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The kinetic energy of any body depends o...

The kinetic energy of any body depends on the frame of reference of the observer. The kinetic energy is given by `1//2 mv_("rel")^(2)`. Similarly the displacement of the object from different frames of reference will be: different. But the forces acting on the body remain unchanged. So work done by the forces as seen from: different frames will be different. But work energy! theorem will still be hold in every inertial reference' frame.
For example, if a block of mass 2kg is moving with, velocity of `1m//s` towards east on a rough surface, its `KE = (1)/(2) xx 2 xx 1^(2) = 1J`
If it comes to rest, its `KE = 0`
work done by friction `= K_(f) - k_(i) = -1 J`
If we observe it form a frame 2 moving with `1m//s` toward east, its initial velocity will appear to be `1 - 1 = 0`
Initial `KE = (1)/(2) xx 2 xx 0^(2) = 0`
Final velocity `= 0 -1 = -1`
Final `KE = (1)/(2) xx 2 xx (-1)^(2) = 1J`
`rArr` Work done by friction `= 1 - 0 = 1J`
According to passage:

A

In `2^(nd)` frame, force of friction was opposite to displacement

B

In `2^(nd)` frame, force of friction was in same direction as displacement

C

In ground frame, force of friction is in same direction as the displacement

D

None of the above

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The correct Answer is:
B
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The kinetic energy of any body depends on the frame of reference of the observer. The kinetic energy is given by 1//2 mv_("rel")^(2) . Similarly the displacement of the object from different frames of reference will be: different. But the forces acting on the body remain unchanged. So work done by the forces as seen from: different frames will be different. But work energy! theorem will still be hold in every inertial reference' frame. For example, if a block of mass 2kg is moving with, velocity of 1m//s towards east on a rough surface, its KE = (1)/(2) xx 2 xx 1^(2) = 1J If it comes to rest, its KE = 0 work done by friction = K_(f) - k_(i) = -1 J If we observe it form a frame 2 moving with 1m//s toward east, its initial velocity will appear to be 1 - 1 = 0 Initial KE = (1)/(2) xx 2 xx 0^(2) = 0 Final velocity = 0 -1 = -1 Final KE = (1)/(2) xx 2 xx (-1)^(2) = 1J rArr Work done by friction = 1 - 0 = 1J Choose correct statement :

The kinetic energy of any body depends on the frame of reference of the observer. The kinetic energy is given by 1//2 mv_("rel")^(2) . Similarly the displacement of the object from different frames of reference will be: different. But the forces acting on the body remain unchanged. So work done by the forces as seen from: different frames will be different. But work energy! theorem will still be hold in every inertial reference' frame. For example, if a block of mass 2kg is moving with, velocity of 1m//s towards east on a rough surface, its KE = (1)/(2) xx 2 xx 1^(2) = 1J If it comes to rest, its KE = 0 work done by friction = K_(f) - k_(i) = -1 J If we observe it form a frame 2 moving with 1m//s toward east, its initial velocity will appear to be 1 - 1 = 0 Initial KE = (1)/(2) xx 2 xx 0^(2) = 0 Final velocity = 0 -1 = -1 Final KE = (1)/(2) xx 2 xx (-1)^(2) = 1J rArr Work done by friction = 1 - 0 = 1J What should be the velocity of an observer so that he will report the work done by friction on the block to be 0:

Frame OF References

Does the work done by a force depend on the frame of reference ?

The kinetic energy of an object depends on the frame of reference in which its motion is measured. Give an example to illustrate this point.

Is work energy theorem valid in noninertial frames?

Reference Frame

Work Depends On The Frame Of Reference

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