Question

9) At a construction site, a small crane is raising two boxes of nails on a plank to the roof. One box has already been opened and is half full, while the other box is new. The boxes, including the nails, weight 10 kg and 20 kg, respectively, and are the same size
a) As the plank tilts towards the heavier box, predict which box of nails will start to slide first. Explain your prediction

Answer 1

Answer:

The two boxes will start sliding at the same angle. Their different masses does not affect when one of the boxes will start sliding.

Explanation:

The two boxes will start sliding when the frictional force,Ff= The gravitational force,Fg

Ff= mgcos theta× coefficient of friction

Fg= mgsintheta

Ff=Fg= mgsintheta=mgcos theta×coefficient of friction

Dividing through with mg on both sides gives

Sintheta=ucostheta

Sintheta/costheta= Tan theta

Theta= tan^-1(coefficient of fricition)

From the solution mass of the boxes and gravity does not affect when the boxes will start sliding.

Answer 2

Box 1 (having a mass of 10 kg) will slide first as it has less inertia than the other box. It will also require less force to overcome static friction between the surface of the plank and that of the first box.