Question

The coefficient of kinetic friction between the 2.0 kg block in figure and the table is 0.290.

a)What is the acceleration of the 2.0 kg block?

Answer 1

There are two ways to do this. The long and proper way or the short and clever way.

First, the long and proper way. Draw a free body diagram, label the unknown tension forces T1 and T2, include the force of friction u*F_N and the force of gravity on blocks 1 and 3. When you're done you will have three unknowns: T1, T2, and a, the acceleration of the entire system. Likewise, using F = ma, you'll have three equations. Three equations, three unknowns-- solve and get your answer. I used to teach college physics and this is the preferred way to solve this problem-- you should try working it out with this method.

Now, if you want the fast and clever way. What is the net force pulling the blocks to the right? You have 3g - 1g - 0.2*2g (gravity on 3, gravity on 1, friction on 2). So total F = 1.6g. Now the total mass M is just 1 + 2 + 3 = 6. Then by F = Ma, you have a = F / M = 1.6 g / 6 = 1.6*9.81 / 6 = 2.616 m/s^2