A-level · Forces & Newton's laws

Forces on an inclined planeExam-style questions

Resolving the weight on a slope into components along (mg sinα) and perpendicular (mg cosα) to the surface, the normal reaction R = mg cosα, and applying F = ma along the slope (acceleration g sinα on a smooth slope).

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13 questions · A-level level · mark scheme and worked solution on each · no sign-up to try

DifficultyAll Level 2 Level 3 Level 4 Level 5

1
Figure 1 shows a small crate $C$ , of mass $3.5$ kg, at rest on a fixed rough plane which is inclined at an angle $\alpha$ to the horizontal, where $\tan\alpha = \dfrac{20}{21}$ Figure 1 — not accurately drawn

The crate is kept at rest by a horizontal force of magnitude $X$ newtons. The force and a line of greatest slope of the plane lie in the same vertical plane.

The crate is modelled as a particle.

The plane exerts a normal reaction of magnitude $60.7$ N on $C$ .

Using the model,
(a) (i) find the magnitude of the frictional force acting on $C$ ,

(ii) state the direction of the frictional force acting on $C$ .

(4 marks)

The horizontal force is then taken away, and $C$ slides down the plane.

The coefficient of friction between the crate and the plane is $0.6$
(b) Find the acceleration of $C$ as it slides down the plane.

(6 marks)
Level 5 · 10 marksTry it
2
A box of mass $6$ kg is pulled at constant speed up a rough plane inclined at $20^\circ$ to the horizontal, by a force of magnitude $P$ newtons acting parallel to the plane.

The coefficient of friction between the box and the plane is $0.3$ . ( $g = 9.8\ \text{m s}^{-2}$ .)

Find the value of $P$ , giving your answer correct to 3 significant figures. (6 marks)
Level 5 · 6 marksTry it