Question

Problem 3 (20 points) In the following figure, a horizontal force F is applied to a large block of mass M with a massless pulley attached to it. While the block M is moving to the right, the other two blocks mi and m2 remain stationary problem relative to M. All surfaces are frictionless for this (a) Draw separate free body diagrams for M(including the massless pulley), mi, and m2 respectively. On the free body diagrams, please only draw and label the forces (not components) that act on the blocks M, m and m2, respectively. Each force must be represented by a distinct arrow for its direction. (b) Find the magnitude of the applied force F so that m and m2 remain stationary relative to M. Express your answer in terms of M, m, m and the magnitude of the gravitational acceleration g. Problem 4 (20 points) A block of mass 2.00 kg rests on the left edge of a block of mass M-8.00 kg. The coefficient of kinetic friction between the two blocks is k-0.300, and the surface on which the 8.00 kg block rests is frictionless. A constant horizontal force of magnitude F-10.0 N is applied to the 2.00 kg block, setting it in motion as shown below. If the distance L that the leading edge of the smaller block travels on the larger block is 3.00 m. (a) Find the time interval that the smaller block make to the right side of the 8.00 kg block as shown below, (Hint: Both blocks are set into motion when F is applied.) (b) How far does the 8.00 kg block move during this time interval.

Answer 1

4)Given,

m = 2 kg ; M = 8 kg ; uk = 0.3 ; F = 10 N ; r = 3 m

Ff = 0.3 x 10 = 3 N

Fnet = 10 - 3 = 7 N

a = F/m = 7/2 = 3.5 m/s^2

a' = 3/8 = 0.38 m/s^2

t = sqrt (2r/(a - a'))

t = sqrt (2 x 3/(3.5 - 0.38)) = 1.4 s

Hence, t = 1.4 s

b)D = 1/2 at^2

D = 0.5 x 0.38 x 1.4^2 = 0.37 m

Hence, D = 0.37 m