6 A box, of mass 3 kg , is placed on a slope inclined at an angle of \(30 ^ { \circ }\) to the horizontal. The box slides down the slope. Assume that air resistance can be ignored.
- A simple model assumes that the slope is smooth.
- Draw a diagram to show the forces acting on the box.
- Show that the acceleration of the box is \(4.9 \mathrm {~ms} ^ { - 2 }\).
- A revised model assumes that the slope is rough. The box slides down the slope from rest, travelling 5 metres in 2 seconds.
- Show that the acceleration of the box is \(2.5 \mathrm {~m} \mathrm {~s} ^ { - 2 }\).
- Find the magnitude of the friction force acting on the box.
- Find the coefficient of friction between the box and the slope.
- In reality, air resistance affects the motion of the box. Explain how its acceleration would change if you took this into account.