A block of mass m1 = 2 kg rests on frictionless wedge of mass m2 = 10 kg whose s

Question

A block of mass m1 = 2 kg rests on frictionless wedge of mass m2 = 10 kg whose surface is inclined at an
angle of = 40, as shown in the figure below. The wedge rests on a frictionless, horizontal floor in the earth's gravitational eld. In order to prevent the block from sliding down the incline, a force of magnitude
F is applied to the wedge on the left side as shown, so that the wedge and block accelerate together with
constant acceleration towards the right. We wish to calculate the required force F.

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a) Draw a free-body diagram for the block.
b) If the block is to refrain from sliding down the incline, what does the direction of its acceleration have to
be? (Give a unit vector in the direction of the acceleration.) How does this compare with the direction
of the total force on the block?
c) Given the direction of the total force in part (b), draw a diagram that shows the corresponding vector
sum of forces in part (a).
d) From your diagram in part (c), calculate the magnitude of the total force on the block, in N.
e) What is the corresponding acceleration of the block, in m/s2?
f) What is the magnitude of the required force F, in N?

Explanation / Answer

a). The direction should be obvious. Block m1 slides horizontally and Block m2 falls vertically. For the acceleration, a, write free body Newton's-law equations for each blcok separately, with the connecting cord tension T acting on both. Eliminate T and solve for a. Both blocks accelerate at the same rate, but in different directions. b) velocity = a t (horizontal direction) c) Displacement = (1/2) a t^2 d) Use the same formula as (c) but different time t

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