Particle on inclined plane

A question is this type if and only if it involves a particle on a rough or smooth inclined plane where you must resolve forces parallel and perpendicular to the plane to find acceleration, friction, normal reaction, or equilibrium conditions.

3 questions · Moderate -0.1

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Edexcel M1 Q4
10 marks Moderate -0.3
A cyclist and her bicycle have a combined mass of 78 kg. While riding on level ground and using her greatest driving force, she is able to accelerate uniformly from rest to 10 ms\(^{-1}\) in 15 seconds against constant resistive forces that total 60 N.
  1. Show that her maximum driving force is 112 N. [4 marks]
The cyclist begins to ascend a hill, inclined at an angle \(\alpha\) to the horizontal, riding with her maximum driving force and against the same resistive forces. In this case, she is able to maintain a steady speed.
  1. Find the angle \(\alpha\), giving your answer to the nearest degree. [4 marks]
  2. Comment on the assumption that the resistive force remains constant
    1. in the case when the cyclist is accelerating,
    2. in the case when she is maintaining a steady speed. [2 marks]
Edexcel M1 Q3
7 marks Moderate -0.3
A car of mass 1250 kg is moving at constant speed up a hill, inclined at an angle \(\alpha\) to the horizontal, where \(\sin \alpha = \frac{1}{10}\). The driving force produced by the engine is 1800 N.
  1. Calculate the resistance to motion which the car experiences. [4 marks]
At the top of the hill, the road becomes horizontal.
  1. Find the initial acceleration of the car. [3 marks]
Edexcel M1 Q5
12 marks Standard +0.3
A cyclist is riding up a hill inclined at an angle of 5° to the horizontal. She produces a driving force of 50 N and experiences resistive forces which total 20 N. Given that the combined mass of the cyclist and her bicycle is 70 kg,
  1. find, correct to 2 decimal places, the magnitude of the deceleration of the cyclist. [4 marks]
When the cyclist reaches the top of the hill, her speed is 3 m s\(^{-1}\). She subsequently accelerates uniformly so that in the fifth second after she has reached the top of the hill, she travels 12 m.
  1. Find her speed at the end of the fifth second. [8 marks]