Is My Solution to This Force/Friction Physics Problem Correct?

[musicfairy]

Can someone check if I did this problem right?

A horizontal force F is applied to a small block of mass m₁ to make It slide along the top of a larger block of mass m₂ and length L. The coefficient of friction between the blocks is $$\mu$$. The larger block slides without friction along a horizontal surface. The blocks start from rest with the small block at one end of the larger block.

a) Find the acceleration of each block. a₁ and a₂, relative to the horizontal surface.

b) In terms of L, a₁, and a₂, find the time t needed for the small block to slide off the end of the larger block.

This is what I did. f is friction, F is the applied force

a)

f = F - m₁a₁
f = m₂a₂
f = $$\mu$$m₁g

$$\mu$$m₁g = F - m₁a₁
a₁ = (F - $$\mu$$m1g) / m1
a₂ = $$\mu$$m1g/m2
b)

L = .5(a1 - a2)t²

t = $$\sqrt{2L / (a1 - a2)}$$

 

[Doc Al]

Looks good to me.

 

[baba89]

Your calculations for the acceleration of each block seem to be correct. However, for part b, the equation you used is not correct. The correct equation should be L = (1/2)(a1 + a2)t^2. This equation can be derived from the kinematic equation x = x0 + v0t + (1/2)at^2, where x0 is the initial position, v0 is the initial velocity, and a is the acceleration. In this case, x0 = 0 and v0 = 0, so the equation simplifies to x = (1/2)at^2. Since the small block slides off the end of the larger block, the displacement, x, is equal to the length of the larger block, L. So, we can write L = (1/2)(a1 + a2)t^2. Solving for t, we get t = sqrt(2L/(a1 + a2)).