Answer to Question #87857 in Classical Mechanics for Stokes

Question

A 12 kg box of supplies falls off a truck that has been parked. the box slides down an icy hill which has an incline of 10 degreees. There is a frictional force if 10n between the surfaces of the box and the hill. The G acceleration is -9.81m/s2.

1) find the weight and the perpendicular and the tangential components.
2) write an equation for the sum of the forces
i) perpenduclar
ii)tangental
3) what is the magnitude and direction of the net force of all forces acting on the box.
4) what is the acceleration
5) what is the frictional coefficient? is this static or kinetic

Answer 1

1)

$$W=mg=(12)(9.81)=117.72N$$

$$W_t=W \sin{10}=117.72 \sin{10}=20.44 N.$$

$$W_p=-W \cos{10}=-117.72 \cos{10}=-115.9 N.$$

2) i)

$$W_p-N=0$$

ii)

$$ma=W_t-F_f$$

3)

$$ma=20.44-10=10.44 N$$

Direction is down the incline.

4)

$$a=\frac{10.44}{12}=0.87m/s^2$$

5)

$$\mu=\frac{F_f}{N}=\frac{F_f}{W_p}=\frac{10}{117.72}=0.085$$

It is kinetic friction.