M2 January 2009 Q3
3. A block of mass 10 kg is pulled along a straight horizontal road by a constant horizontal force of magnitude 70 N in the direction of the road. The block moves in a straight line passing through two points \(A\) and \(B\) on the road, where \(AB = 50\) m. The block is modelled as a particle and the road is modelled as a rough plane. The coefficient of friction between the block and the road is \(\tfrac{4}{7}\).
(a) Calculate the work done against friction in moving the block from \(A\) to \(B\). (4)
The block passes through \(A\) with a speed of 2 m s\(^{-1}\).
(b) Find the speed of the block at \(B\). (4)
| Scheme | Marks |
|---|---|
| \(R(\updownarrow): R = 10g\) | B1 |
| \(F = \mu R \ \Rightarrow\ F = \dfrac{4}{7}(10g) = 56\) | B1 |
| \(\therefore\) WD against friction \(= \dfrac{4}{7}(10g)(50)\) | M1 |
| 2800(J) | A1 |
| (4) |
| Scheme | Marks |
|---|---|
| \(70(50) -\) “2800” \(= \tfrac{1}{2}(10)v^2 - \tfrac{1}{2}(10)(2)^2\) | M1* A1ft |
| \(700 = 5v^2 - 20,\ \ 5v^2 = 720 \Rightarrow v^2 = 144\) | d*M1 |
| Hence, \(v = 12\) (m s\(^{-1}\)) | A1 cao |
| (4) | |
| (8 marks) |
Or (b)
| N2L\((\rightarrow)\): \(\ 70 - \dfrac{4}{7}R = 10a\) | M1* |
| \(70 - \dfrac{4}{7} \times 10g = 10a,\ \ (a = 1.4)\) | A1ft |
| \(AB(\rightarrow)\): \(\ v^2 = (2)^2 + 2(1.4)(50)\) | d*M1 |
| Hence, \(v = 12\) (m s\(^{-1}\)) | A1 cao |
(4)