s.

Assume that air resistance remains constant at 400 N during this time. Find

(a) the average power developed by the engine in hp (32hp)

(b) the instantaneous power output of the engine at t =12.0 s, just before the car stops

accelerating. (63.9hp)

4. A 650kg elevator starts from rest and moves upward for 3.00 s with constant

acceleration until it reaches its cruising speed, 1.75 m/s. What is the average power of

the elevator motor during this period? (7.92hp)