• A Level Maths

Demo

• A Level
• Friction

1. A particle of mass 10 kg is pulled by a force of 20 N acting at an angle of 20° above the horizontal. The particle lies on a rough horizontal surface, and accelerates at 1 m s^-2. Find the coefficient of friction between the particle and the surface.

0.0965

2. A particle of mass 0.4 kg is placed on a rough plane, which makes an angle of 50° to the horizontal. The coefficient of friction between the particle and the plane is 0.5. Find the acceleration of the particle.

4.36

3. A particle of mass 3 kg lies on a rough slope which is at an angle of 30° to the horizontal. The particle is held in position by a force of 10 N acting up and parallel to the slope, and is on the verge of slipping down the plane. Find the coefficient of friction between the particle and the plane.

0.185

4. A particle of mass 8 kg is released from rest on a rough slope which is angled at 30° to the horizontal. 3 seconds after being released, the particle has travelled 5 m down the slope. Find the coefficient of friction between the particle and the slope.

0.446

5. A particle of mass 2 kg is being pulled up a rough slope that is angled at 20° to the horizontal by a force of 15 N. The force is acting at an angle of 30° above the slope, and the particle accelerates at 1 m s^-2. Find the coefficient of friction between the particle and the slope.

0.393

6. A particle of mass 2 kg lies in equilibrium on a rough slope inclined at an angle of 30° to the horizontal. When a force of 30 N, acting parallel to the slope, attempts to pull the particle up the slope, the particle remains in equilibrium. Find the minimum value of the coefficient of friction between the particle and the slope.

1.19

7. A particle of mass 5 kg lies on a rough slope inclined at 40° to the horizontal. A horizontal force $F$ is pushing the particle, which is accelerating up the slope at 3 m s^-2. Given that the coefficient of friction between the particle and the slope is 0.3, calculate the magnitude of $F$.

75.2

8. A particle of mass 20 kg is released from rest on a rough slope, inclined at an angle of 35° to the horizontal. The coefficient of friction between the particle and the slope is 0.1. Find the distance the particle travels down the slope after 2 seconds.

9.64

9. A particle of mass $m$ kg is released from rest on a rough slope that is angled at $\theta$ to the horizontal. The coefficient of friction between the particle and the slope is $\mu$. Find the acceleration of the particle in terms of $\theta$ and $\mu$.

$g\sin\theta - \mu g\cos\theta$

10. A particle of mass 1 kg lies on a rough slope which is at an angle of 40° to the horizontal. The coefficient of friction between the particle and the slope is 0.3. A light, inextensible string, at an angle of 20° above the slope, is attached to the top of the particle, which is in limiting equilibrium. Find the range of possible values for the tension in the string.

$4.83 \leqslant T \leqslant 8.20$

11. A particle of mass 5 kg is projected up a rough slope at 16 m s^-1. The particle comes to rest after 5 seconds, and the slope is inclined at an angle of 10° to the horizontal. Determine whether the particle will remain at rest, or if it will begin sliding back down the slope.

It will slide back down.

12. A particle is projected up a rough slope with speed 15 m s^-1. The slope is angled at $\theta$ to the horizontal, where $\tan\theta = \dfrac{3}{4}$. The coefficient of friction between the particle and the slope is $0.2$. Find the time taken for the particle to return to its initial position.

4.66