AQA A Level Maths
An object is pulled along a horizontal surface. The normal reaction between the surface and the object is 125 newtons.
The object experiences a constant frictional force of 40 newtons.
Find the value of the coefficient of friction.
Circle your answer.
0.245 0.32 0.5 3.125
Also involves Resolving forces · Equilibrium of a particle
– 2 16 In this question use g = 9.8 m s
A sledge is pulled in a straight line up a rough path, as shown in the diagram.
The path is inclined at an angle of 20° to the horizontal.
The sledge is pulled by a light, inextensible rope inclined at an angle of 30° to the path.
The mass of the sledge is 10 kilograms.
In one model, the sledge moves at a constant speed and experiences a combined resistance force of 15 newtons.
Find the tension in the rope for this model.
In a different model, the sledge experiences no air resistance.
The tension in the rope for this model is 54 N
The coefficient of friction between the sledge and the path is 0.2
Find the acceleration of the sledge for this model.
State an assumption you have used to answer both parts (a) and (b).
Also involves Constant acceleration formulae
In this question use 
= 9
8 m s
2
A particle, Q, moves in a straight line across a rough horizontal surface.
A horizontal driving force of magnitude D newtons acts on Q
Q moves with a constant acceleration of 0.91 m s
2
Q has a weight of 0.65 N
The only resistance force acting on Q is due to friction.
The coefficient of friction between Q and the surface is 0.4
Find D
In this question use 
9.8 m s
2
A rough wooden ramp is 10 metres long and is inclined at an angle of 25
above the horizontal. The bottom of the ramp is at the point O.
A crate of mass 20 kg is at rest at the point A on the ramp.
The crate is pulled up the ramp using a rope attached to the crate.
Once in motion, the rope remains taut and parallel to the line of greatest slope of the
The tension in the rope is 230 N
The crate accelerates up the ramp at 1.2 m s
2
Find the coefficient of friction between the crate and the ramp.
The crate takes 3.8 seconds to reach the top of the ramp.
Find the distance OA.
Other than air resistance, state one assumption you have made about the crate in answering part (b)(i).
Also involves Connected particles
Block A, of mass 0.2 kg, lies at rest on a rough plane. The plane is inclined at an angle 
to the horizontal, such that tan 
A light inextensible string is attached to A and runs parallel to the line of greatest slope until it passes over a smooth fixed pulley at the top of the slope.
The other end of this string is attached to particle B, of mass 2 kg, which is held at rest so that the string is taut, as shown in the diagram below.
B is released from rest so that it begins to move vertically downwards with an
Show that the coefficient of friction between A and the surface of the inclined plane is 0.17
In this question use 
9.81 m s
2
When A reaches a speed of 0.5 m s
1 the string breaks.
Find the distance travelled by A after the string breaks until first coming to rest.
State an assumption that could affect the validity of your answer to part (b)(i).
A wooden crate rests on a rough horizontal surface.
The coefficient of friction between the crate and the surface is 0.6
A forward force acts on the crate, parallel to the surface.
When this force is 600 N, the crate is on the point of moving.
Find the weight of the crate.
Circle your answer.
1000 N 100 kg 360 N 36 kg
Also involves Resolving forces
Lizzie is sat securely on a wooden sledge.
The combined mass of Lizzie and the sledge is M kilograms.
The sledge is being pulled forward in a straight line along a horizontal surface by means of a light inextensible rope, which is attached to the front of the sledge.
This rope stays inclined at an acute angle 
above the horizontal and remains taut as the sledge moves forward.
The sledge remains in contact with the surface throughout.
The coefficient of friction between the sledge and the surface is 
and there are no other resistance forces.
Lizzie and the sledge move forward with constant acceleration, a m s
2
The tension in the rope is a constant T Newtons.
Show that
It is known that when M 
30, 
30
, and T 
40, the sledge remains at rest.
Lizzie uses these values with the relationship formed in part (a) to find the value for
Explain why her value for 
may be incorrect.
Also involves Resolving forces
In this question use 9.8 m s
2
A boy attempts to move a wooden crate of mass 20 kg along horizontal ground. The coefficient of friction between the crate and the ground is 0.85
The boy applies a horizontal force of 150 N. Show that the crate remains stationary.
Instead, the boy uses a handle to pull the crate forward. He exerts a force of 150 N, at an angle of 15
above the horizontal, as shown in the diagram.
Determine whether the crate remains stationary.
Fully justify your answer.
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