Mathematics 9709 · AS & A Level · Newton's laws of motion
Newton's laws of motion — practice question
A particle of mass $30\,\text{kg}$ rests on a plane that is inclined at $20^\circ$ to the horizontal. It is initially at rest and is then pulled up the plane by a force of magnitude $200\,\text{N}$ acting parallel to the line of greatest slope.
(i(a))[2]
Given that the plane is smooth, find the acceleration of the particle.
(i(b))[2]
Find the change in kinetic energy after the particle has travelled $12\,\text{m}$ up the plane.
(ii(a))[4]
Suppose instead that the plane is rough and the coefficient of friction between the particle and the plane is $0.12$. Find the acceleration of the particle.
(ii(b))[4]
The force of magnitude $200\,\text{N}$ is now applied at an angle of $10^\circ$ above the line of greatest slope. Find the acceleration of the particle.
Worked solution & mark scheme
This 12-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Use Newton’s second law along the plane: $200 - 30g\sin 20 = 30a$” …