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.
Solution:  
Given, m=2kg,u=0, m=0.1,t=10s
Applied force F=7N
Force due to friction f=µmg=0.1×2×9.8=1.96N
Net force under which body moves F=Ff=71.96=5.04N
Therefore acceleration with which body moves
a=Fm=
5.04
2
=2.52ms2

Therefore distance moved by the body in 10 seconds
S=ut+
1
2
a
t2
=0×10+
1
2
×2.52
×102
=126m
(a) Work done by the applied force in 10 s
W=F×S=7×126=882J
(b) Work done by the friction force in 10 s
W=f×S=1.96×126 =246.9J=247J
(c) Work done by the net force on body in 10 s
W=F×S=5.04×126=635J
(d) Initial kinetic energy
=
1
2
m
u2
=
1
2
m
×(0)2
=0

Final kinetic energy
=
1
2
m
v2
=
1
2
×2
×(25.2)2
=635J

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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