M2 January 2008 Q1
1. A parcel of mass 2.5 kg is moving in a straight line on a smooth horizontal floor. Initially the parcel is moving with speed 8 m s\(^{-1}\). The parcel is brought to rest in a distance of 20 m by a constant horizontal force of magnitude \(R\) newtons. Modelling the parcel as a particle, find
(a) the kinetic energy lost by the parcel in coming to rest, (2)
(b) the value of \(R\). (3)
| Scheme | Marks |
|---|---|
| KE lost is \(\dfrac{1}{2} \times 2.5 \times 8^2 = 80\) (J) | M1 A1 |
| (2) |
| Scheme | Marks |
|---|---|
| Work energy \(80 = R \times 20\) ft their (a) | M1 A1 ft |
| \(R = 4\) | A1 |
| (3) | |
| (5 marks) |
Alternative to (b)
| \(0^2 = 8^2 - 2 \times a \times 20 \ \Rightarrow\ a = (-)1.6\) | |
| N2L \(R = 2.5 \times 1.6\) ft their \(a\) | M1 A1ft |
| \(= 4\) | A1 |
(3)