Practice Paper Mechanics 1 (Edexcel International A Level Maths: Pure 4)

Practice Paper Questions

1a
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3 marks

Two particles, P and Q, with masses 3 m and 5 m respectively are moving towards each other in opposite directions along the same straight line on a smooth horizontal plane. They collide directly. Immediately before the collision, the speed of P is 3 u and the speed of Q is 2 u. Immediately after the collision, the speed of P is halved and its direction of motion is reversed.

Find the speed of Q immediately after the collision.

1b
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1 mark

State whether the direction of motion of Q is changed immediately after the collision.

1c
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3 marks

Find the magnitude of the impulse exerted by Q on P in the collision.

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2a
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5 marks

A train leaves station O, from rest with constant acceleration 0.2 space straight m space straight s to the power of negative 2 end exponent. 125 space seconds later it passes a signal at which point the train decelerates uniformly until coming to rest at station X 75 seconds later.

Find the distance between station O and station X.

2b
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3 marks

The train then leaves station X  but travels in the opposite direction with constant acceleration 0.1 space straight m space straight s to the power of negative 2 end exponent. The train does not stop at station O but 300 space seconds after leaving station it passes a signal indicating that station Y  is 850 m away. At this point the train decelerates uniformly so it comes to rest at station Y.

Find the distance between station O and station Y

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3a
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2 marks

A particle of mass 3 kg starts from rest and is acted upon by three forces, bold F subscript bold 1 bold comma bold space bold F subscript bold 2 bold space and bold space bold F subscript bold 3 given in vector form as

bold F subscript bold 1 equals left parenthesis negative bold i plus 3 bold j right parenthesis space straight N space space space space space space space space space bold F subscript bold 2 equals left parenthesis 2 bold i minus 2 bold j right parenthesis space straight N space space space space space space space space space bold F subscript bold 3 equals left parenthesis negative 5 bold i plus b bold j right parenthesis space straight N

where b is a constant. The resultant of forces bold F subscript bold 1 bold comma bold space bold F subscript bold 2 bold space and bold space bold F subscript bold 3 is bold R.

Given that bold R acts on a bearing of 225 degree:

Find the value of the constant b.

3b
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3 marks

Work out the magnitude of the acceleration of the particle.

3c
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3 marks

Find the total distance travelled by the particle in the first 4 seconds of its motion.

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4a
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4 marks

In a warehouse a hydraulic lift is being used to raise a large crate as shown in the diagram below:

rKXWfEEu_6

The crate has a mass of 1200 kg and the platform of the lift has a mass of 300 kg. The lifting force is transmitted to the platform by means of a vertical rod of negligible mass.

Starting from rest, the platform and crate are accelerated vertically upwards at a constant rate so that they reach a velocity of 3 m s-1 after 2 seconds.

Find the thrust in the rod.

4b
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3 marks

Find the force exerted by the crate on the lifting platform.

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5
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4 marks

Starting from rest a toy boat experiencing a constant acceleration of left parenthesis 0.5 bold i plus 0.2 bold j right parenthesis space m space s to the power of negative 2 end exponent takes 12 seconds to sail across a pond. Find the distance the toy boat sails across the pond, giving your answer to three significant figures.

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6a
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3 marks

A particle moves under constant acceleration left square bracket left parenthesis 2 q plus 1 right parenthesis bold i plus left parenthesis q minus 1 right parenthesis bold j right square bracket space m space s to the power of negative 2 end exponent. In a 6 second time period, the particle has initial velocity left square bracket 5.2 bold i plus left parenthesis 1 minus 2 p right parenthesis bold j right square bracket space m space s to the power of negative 1 end exponent and final velocity left square bracket left parenthesis 27 p plus 4 right parenthesis bold i plus 5.2 bold j right square bracket space m space s to the power of negative 1 end exponent where p and q are constants.

Show that 

27 p minus 12 q equals 7.2 space space space space space space space space space and space
2 p minus 6 q equals negative 10.2

6b
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2 marks

Find the values of p and q.

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7a
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3 marks

A particle of mass 15 kg is sliding down a rough slope that is angled 25° to the horizontal. The coefficient of friction between the particle and the slope is 0.3.

Calculate the frictional force between the particle and the slope.

7b
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3 marks

Hence calculate the acceleration of the particle down the slope.

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8a
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3 marks

A particle is being pulled up a smooth slope by a force of 60 N that acts at an angle of 15 degree to the slope. The slope is inclined at 25 degree to the horizontal, as shown in the diagram below:

u90kF70s_5The particle experiences an acceleration of 0.3 m s-2 parallel to the slope in the upwards direction.

Use the information provided above to calculate the mass of the particle.

8b
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3 marks

Calculate the normal reaction force of the slope on the particle.

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9
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5 marks

A B C is a triangular lamina in which angle A C B is a right angle, and the lengths of sides A B and B C are 58 cm and 42 cm respectively. Three forces are applied to the lamina at points A comma space B space and space C as shown in the diagram below:

N7EHCCRs_19

Calculate the resultant moment of the three forces about point C.

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10
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7 marks

A B is a non-uniform rod of mass 10 kg and length 3 m. A B rests horizontally on two supports placed at points C and D, where A C equals D B equals 0.6 space m as shown in the diagram below:

9AmKmcET_21

Esmerelda attaches a 9 kg mass to the rod at a point 0.4 m to the left of D, and measures the reaction force at C. She then removes the mass and reattaches it to the rod at a point 0.4 m to the right of D, and again measures the reaction force at C. She finds that in her second measurement the reaction force at C is only one third the size of the reaction force at C in her first measurement.

By modelling the attached mass as a particle, use the above information to determine the position of the centre of mass of rod A B. Give the position in your answer as the distance of the centre of mass from point A.

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11a
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3 marks

A TV camera runs along a horizontal track next to the pitch at a football match. The pitch is 80 space m long and the camera is initially positioned at the halfway line. The camera moves from rest at a constant velocity and after 6 seconds has displacement 24 space m.

It then moves back to the halfway line at a constant velocity, taking 12 seconds to do so. For the next 6 seconds the camera moves with constant velocity negative 3 space m s to the power of negative 1 end exponent.

Sketch a displacement-time graph to illustrate the motion of the camera.

11b
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2 marks
(i)
Write down the final displacement of the camera.
(ii)
Write down the distance of the camera from the halfway line at the end of the motion.

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12a
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4 marks

A snooker ball is struck such that it travels in a straight line up and down a snooker table. The graph below shows the velocity of the ball, v space m s to the power of negative 1 end exponent, at time t seconds.

28


Write down the times at which the snooker ball hits a cushion and hence, find the length of the snooker table.

12b
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3 marks

Show that the snooker ball comes to rest in exactly the same place it was struck from.

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