(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

I am having trouble with a problem from Physics for Scientists and Engineers by Tipler and Mosca, 6th edition, 5.56

A 100-kg mass is pulled along a frictionless surface by a horizontal force F such that its acceleration is a1=6.00m/s^2. A 20.0-kg mass slides along the top of the 100-kg mass and has an cceleration of a2=4.00m/s^2. (It thus slides backward relative to the 100-kg mass. (a)What is the frictional force exerted by the 100-kg mass on the 20.0 kg mass? (B)What is the net force acting on the 100-kg mass? What is the force F? (C) After the 20.0-kg mass falls off the 100-kg mass, what is the acceleration of the 100-kg mass? (Assume that the force F does not change).

2. Relevant equations

For my free body diagram, postive x and y are to the right and up, respectively.

I attempted to solve this problem using relative acceleration and setting a=0.

a=a1-ar

a=a2+ar

a1=6.00, a2=4.00. Therefore, ar=1.00m/s^2 (?)

3. The attempt at a solution

(a) Fnetm2y=Fn- m2 g=0

So Fn=m2g

Fnetm2x=m2a2

-fk=-[tex]\mu[/tex]k m2 g=m2a2

-[tex]\mu[/tex]kg=a2=a-ar

Therefore, [tex]\mu_{}[/tex]k=.1019

And fk=(.1019)(20kg)(9.81m/s^2)=20.0N (?)

(b)

Force F=(m1+m2)ar=(120kg)(1.00m/s^2=120N (?)

(c) F=m ar when m2 falls off

so 120N=(100kg)ar

ar=1.20m/s^2

ar=a1-a

a=4.80m/s2

I am not sure about my answers because I don't know whether or not I used the relative acceleration concept correctly. Are my answers correct? Is this the only way to do the problem? Is there a way that it can be solved without using relative accelerations?

I googled this problem and found a site that solved it very differently and got different answers. I am not allowed to insert the link here. It did not use relative accelerations.

Any comments and/or answers would be very much appreciated. Thanks!!

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# Homework Help: Problem involving kinetic friction and relative accelerations

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