Practice Paper 3 (Mechanics) (Edexcel A Level Maths: Mechanics)

Practice Paper Questions

1
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4 marks

Starting from rest a toy boat experiencing a constant acceleration of open parentheses 0.5 bold i space plus space 0.2 bold j close parentheses space straight m space straight 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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2
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8 marks

Two particles A and B, of masses 2.7 kg and 2.2 kg respectively, are connected by means of a light inextensible string.  Particle A is held motionless on a rough fixed plane inclined at 25° to the horizontal.  The string passes over a smooth light pulley fixed at the top of the plane so that B is hanging vertically downwards as shown in the diagram below:

mech-3-3-h-q9

The string between A and the pulley lies along a line of greatest slope of the plane, and B hangs freely from the pulley.  The coefficient of friction between particle A and the plane is μ.

 

The system is released from rest with the string taut.  Given that particle B descends 1.82 m in the first 3 seconds after it is released, find the value of μ.

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3
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9 marks

In the following diagram AB is a ladder of length 2a and mass ml.  End A of the ladder is resting against a rough vertical wall, while end B rests on rough horizontal ground so that the ladder makes an angle of θ with the ground as shown below:

 4-1-vh-qu8 

A person with mass mp is standing on the ladder a distance d from end B. The ladder may be modelled as a uniform rod lying in a vertical plane which is perpendicular to the wall, and the person may be modelled as a particle. The coefficient of friction between the wall and the ladder is μA, and the coefficient of friction between the ground and the ladder is μB. It may be assumed that 0 less than theta less than 90 degree.

 

Given that the ladder is at rest in limiting equilibrium, show that

 R subscript B equals fraction numerator a m subscript l plus d m subscript p over denominator 2 a mu subscript B left parenthesis mu subscript A plus t a n space theta right parenthesis end fraction space g 

where RB is the normal reaction force exerted by the ground on the ladder at point B and where g is the constant of acceleration due to gravity.

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4
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5 marks

In this question, use bold italic g bold equals bold 10 bold space bold m bold space bold s to the power of bold minus bold 2 end exponent for the acceleration due to gravity.

The graph below shows the trajectory of a projectile, with x and y being measured in metres.

edexcel-al-maths-mechanics-topic-2-6-vh---q8

Use the graph to help determine

(i)
the time of flight of the projectile in seconds

(ii)
the initial velocity of the projectile in the form left parenthesis u subscript x bold i space plus space u subscript y bold j right parenthesis space straight m space straight s to the power of negative 1 end exponent

(iii)
the speed, to three significant figures, of the projectile at launch

(iv)
the angle to the horizontal at which the projectile was launched, giving your answer to one decimal place

(v)
the maximum height reached by the projectile.

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5a
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6 marks

At time t seconds, a particle P has acceleration a m s−2, where

 bold a equals left parenthesis 4 straight t minus 3 right parenthesis bold i plus left parenthesis 4 straight t plus 5 right parenthesis bold j                              t space greater or equal than space 0.

Initially P starts at the origin O and moves with velocity open parentheses negative 5 bold j close parentheses space straight m space straight s to the power of negative 1 end exponent.

 

Find the distance between the origin and the position P of when t space equals space 6.

5b
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5 marks

Find the value of t at the instant when P is moving in the direction of bold i space plus space 2 bold j.

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6a
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2 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 straight m space straight s to the power of negative 1 end exponent, at time t space seconds after being struck.

edexcel-al-maths-mechanics-topic-2-1-h---q7

(i)
When did the snooker ball hit a cushion?

(ii)
Find the percentage reduction in the speed of the ball when it hits the cushion?
6b
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3 marks
(i)
Find the magnitude of the acceleration of the snooker ball before it hits the cushion.

(ii)
Show that the magnitude of acceleration of the snooker ball after it hits the cushion is
                     
                     fraction numerator 15 over denominator 10 T space minus space 6 end fraction space straight m space straight s to the power of negative 2 end exponent
6c
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4 marks

When the snooker ball comes to rest it has displacement 0.3 m. Find the value of T and the total distance travelled by the ball.

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7
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4 marks

Two particles A and B have masses of 3 kg and mB kg respectively. The particles are connected by a light inextensible string that passes over a smooth light fixed pulley as shown in the diagram below:

edexcel-al-maths-mechanics-topic-3-2-h---q7

The particles are released from rest with the string taut and particle A begins to accelerate downwards at a rate of 7 space straight m space straight s to the power of negative 2 end exponent.

Find the value of mB.

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