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

Practice Paper Questions

1a
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3 marks

A skateboarder moves off from rest from the top of a ramp and passes through the point P with a speed of 2 m s-1.  The point Q is 4 m vertically below P.

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Assuming that there is no resistance to motion, find the speed with which the skateboarder passes through Q.

1b
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3 marks

Assuming instead that there is a constant resistance to motion, and that the work done against this resistance is 333 J, find the speed with which the skateboarder passes through Q if the skateboarder and equipment can be modelled as a particle of mass   60 kg.

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2a
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3 marks

A car of mass 850 kg is moving up a straight road, inclined at an angle theta to the horizontal, along the line of greatest slope, where sin space theta space equals 1 over 50.  The engine of the car is working at a constant rate of 12.1 kW and the car is moving with a constant speed of v m s-1.  The resistance to motion on the car from non-gravitational forces is R space straight N and acts parallel to the slope.

Justifying your answer, show that

R equals 12100 over v minus 17 g.

2b
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2 marks

The car later moves down the same hill along the line of greatest slope. It travels at the same speed as it did when it travelled up the hill.  The resistance to motion on the car from non-gravitational forces has increased to open parentheses R plus 300 close parentheses space straight N and the engine is now working at a constant rate of P kW.

Show that 

R equals space fraction numerator 1000 P over denominator v end fraction plus 17 g minus 300.

2c
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5 marks

Given that  P =11.4, find the values of v and R.

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3a
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4 marks

The acceleration, a space straight m space straight s to the power of negative 2 end exponent, of a particle moving in a straight line at time straight t space seconds is given by a equals 4 t minus 7 for  0 less or equal than t less or equal than 6. Initially the velocity of the particle is 3 space straight m space straight s to the power of negative 1 end exponent.

Find the time(s) when the particle is instantaneously at rest.

3b
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5 marks

Find the exact total distance travelled by the particle in the first 6 seconds of motion.

Show your method clearly.

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4a
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4 marks

Kelsie is playing squash. The squash ball, of mass 0.025 kg, is moving with velocity open parentheses negative 2 bold i plus 3 bold j close parentheses m s-1  when Kelsie strikes it with her squash racket.  Immediately after being struck, the ball has velocity space open parentheses 23 bold i plus 15 bold j close parentheses spacem s-1.

Find the magnitude of the impulse exerted by the racket on the ball.

4b
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2 marks

Find the angle between the vector bold i bold spaceand the impulse exerted by the racket.  Give your answer to 1 decimal place.

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5a
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3 marks

A non-uniform rod A B, of mass m kg and length 1.5 m, is resting against a rough wall at the point A and is held in limiting equilibrium by a light inextensible string attached to it at the point B.  The other end of the string is attached to the wall at the point C vertically above A such that A C equals 2 space straight m.4

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Given that the tension in the string is 17 N, find the distance from A of the centre of mass of the rod, in terms of the mass, m.

5b
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5 marks

Given that the coefficient of friction between the wall and the rod at the point A is 0.3, find the mass of the rod and the distance from A of the centre of mass of the rod.

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6a
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5 marks

Two smooth spheres S space and space T with the same radii have masses 4 m and 7 m respectively. The spheres are moving in opposite directions along a straight line on a smooth horizontal table when they collide directly. Immediately before the collision, the speed of S is 5 u and the speed of T is 2 u. The collision causes the directions of motion to be reversed for both S and T. The coefficient of restitution between S space and space T is e.

By modelling the spheres as particles, show that the speed of T immediately after the collision is 2 over 11 open parentheses 3 plus 14 e close parentheses u.

6b
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4 marks

Find the range of possible values of e.

6c
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2 marks

Given that the speed of T immediately after the collision is 34 over 11 u, explain why there is no change in the total kinetic energy before and after the collision.

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7a
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6 marks

A rectangular lamina, with vertices A B C D, is made from a uniform material of length 16 cm and width 4 cm as shown in Figure 1 below. A fold is created by taking vertex D to the opposite side of the rectangle such that the side C D is coincident with the side B C, creating a fifth vertex E as shown in Figure 2 below.

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Figure 1

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Figure 2

Find the position of the centre of mass of the folded lamina in Figure 2, giving your answer as distances from the sides A B and A E.

7b
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4 marks

The folded lamina in Figure 2 is allowed to freely pivot around the point that is 1 cm vertically above point E. When in equilibrium find the angle between the downward vertical and the side B C.

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8a
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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.

8b
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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.

8c
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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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9a
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4 marks

A particle’s velocity is modelled by the equation

bold r with bold dot on top bold space equals space open parentheses open parentheses t to the power of 1 half end exponent minus t close parentheses bold i space plus space open parentheses 4 left parenthesis t plus 1 right parenthesis to the power of negative 1 end exponent plus 5 t to the power of 3 over 2 end exponent close parentheses bold j close parentheses straight m space straight s to the power of negative 1 space end exponent space space space space space space space space space space space space space space space t greater or equal than 0 space space space space space space

where t is the time in seconds.

The particle’s initial position is (3 , 5), find the position vector of the particle, bold r m, at time t seconds.

9b
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3 marks

Find the time at which the particle’s acceleration, bold r with.. on top bold space straight m space straight s to the power of negative 2 end exponent is zero in the horizontal left parenthesis bold i right parenthesis direction.

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