Energy method - driving force up incline, find speed

Uses work-energy principle on an inclined plane with a driving force acting uphill, where the unknown is the speed at a point, given work done by engine/force and resistance information.

2 questions · Standard +0.0

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CAIE M1 2013 June Q2
5 marks Moderate -0.3
2 A car of mass 1250 kg travels from the bottom to the top of a straight hill of length 600 m , which is inclined at an angle of \(2.5 ^ { \circ }\) to the horizontal. The resistance to motion of the car is constant and equal to 400 N . The work done by the driving force is 450 kJ . The speed of the car at the bottom of the hill is \(30 \mathrm {~m} \mathrm {~s} ^ { - 1 }\). Find the speed of the car at the top of the hill.
OCR MEI Further Mechanics Major 2022 June Q6
7 marks Standard +0.3
In this question the box should be modelled as a particle. A box of mass \(m\) kg is placed on a rough slope which makes an angle of \(\alpha\) with the horizontal.
  1. Show that the box is on the point of slipping if \(\mu = \tan \alpha\), where \(\mu\) is the coefficient of friction between the box and the slope. [2]
A box of mass 5 kg is pulled up a rough slope which makes an angle of 15° with the horizontal. The box is subject to a constant frictional force of magnitude 3 N. The speed of the box increases from 2 m s\(^{-1}\) at a point A on the slope to 5 m s\(^{-1}\) at a point B on the slope with B higher up the slope than A. The distance AB is 10 m. \includegraphics{figure_6} The pulling force has constant magnitude \(P\) N and acts at a constant angle of 25° above the slope, as shown in the diagram.
  1. Use the work–energy principle to determine the value of \(P\). [5]