Question

Two crates, of mass m1 = 60kg and m2 = 129kg , are in contact and at rest on a horizontal surface. ForceF = 690N is exerted on the 60-kg crate. The coefficient of kinetic friction is 0.18. Determine the magnitude of the force that each crate exerts on the other.

Answer 1

Let:
m be the mass of the lighter crate,
M be the mass of the heavier crate,
P be the applied force,
F be the reaction between the crates,
u be the coefficient of friction,
g be the acceleration due to gravity.

(a)
Considering the crates together:
P - u(M + m)g = (M + m)a
a = P / (M + m) - ug ...(1)

a = 690 / (129 + 60) - 0.18 * 9.81
= 1.88 m/s to 3 sig. fig.

(b)
Considering the smaller crate alone:
P - F - umg = ma
F = P - umg - ma

Substituting for a from (1):
F = P - umg - mP / (M + m) + umg
= PM / (M + m) ...(2)

F = 690 * 129 / (129 + 60)
= 470.9N to 4 sig. fig.

Answer 2

total acce leration of both=690-333.396/189=1.88m/sec^2

considering second body

N-227.556=129(1.88)

N=470.076N this is the force