M1 June 2015 Q4
4.
A lift of mass 200 kg is being lowered into a mineshaft by a vertical cable attached to the top of the lift. A crate of mass 55 kg is on the floor inside the lift, as shown in Figure 2. The lift descends vertically with constant acceleration. There is a constant upwards resistance of magnitude 150 N on the lift. The crate experiences a constant normal reaction of magnitude 473 N from the floor of the lift.
| Scheme | Marks |
|---|---|
| For crate, \(55g - 473 = 55a\) | M1 A1 |
| \(a = 1.2\) m s\(^{-2}\) | A1 |
| (3) |
Notes
M1 for an equation in \(a\) only, with usual rules.
First A1 for a correct equation
Second A1 for 1.2 (m s\(^{-2}\)). Allow −1.2 (m s\(^{-2}\)) if appropriate
| Scheme | Marks |
|---|---|
| For system, \(55g + 200g \pm T - 150 = 255a\) | M1 A2 |
| Magnitude = 2040 N or 2000 N | A1 |
| OR | |
| For lift, \(200g + 473 - 150 \pm T = 200a\) | M1 A2 |
| Magnitude = 2040 N or 2000 N | A1 |
| (4) | |
| (7 marks) |
Notes
M1 for an equation, in \(T\) and \(a\), for the system or the lift only, with usual rules. (\(a\) does not need to be a numerical value)
A2 (-1 each error) for a correct equation (Allow \(\pm T\)). We do not need to see a numerical value for \(a\).
Third A1 for 2040 (N) or 2000 (N)
N.B. In both parts of this question use the mass which is being used to guide you as to which part of the system is being considered.