# A question about work and energy

#### Prem1998

1. Homework Statement
Consider two observers moving with respect to each other at a speed v along a straight line. They observer a block of mass m moving a distance x on a rough surface. The following quantity (or quantities) will be same as observed by the two observers:
(a) kinetic energy of the block at time t
(b) work done by friction
(c) total work done on the block
(d) acceleration of the block

2. Homework Equations
This is only a thoughtful question so I don't think equations are needed. But if it is a rule, then:
KE=1/2mv^2 W= integration Fdx or FX when F is constant, etc.

3. The Attempt at a Solution
I figured out that the answers should be b,c and d. It can't definitely be 'a' because the velocity of the block seen by both observers will be different. Now, since none of the observers are accelerating themselves, so they both will see the same acceleration of the block, so 'd' is correct. It is not a relativistic physics question, so 'm' will be the same for both. So, resultant force F=ma will also be same for both. And, distance moved, x is also same for both. So, total work done should be same, hence, 'c' is correct. Again, for both observers, the normal reaction on the block is same and coefficient of kinetic friction is also same. So, both observers will observe the same frictional force on the block and again the same distance moved 'x'. So, work done by friction is also same. Hence, b is correct.
But, in the answers section in the book, it was written that only 'd' is correct. Doesn't assuming that 'd' is correct lead to the conclusion that 'b' and 'd' are also correct?

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#### conscience

And, distance moved, x is also same for both.
Why do you think that distance moved would be same for both the observers ?

#### Prem1998

Why do you think that distance moved would be same for both the observers ?
Why would the distance 'x' change? There is negligible length contraction here.

#### conscience

If the two observers are moving with respect to each other ,they cannot measure same displacement of the block .

#### Prem1998

If the two observers are moving with respect to each other ,they cannot measure same displacement of the block .
Oh, I'm sorry. So, that eliminates 'b' and 'c' even if the resultant and frictional forces are same for both observers. Thanks. Isn't the question incomplete as it did not say in the book that v=/=0. I mean, v could be 0 leading to the same value of 'x'.

#### conscience

Isn't the question incomplete as it did not say in the book that v=/=0. I mean, v could be 0 leading to the same value of 'x'.
The question clearly states that the two observers are moving relative to each other
That rules out the possibility of them being at rest .

Instead if the question had only stated that there are two moving observers , then there could have been a possibility that the two observers were at rest with respect to each other measuring same displacement of the block .

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