Work-energy method on incline

A question is this type if and only if you must use the work-energy principle (work done by engine minus work done against resistance minus change in PE equals change in KE) to find a quantity such as driving force, distance, or speed over a stretch of inclined road.

4 questions · Standard +0.5

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CAIE M1 2021 June Q5
9 marks Standard +0.3
5 A car of mass 1400 kg is towing a trailer of mass 500 kg down a straight hill inclined at an angle of \(5 ^ { \circ }\) to the horizontal. The car and trailer are connected by a light rigid tow-bar. At the top of the hill the speed of the car and trailer is \(20 \mathrm {~m} \mathrm {~s} ^ { - 1 }\) and at the bottom of the hill their speed is \(30 \mathrm {~m} \mathrm {~s} ^ { - 1 }\).
  1. It is given that as the car and trailer descend the hill, the engine of the car does 150000 J of work, and there are no resistance forces. Find the length of the hill.
  2. It is given instead that there is a resistance force of 100 N on the trailer, the length of the hill is 200 m , and the acceleration of the car and trailer is constant. Find the tension in the tow-bar between the car and trailer.
Pre-U Pre-U 9795/2 2013 November Q8
Standard +0.3
8 A car of mass 1 tonne reaches the foot of an incline travelling at \(30 \mathrm {~m} \mathrm {~s} ^ { - 1 }\). It reaches the top of the incline 50 seconds later travelling at \(10 \mathrm {~m} \mathrm {~s} ^ { - 1 }\). The length of the incline is 1200 m and the angle made with the horizontal is \(\sin ^ { - 1 } \left( \frac { 1 } { 8 } \right)\). The constant resistance to motion is 400 N . Find the average power developed by the engine of the car.
Pre-U Pre-U 9795/2 2015 June Q9
6 marks Standard +0.3
9 A car of mass 800 kg is descending a straight hill which is inclined at \(2 ^ { \circ }\) to the horizontal. The car passes through the points \(A\) and \(B\) with speeds \(10 \mathrm {~m} \mathrm {~s} ^ { - 1 }\) and \(25 \mathrm {~m} \mathrm {~s} ^ { - 1 }\) respectively. The distance \(A B\) is 400 m .
  1. Assuming that resistances to motion are negligible, calculate the work done by the car's engine over the distance from \(A\) to \(B\).
  2. Assuming also that the driving force produced by the car's engine remains constant, calculate the power of the car's engine at the mid-point of \(A B\).
Pre-U Pre-U 9795/2 2014 June Q9
11 marks Challenging +1.2
An engine is travelling along a straight horizontal track against negligible resistances. In travelling a distance of 750 m its speed increases from 5 m s\(^{-1}\) to 15 m s\(^{-1}\). Find the time taken if the engine was
  1. exerting a constant tractive force, [2]
  2. working at constant power. [9]