Practice Paper Mechanics 1 (Edexcel International AS Maths: Pure 2)

Practice Paper Questions

1a
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6 marks

Lucy and Fran are driving monster trucks along the same straight line in opposite directions towards each other. The combined mass of Lucy and her truck is 5400 kg and the combined mass of Fran and her truck is 4700 kg. They collide directly. Immediately before the collision, Lucy’s truck is moving with speed 4 space m space s to the power of negative 1 end exponent and Fran’s truck is moving with speed 5 space m space s to the power of negative 1 end exponent. Immediately after the collision, Lucy and Fran’s monster trucks are moving at the same speed.

(i)
Given that Lucy and Fran’s monster trucks are moving in the same direction after the collision, find the speed at which they both travel.
(ii)
State which person’s direction of motion has been reversed.
(iii)
Calculate the change in momentum of Fran’s monster truck due to the collision.
1b
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4 marks

Given instead that Lucy and Fran’s monster trucks bounce off each other and move in opposite directions with equal speeds after the collision, calculate the speed at which they both travel.

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2a
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3 marks

A particle is projected upwards from ground level with velocity u space straight m space straight s to the power of negative 1 end exponent. 6 seconds later it has a velocity of 1.2 space straight m space straight s to the power of negative 1 end exponent. Find the value of u.

2b
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3 marks

Find the displacement of the particle, from its initial position, 4 seconds later.

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3a
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2 marks

Melody is practising her skateboarding skills along a horizontal stretch of ground. She starts from rest and accelerates uniformly for 4 seconds at which point she has reached the speed v space m s to the power of negative 1 end exponent. Melody then travels at this speed for 10 seconds. She then decelerates uniformly until she comes to rest which takes 5 seconds.

Sketch a velocity-time graph for the motion of the skateboard.

3b
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2 marks

During the motion, Melody travels 174 metres.

Find the value of v.

3c
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3 marks

Sketch an acceleration-time graph for the motion of the skateboard.

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4
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6 marks

A particle of mass 0.7 kg is on a rough plane which is angled at 35 degree to the horizontal.  The particle is being held at rest by a force of P N acting up the plane along the line of greatest slope.

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Given that the coefficient of friction between the particle and the plane is 0.35, and that the particle is on the point of slipping up the plane, find the value of P.

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5a
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6 marks

A B is a non-uniform rod of mass 12 kg and length 4 m. A B is held horizontally in equilibrium by a support placed at point C and a vertical wire attached to point D such that A C space equals space 0.8 space m and D B space equals space 1 space m as shown in the diagram below:

4-1-h-qu6

A weight of mass 15 kg is attached to the rod at point B and the rod is at the point of tilting about point D.  The weight is then removed.

 

Find the ratio of the reaction force at C to the tension in the wire at D when there are no external weights attached to the rod.  Give your answer in the form p space colon space q where p and q are integers with no common factors other than 1.

5b
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3 marks

The 15 kg weight is then attached to the rod between points A and C.

Find the greatest distance to the left of point C that the weight can be attached without the rod beginning to tilt.

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6
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6 marks

It takes three minutes for a particle to travel left parenthesis 1.62 bold i plus 2.16 bold j right parenthesis space k m with constant acceleration. The particle’s velocity at the start of the three minutes is half of its velocity at the end. Find the magnitude of the acceleration giving your answer as a fraction, in metres per square second.

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7a
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2 marks

Two forces bold F subscript bold 1 and bold F subscript bold 2 act on a particle, where bold F subscript bold 1 equals space left parenthesis 5 bold i space minus space 3 bold j right parenthesis  newtons and bold F subscript 2 equals space left parenthesis x bold i space plus space straight y bold j right parenthesis newtons.
 newtons.

The resultant force bold R acting on the particle is given by bold R equals bold F subscript 1 plus bold F subscript 2, and acts in a direction parallel to the vector left parenthesis negative bold i space minus space 3 bold j right parenthesis.

Find the angle between bold R and the vector j, giving your answer in degrees correct to 2 decimal places.

7b
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3 marks

Show that 3 x space minus space y space equals space minus 18.

7c
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3 marks

Given that y space equals space minus 3, find the magnitude of R.

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8a
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3 marks

Two masses A and B are placed in a light scale-pan, with mass A resting on top of mass B as shown in the diagram below:

3-2-q6-a-level-maths-mechanics

Mass A has a mass of  700 g  and mass B has a mass of  900 g.  The scale-pan is attached to a vertical light inextensible string.

Using the string, the scale-pan is raised vertically with an acceleration of 0.7 space straight m space straight s to the power of negative 2 end exponent.

Find:

the tension in the string

8b
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2 marks

the force exerted on mass A by mass B

8c
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1 mark

the force exerted on mass B by mass A

8d
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2 marks

the force exerted on mass B by the scale-pan.

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9
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6 marks

A scientist has set up a device to measure the frictional resistance force between a block B and a rough horizontal tabletop.  Block B has a mass of 4.5 kg, and it is connected by a light inextensible string to a metal sphere A of mass 3.5 kg.  The string passes over a smooth light fixed pulley at the edge of the table so that A is hanging vertically downwards as shown in the diagram below:

edexcel-al-maths-mechanics-topic-3-2-h---q8

The string between B and the table is horizontal, and the frictional resistance between B and the table is modelled as a constant force of magnitude Ff  N.

The system is released from rest with the string taut and with sphere A exactly 1 metre above the ground.

Given that sphere A strikes the ground 0.8 seconds after it is released, determine the value of Ff.

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10
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9 marks

Luke Cloudwalker is a robotics engineer. Luke propels a robot along a straight path with initial speed 3 space m s to the power of negative 1 end exponent and uses a remote control to change its speed. Throughout the journey, the robot travels along the same straight path. The acceleration-time graph below shows the motion of the robot.

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(i)
Calculate how far the robot is from its starting point after 24 seconds.
(ii)
Find the total distance travelled by the robot during the first 24 seconds of motion.

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