Example 1 (Particle sliding down a smooth plane)

A particle of mass 5 kg is released from rest on a smooth plane inclined at 30 degrees to the horizontal. Find the acceleration of the particle, the normal contact force and the speed after 3 seconds.

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Newton's Law of Motion, F=ma on a smooth inclined plane : example 1 : ExamSolutions

Example 2 – Particle being pulled up a slope by a rope at an angle with constant speed

A sledge of mass 6 kg is pulled at a constant speed up a slope inclined at 30 degrees to the horizontal by a rope inclined at 25 degrees to the slope. If the resistance from the icy slope is 1 N. Modelling the sledge as a particle, find the tension in the rope and the normal contact force.

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Newton's Law of Motion, F=ma on a smooth inclined plane : example 2 : ExamSolutions

Example 3 – Particle projected up a smooth inclined plane – take care with signs

A particle of mass 3 kg is projected up a smooth plane inclined at 20° to the horizontal at a speed of 2 ms-1. How far up the slope does the particle travel before it comes to instantaneous rest?

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Newton's Law of Motion, F=ma on a smooth inclined plane : example 3 : ExamSolutions