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Old Nov 7th 2010, 09:04 AM   #1
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Book sliding on an incline problem

There is a 1.0 kg book on an incline that is connected by a string to a 500 gram coffee cup. The cup is hanging off the end of the incline, dangling in air at a 90 degree angle with the floor. The book is given a push up the slope and released with a speed of 3.0 m/s. The coefficient of static friction is 0.50 and kinetic friction coefficient is 0.20.

Determine how far the book slides.
At the highest point, does the book stick to the slope or does it slide back down?

Using Newton's Third Law F = ma

I think the net force acting on this system would be the force from the push which gives the book an upward velocity of 3.0 m/s and then subtracted from that would be the force of kinetic friction and of course the force of gravity.

Or, since the force of push is already over and it resulted in the upward speed of 3.0 would ma just equal the force of gravity plus the force of kinetic friction????

If this second idea is correct I can get the acceleration and then plug it into the kinematic equation : velocity final squared is equal to velocity initial squared plus acceleration times change in distance.

When I do this however, I do not get the answer that has been provided to me.

I am also wondering if I should be using the mass of the cup and the book for the force of g and then only the mass of the book for force of kinetic friction. I believe I should also multiply both force of g and force of friction by cos 20 degrees and sin 20 degrees respectively.

Any help in correcting my assumptions would be appreciated. Frostking
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Old Nov 7th 2010, 10:13 PM   #2
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Yes, you should be using the 0.5 kg kg cup. Gravity acting on it provides an additional force for the upwards motion of the book.

The resultant forces on the book is:

m_bgsin(theta) - F_kf - T = m_ba

That on the cup:

T - m_cg = m_ca

Where T is the tension in the string, F_kf is the force of kinetic friction, m_b the mass of the book and m_c the mass of the cup.

Find the acceleration a of the whole system (it should be negative since we know that the book stops somewhere).

Then ue kinematics equations to get the distance, time, etc, anything that you will require.
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