Work, Power and Energy
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Question : 2
Total: 30
A body of mass 2 kg initially at rest moves under the action of an applied horizontal force of 7 N on a table with coefficient of kinetic friction = 0.1. Compute the
(a) work done by the applied force in 10 s,
(b) work done by friction in 10 s,
(c) work done by the net force on the body 10 s,
(d) change in kinetic energy of the body in 10 s. Interpret your result.
(a) work done by the applied force in 10 s,
(b) work done by friction in 10 s,
(c) work done by the net force on the body 10 s,
(d) change in kinetic energy of the body in 10 s. Interpret your result.
Solution:
Given, m = 2 k g , u = 0 , m = 0.1 , t = 10 s
Applied forceF = 7 N
Force due to frictionf = µ m g = 0.1 × 2 × 9.8 = 1.96 N
Net force under which body movesF ′ = F – f = 7 – 1.96 = 5.04 N
Therefore acceleration with which body moves
a = F ′ m =
= 2.52 m s − 2
Therefore distance moved by the body in 10 seconds
S = u t +
a t 2 = 0 × 10 +
× 2.52 × 10 2 = 126 m
(a) Work done by the applied force in 10 s
W = F × S = 7 × 126 = 882 J
(b) Work done by the friction force in 10 s
W = – f × S = – 1.96 × 126 = – 246.9 J = – 247 J
(c) Work done by the net force on body in 10 s
W = F ′ × S = 5.04 × 126 = 635 J
(d) Initial kinetic energy
=
m u 2 =
m × ( 0 ) 2 = 0
Final kinetic energy
=
m v 2 =
× 2 × ( 25.2 ) 2 = 635 J
Change in kinetic energy = Final K.E. – Initial K.E. = 635 – 0 = 635
This shows that change in kinetic energy of the body is equal to work done by net force on the body.
Applied force
Force due to friction
Net force under which body moves
Therefore acceleration with which body moves
Therefore distance moved by the body in 10 seconds
(a) Work done by the applied force in 10 s
(b) Work done by the friction force in 10 s
(c) Work done by the net force on body in 10 s
(d) Initial kinetic energy
Final kinetic energy
Change in kinetic energy = Final K.E. – Initial K.E. = 635 – 0 = 635
This shows that change in kinetic energy of the body is equal to work done by net force on the body.
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