Question

A crate weighing 302 N is shoved across the floor of an apartment by a force of 401 N exerted downward at an angle of 35.2^o below the horizontal. The coefficient of kinetic friction between crate and floor is 0.570.
a. Sketch a free body diagram of the crate.
b. Write out any components (no numbers yet).
c. Sum forces on the free body diagram (no numbers yet).
d. Determine how long it takes to move the crate 4.00 m, starting from rest?

Answer 1

Given,

W = 302 N ; F = 401 N ; theta = 35.2 deg ; uk = 0.570

m = 302/9.8 = 30.82

a)Free body diagram uploaded

b)The component of weight and frictional force and applied force acting on the box

Ff = uk (w + F sin(theta))

F = F cos(theta)

c)Fnet = F cos(theta) - Ff

d)Fnet = ma = 401 x cos35.2 - 0.57 (302 + 401 sin35.2) = 23.31

a = 205.5/30.82 = 0.77 m/s^2

We know from eqn of motion

s = ut + 1/2 at^2

t = sqrt(2s/a) = sqrt (2 x 4/0.77) = 3.22 s

Hence, t = 3.22 s