Interesting sliding

A 60 kg 60\si{\kilo\gram} man running at an initial speed of 4 m / s \SI[per-mode=symbol]{4}{\meter\per\second} jumps on a 120 kg 120\si{\kilo\gram} cart initially at rest. After reaching the top of the cart, the person slides on the cart's surface and finally comes to rest relative to the cart. The coefficient of friction between the cart and the person's feet is 0.4 0.4 , while the friction between the cart and ground can be neglected.

How long (in seconds) does the frictional force act on the person?

Details and Assumptions:

  • Take g = 10 m / s 2 g=\SI[per-mode=symbol]{10}{\meter\per\second\squared} .


The answer is 0.66666.

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2 solutions

Steven Chase
Nov 9, 2016

nice problem! but isnt it overrated?

Rohith M.Athreya - 4 years, 7 months ago

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Thanks. I have manually lowered the rating. It was originally seeded at level 5.

@Sparsh Sarode Please help us by setting reasonable original levels for your problems.

Calvin Lin Staff - 4 years, 7 months ago

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Oops! Sry, it was by mistake...

Sparsh Sarode - 4 years, 7 months ago

I guess that during 2/3 seconds a part of the persons kinetic energy is transformed into heat. Hence, the final velocity is less than caculated and time to reach is somewhat shorter. In addition, the runner has to exercise hard to do a jump without additional acceleration in running direction.

Jochem König - 4 years, 6 months ago
Prakhar Bindal
Nov 14, 2016

Final velocities will be 4/3 m/sec when slipping will stop (by momentum conservation)

acceleration of man = 4 m/sec^2

4/3 = 4-4t

t = 2/3!

Can't I directly use conservation of momentum like Mass of man * velocity = mass of cart * its velocity

To get velocity of cart as 2?

Priyanshu Mishra - 4 years, 6 months ago

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It is man * velocity =( masses of cart +man ) * their velocity.

Niranjan Khanderia - 4 years, 6 months ago

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Oh i see there. Thanks for the correction.

Priyanshu Mishra - 4 years, 6 months ago

Nice solution. Since no external force is acting momentum conserved, though the system losses energy as friction heat. Acceleration of the man is - 4./sec 2 ^2 . Just adding a little detail. +1).

Niranjan Khanderia - 4 years, 6 months ago

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thank you sir!

Prakhar Bindal - 4 years, 6 months ago

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