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 parcel $P$ of mass $m$ on a straight chute.Figure 1 — not accurately drawn

The chute is modelled as a rough plane inclined at an angle $\alpha$ to the horizontal, where $\tan\alpha = \dfrac{28}{45}$

The parcel is modelled as a particle. The coefficient of friction between the parcel and the chute is $\mu$ , where $\mu < \dfrac{28}{45}$

$P$ is released from rest and moves down a line of greatest slope of the chute. Air resistance is ignored.

Using the model,
(a) find, in terms of $m$ and $g$ , the magnitude of the normal reaction of the chute on $P$ ,

(2 marks)
(b) show that the acceleration of $P$ down the chute is $\dfrac{1}{53}g(28 - 45\mu)$

(4 marks)
(c) State what would happen to $P$ on its release if, instead, $\mu \geqslant \dfrac{28}{45}$

(1 mark)
Level 4 · 7 marksTry it
2
A box of weight $40$ N rests on a rough ramp inclined at an angle $\theta$ to the horizontal. A horizontal force of magnitude $20$ N pushes the box towards the ramp, and this force acts in the vertical plane that contains a line of greatest slope of the ramp (see diagram).
(a) Make a copy of the diagram and show on it all the forces acting on the box.

(1 mark)

The box stays at rest, and the coefficient of friction between the box and the ramp is $0.25$ .
(b) Determine the least possible value of $\tan\theta$ .

(5 marks)
Level 4 · 6 marksTry it