- A car of mass 600 kg pulls a trailer of mass 150 kg along a straight horizontal road. The trailer is connected to the car by a light inextensible towbar, which is parallel to the direction of motion of the car. The resistance to the motion of the trailer is modelled as a constant force of magnitude 200 N . At the instant when the speed of the car is \(v \mathrm {~ms} ^ { - 1 }\), the resistance to the motion of the car is modelled as a force of magnitude \(( 200 + \lambda v ) \mathrm { N }\), where \(\lambda\) is a constant.
When the engine of the car is working at a constant rate of 15 kW , the car is moving at a constant speed of \(25 \mathrm {~m} \mathrm {~s} ^ { - 1 }\)
- Show that \(\lambda = 8\)
Later on, the car is pulling the trailer up a straight road inclined at an angle \(\theta\) to the horizontal, where \(\sin \theta = \frac { 1 } { 15 }\)
The resistance to the motion of the trailer from non-gravitational forces is modelled as a constant force of magnitude 200 N at all times. At the instant when the speed of the car is \(v \mathrm {~m} \mathrm {~s} ^ { - 1 }\), the resistance to the motion of the car from non-gravitational forces is modelled as a force of magnitude \(( 200 + 8 v ) \mathrm { N }\).
The engine of the car is again working at a constant rate of 15 kW .
When \(v = 10\), the towbar breaks. The trailer comes to instantaneous rest after moving a distance \(d\) metres up the road from the point where the towbar broke. - Find the acceleration of the car immediately after the towbar breaks.
- Use the work-energy principle to find the value of \(d\).