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

Practice Paper Questions

1
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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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2a
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5 marks

Two stones are slid across a large icy pond. The first stone is released from rest at the origin with constant acceleration left parenthesis 2 bold i space plus space 3 bold j right parenthesis space straight m space straight s to the power of negative 2 end exponent. The second stone is released from rest from the position with coordinates left parenthesis 50 comma space minus 100 right parenthesis with constant acceleration  left parenthesis bold i space plus space 5 bold j right parenthesis space straight m space straight s to the power of negative 2 end exponent.

 

(i)
Find the position vectors of both stones after 5 seconds.

(ii)
Find the distance between the two stones after 5 seconds.
2b
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2 marks

Show that the two stones collide after 10 seconds.

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3a
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4 marks

A stone is thrown from the edge of a deep cave such that it will fall into the cave and has velocity

bold v equals left parenthesis left parenthesis 0.4 t right parenthesis bold i plus left parenthesis 2 minus 0.3 t squared right parenthesis bold j right parenthesis space straight m space straight s to the power of negative 1 end exponent

at time t seconds after it is thrown. 

Find the position of the stone at the time it is about to fall into the cave (rather than being in the air above the cave).

3b
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3 marks

Find the maximum height above the cave the stone reaches.

3c
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2 marks

The deepest known cave in the world has a depth of 2212 m. (The Veryovkina Cave in Georgia.) The model above suggests the stone would take around 28 space seconds to reach this depth. Consider the average speed and the acceleration of the stone to highlight a problem with this model.

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4
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8 marks

In the following diagram A B is a ladder of length 10 m and mass 34 kg.  End A of the ladder is resting against a smooth vertical wall, while end B rests on rough horizontal ground so that the ladder makes an angle of 60 degree with the ground as shown below:

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A housepainter with a mass of 75 kg has decided to climb up the ladder without taking any additional precautions to prevent the bottom of the ladder from slipping.  The ladder may be modelled as a uniform rod lying in a vertical plane perpendicular to the wall, and the housepainter may be modelled as a particle.  The coefficient of friction between the ground and the ladder is 0.4.

Luckily, the housepainter’s partner convinces him not to climb up the ladder without providing some additional support at the bottom to prevent slipping.  If the housepainter had continued with his original plan, however, how far above the ground would he have been when the ladder began to slip?

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5a
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3 marks

A golfer strikes a ball from ground level with velocity left parenthesis 20 bold i bold space plus space 28 bold j right parenthesis space straight m space straight s to the power of negative 1 end exponent.

Find the distance the golf ball will travel before first hitting the ground.

5b
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4 marks

Show that by reducing the angle of the strike above the horizontal by 10 space degrees the golfer can achieve approximately 7 m more distance before the ball lands.

5c
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1 mark

Give a reason why the golfer may not want to achieve a longer distance with their shot.

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6a
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2 marks

To crash test cars, a computer‑controlled car is accelerated along a horizontal track and crashed into a wall. The maximum length of track available is 1.1 km long.

During a crash test, 20 space km of track is required to increase a car’s speed from rest to 5 space straight m space straight s to the power of negative 1 end exponent. From this point onwards a car is accelerated at a constant rate. This is set to space 2.1 space straight m space straight s to the power of negative 2 end exponent but can be varied up or down by 30% prior to a test being carried out.

 

Find the acceleration of a car during the first 20 m of a crash test.

6b
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3 marks

Determine if it is possible to crash test a car at a speed of 250 space km space straight h to the power of negative 1 end exponent.

6c
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5 marks

A crash test is unreliable if it takes under 10 seconds.
Find the lowest speed, in kilometres per hour, a car can be reliably crash tested at.

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7
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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, space 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-m---q7

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

(ii)
By how much did the speed of the ball reduce when it hit the cushion?

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