A block of mass m = 1.85 kg rests on the left edge of a block of larger mass M = 6.65 kg. The coefficient of kinetic friction between the two blocks is 0.310, and the surface on which the 6.65kg block rests is frictionless. Aconstant horizontal force of magnitude F = 20.10 N is applied to the 1.85 kg block, setting it in motion as shown in the figure, part (a). If the distance L that the leading edge of the smaller block travels on the larger block is 2.80m, how long will it take before this block reaches the right side of the 6.65 kg block, as shown in the figure, part (b)? Use g = 9.81m/s2
How far does the 6.65kg block move in the process?
The Attempt at a Solution
I've drawn the FBDs for both masses.
In the first case, we have that for the smaller mass, there is friction acting in the opposite direction to motion and the force applied, weight and the normal force. For the other case, the larger mass, we have the frictional force (opposite to the one that the smaller mass experiences), the normal force and the weight.
I've thought that the accelerations MUST be different as they aren't moving with the same acceleration (they aren't connected). I keep getting that the net force on the smaller mass is:
ma = F - μkN
And then, the value of the acceleration would be 7.77m/s2. Then i solved for time and i got 0.849s but apparently it's wrong.
In the other case, i calculated the acceleration of the other block which is just the frictional force. The acceleration turns out to be 0.846m/s2 and the distance should be 0.305m
I keep getting wrong answers for these exercises. What am i doing wrong? Thank you very much.