CHAPTER 5 WORK AND ENERGY

Example 5.11 :

m1 u1 m1  m2

m2 h

Figure 5.18

A bullet of mass, m1=5.00 g is fired into a wooden block of mass,
m2=1.00 kg suspended from some light wires as shown in Figure

5.18. The block, initially at rest. The bullet embeds in the block, and

together swing through a height, h=5.50 cm. Calculate

a. the initial speed of the bullet.

b. the amount of energy lost to the surrounding.

51

Solution : m1  5.00 103 kg; m2  1.00 kg; h  5.50 102 m

a v12  0
.

u2  0 m1  m2

m1 u1 m2 u12 h

(1) m1  m2 (3)

(2)

Applying the principle of conservation of energy involving the situation (2) and (3),

 E2  E3 K U 1 m1  m2 u12 2  m1  m2 gh
2
u12  2gh 
 29.81 5.50 102 u12  1.04 m s1

52

Solution : m1  5.00 103 kg; m2  1.00 kg; h  5.50 102 m

Applying the principle of conservation of linear momentum

involving the situation (1) and (2),

  
p1  p2

m1u1  m1  m2 u12

   5.00 103 u1  5.00 103 1.00 1.04
u1  209 m s1

b. The energy lost to the surrounding, Q is given by

 Q  E1  E2
1 1
Q  2 m1 u12  2 m1  m 2 u12 2

   Q  1 5.00 103 2092  1 5.00 103 1.00 1.042
22

Q  109 J 53

Example 5.12 :

Smooth
pulley

Q

2m
P

Figure 5.19

Objects P and Q of masses 2.0 kg and 4.0 kg respectively are
connected by a light string and suspended as shown in Figure
5.19. Object Q is released from rest. Calculate the speed of Q at
the instant just before it strikes the floor.

54

Solution : mP  2.0 kg; mQ  4.0 kg; h  2 m; u  0

Smooth Smooth
pulley pulley

Q vP

2m 2m Q v

P

Initial Final

Applying the principle of conservation of mechanical energy,

 Ei  Ef UQ UP  KP  KQ 1
1 2
mQ gh  mP gh  2 mPv 2  mQ v 2
1
4.09.812  2.09.812  2.0v2  1 4.0v2

v  3.62 m s1 2 2

55

Exercise :

1. If it takes 4.00 J of work to stretch a spring 10.0 cm from its

initial length, determine the extra work required to stretch it an

additional 10.0 cm. ANS. : 12.0 J

2. A book of mass 0.250 kg is placed on top of a light vertical

spring of force constant 5000 N m1 that is compressed by 10.0

cm. If the spring is released, calculate the height of the book rise

from its initial position. ANS. : 10.2 m

3. A 60 kg bungee jumper jumps from a bridge. She is tied to a
bungee cord that is 12 m long when unstretched and falls a total
distance of 31 m. Calculate
a. the spring constant of the bungee cord.
b. the maximum acceleration experienced by the jumper.

ANS. : 100 N m1; 22 m s2

56

4.

Figure 5.20

A 2.00 kg block is pushed against a light spring of the force

constant, k = 400 N m-1, compressing it x =0.220 m. When the

block is released, it moves along a frictionless horizontal surface

and then up a frictionless incline plane with slope  =37.0 as

shown in Figure 5.20. Calculate

a. the speed of the block as it slides along the horizontal

surface after leaves the spring.

b. the distance travelled by the block up the incline plane before

it slides back down.

ANS. : 3.11 m s1; 0.81 m 57

5. u C

A

10 m

BD

Figure 5.21

A ball of mass 0.50 kg is at point A with initial speed, u =4 m s1
at a height of 10 m as shown in Figure 5.21 (Ignore the frictional
force). Determine

a. the total energy at point A,

b. the speed of the ball at point B where the height is 3 m,

c. the speed of the ball at point D,

d. the maximum height of point C so that the ball can pass over

it.

ANS. : 53.1 J; 12.4 m s1; 14.6 m s1; 10.8 m

58

THE END…

Next Chapter…

CHAPTER 6 :
Gravitation

59