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

Practice Paper Questions

1a
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3 marks

AB is a non-uniform rod of length 1 m and weight 30 N. AB rests horizontally on supports placed at points C and D, withspace A C space equals space 0.35 space straight m space and space space D B space equals space 0.25 space straight m space  as shown in the diagram below:

4-1-m-qu4



Given that the centre of mass of AB is 0.45 m from point A, calculate the reaction force at each of the support points.

1b
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3 marks

Given that the reaction force at C is 9 N, find:

(i)
the location of the centre of mass of AB

(ii)
the reaction force at D.

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2a
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4 marks

Two particles, A and B, with masses 7 m and 4 m respectively are moving towards each other in opposite directions along the same straight line on a smooth horizontal plane when they collide directly. Immediately before the collision, the speed of Ais 3 uand the speed of B is 5 u. Immediately after the collision, the speed of Ais v subscript A and the speed of B is v subscript B.

The direction of motion of Ais reversed after the collision.

Show that v subscript B space end subscript greater than u over 4.

2b
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1 mark

State whether the direction of motion of B is reversed after the collision.

2c
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3 marks

Given that v subscript B is double v subscript A, find the values of v subscript A and v subscript B.

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3a
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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 straight m 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.

3b
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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.

3c
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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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4
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5 marks

Jenna takes her two dogs Gamma and Omega for a walk in the park. Both dogs slip their leads and run off in different directions. When they stop, Gamma’s displacement from Jenna is open parentheses 226 bold i minus 105 bold j close parentheses space straight m, Omega’s displacement from Jenna is open parentheses negative 65 bold i minus 243 bold j close parentheses space straight m.To collect the dogs Jenna walks at a constant speed directly to one dog then the other.

Jenna must decide which order to collect the dogs so that they are both retrieved as quickly as possible.

(i)
Use vector methods to show which order Jenna should collect her dogs in and the total distance, to the nearest meter, that she must walk.

(ii)
Calculate the direction of Jenna’s final displacement from her starting point. Giving your answer as a bearing.

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5
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6 marks

A particle of mass 0.9 kg is at rest on a rough horizontal plane.  A force of magnitude P N is acting on the particle at an angle of 40° to the horizontal.

mech-3-3-h-q6

Given that the coefficient of friction between the plane and the particle is 0.3, and that the particle is on the point of moving to the right under the influence of the force, find the value of P.

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6a
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3 marks

A particle of mass 12 kg is being pushed up a smooth slope by a force of 50 N that acts horizontally. The slope is inclined at 20 degree to the horizontal, as shown in the diagram below:

mech-3-3-h-q4

Calculate the acceleration of the particle up the slope.

6b
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3 marks

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

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7a
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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?
7b
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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
7c
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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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8
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8 marks

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9a
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4 marks

9b
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3 marks

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10a
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2 marks

10b
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6 marks

10c
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2 marks

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