Practice Paper Mechanics 2 (Edexcel International A Level Maths: Pure 4)

Practice Paper Questions

1a
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3 marks

A cyclist is travelling up a straight road inclined at 5° to the horizontal along the line of greatest slope.  All resistances to motion can be neglected.  The cyclist is working at a constant rate of 300 W.  

Given that the acceleration of the cyclist is 0.5 m s-2 at the instant when he is travelling up the hill with speed 2 m s-1, find the total mass of the cyclist and his bicycle.

1b
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3 marks

At the top of the hill, the cyclist turns around and travels down the hill producing a constant power of 100 W.

Find the acceleration of the cyclist at the instant he reaches the speed 5 m s-1.

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2a
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2 marks

The position vector of a particle at time t seconds is given by

 bold r bold space equals space left parenthesis 12 e to the power of negative 0.1 t end exponent right parenthesis bold i bold space plus space left parenthesis 24 e to the power of negative 0.2 t end exponent right parenthesis bold j space space straight m

(i)
Write down the initial position of the particle.

(ii)
Briefly explain why the particle gets closer to the origin but never actually meets it.
2b
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2 marks

Find an expression for the velocity of the particle at time t seconds.

2c
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3 marks
(i)
Find an expression for the acceleration of the particle at time t seconds.

(ii)
Find the magnitude of acceleration of the particle at time t space equals space 4 seconds, giving your answer to three significant figures.

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3a
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3 marks

A uniform lamina is made using a uniform circular disc, made from a uniform material, with a rectangular hole cut from it. Representing the disc on the x minus y plane the circle has equation x squared plus y squared equals 144 and the rectangle has vertices at the intersections of the four lines x equals negative 6 comma space x equals 2 comma space y equals 6 space and space y equals 8, as shown in the diagram below.

q3-hard-2-1-center-of-mass-edexcel-a-level-mechanics

Find the exact coordinates of the centre of mass of the disc after the rectangular hole has been removed from it.

3b
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4 marks

The lamina is suspended freely from the point left parenthesis 0 comma space 12 right parenthesis. Show that the angle the downward vertical makes with the radius of the circle to the point left parenthesis 0 comma space 12 right parenthesis is less than 0.5°.

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4a
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4 marks

q3-medium-4-1-collisions-edexcel-a-level-mechanics

A particle P of mass 6 kg is moving with speed 12 m s-1 in a horizontal plane when it receives an impulse.  Immediately after receiving the impulse, P is moving with speed 25 m s-1 at an angle of 45° to the horizontal as shown in the diagram above.

Find the magnitude of the impulse.

4b
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2 marks

Find the acute angle between the direction of the impulse and the horizontal.

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5a
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7 marks

A non-uniform rod space A B spaceof length 2 m and weight 20 N is resting on two parallel pegs at points X and Y such that 0.8 m and A Y equals1.8 m.  The rod is resting on rough ground at an angle of theta degree with the horizontal such that tan space theta equals 0.75 and is in limiting equilibrium.  The coefficient of friction between the rod and each peg is 0.3 and between the rod and the ground is 0.4.  

q5-hard-5-1-moments-edexcel-a-level-mechanics

Given that the normal reaction at the point X is twice the normal reaction at the point Y, calculate the normal reaction force at each peg and the ground.

5b
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3 marks

Find the distance of the centre of mass of the rod from the point A.

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6
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5 marks

A toboggan team consisting of two children and their sled are moving down a 400 m long uneven course of varying gradients.  They start from rest at the top of the course and do no work as they move down the course.  The frictional force on the sled is 8 N and all other resistance forces can be ignored.  The vertical height of the hill is 35 m.  Find the speed that the team is moving at when they reach the end of the course.  You may consider the two children and their sled as a single particle of mass 100kg.

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7a
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4 marks

Two children in a sledge are being pulled up a smooth hill inclined at 10° to the horizontal by a light, inextensible rope inclined at 30° to the direction of motion.  The tension in the rope as it is being pulled has magnitude 120 N and the sledge moves forward 15 metres along the line of greatest slope from the point space A spaceto the point B.

i)
Draw a diagram showing the motion of the sledge between the points A and B, labelling all forces acting on the sledge.

ii)
Calculate the total work done by the tension in the rope as the sledge is moved up the slope from A to B.
7b
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2 marks

Once the sledge reaches point B it is then released from rest and accelerates down the hill.  At the point where the sledge has 440 J of kinetic energy, it is moving with speed of 4 m s-1.  Find the total mass of the sledge and the two children.

7c
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3 marks

Find the speed of the sledge at the instant when it has reached the point where it started at the bottom of the hill.

7d
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2 marks

State two assumptions you have made in your answer to part (c)

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8a
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3 marks

A golfer strikes a ball from ground level with velocity 28 space straight m space straight s to the power of negative 1 end exponent at an angle of 60 degree to the horizontal.

Write down the initial velocity of the golf ball in the form open parentheses p bold i space plus space q bold j close parentheses space straight m space straight s to the power of negative 1 end exponent, giving the values of p space and space q as exact values.

8b
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4 marks

A tree of height 16 space straight m stands in the path of the flight of the golf ball 56 space straight m from the point where it is struck.  Determine whether or not the golf ball strikes the tree.

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9
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5 marks

For a particle modelled as a projectile with initial velocity U m s−1 at an angle of alpha degree above the horizontal, show that the equation of the trajectory of the particle is given by

y equals left parenthesis t a n space alpha right parenthesis space x minus fraction numerator g x squared over denominator 2 U squared c o s squared space alpha end fraction

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10a
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7 marks

Two particles P space and space Q with masses 0.5 kg and 0.9 kg respectively are moving towards each other in opposite directions along a straight line on a smooth horizontal surface.  They collide directly. Immediately before the collision, P has speed 5 m s-1 and Q has speed 7 m s-1.  The coefficient of restitution between P space and space Q is 3 over 8.

Find the speed of P and the speed of Q immediately after the collision.  Clearly state the direction of motion of each particle.

10b
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3 marks

Calculate the kinetic energy lost in the collision.

10c
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1 mark

Give one form of energy into which the lost kinetic energy could have been transformed.

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