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Practice Paper for Edexcel GCE

Mechanics M2

Advanced/Advanced Subsidiary

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1. A ball of mass 0.2 kg is moving with velocity 13j m s1when it is hit by a bat. The

impulse received by the ball is (2.4i + 3.6j) N s. The ball is modeled as a particle.

(a) Find the velocity of the ball immediately after being hit.

(3)

(b)

Hence show that the impact does not change the speed of the ball.

(3)

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___________________________________________________________________________ Q1

(Total 6 marks)

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2. [The centre of mass of a semi-circular lamina of radius r is3

4rfrom the centre.]

8 cm

10 cm

D C

BA

O

Figure 1Figure 1 shows a lamina that is made by removing a semicircle of centre Ofrom a

uniform rectangular piece of plywoodABCD, whereAB= 8 cm andBC= 10 cm.

(a)

Write down the distance of the centre of mass of the lamina fromAD.

(1)(b) Calculate, to 3 significant figures, the distance of the centre of mass of the lamina

fromAB.

(6)

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___________________________________________________________________________ Q2

(Total 7 marks)

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3.

Figure 2Figure 2 shows three uniform rods, made from the same material, welded to form a rigid

triangular frameworkABC. Each of the joints atA, B and Chas mass m. RodAChaslength 8land mass 4m. RodBChas length 6land mass 3m. AngleACBis a right angle.

(a) (i) Express the length of rodABin terms of l.

(1)

(ii) Express the mass of rodABin terms of m.

(1)

(b)

Find the distance of the centre of mass of the framework fromAC.

(4)

The horizontal distance between the centre of mass of the framework andBCis l15

44.

The framework is freely suspended fromBand hangs in equilibrium.

(c)

Find the angle whichBCmakes with the vertical.

(3)

C (m)(m)

B(m)

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___________________________________________________________________________ Q3

(Total 9 marks)

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4. A particle Pof mass 5 kg is acted on by a constant force F. At time tseconds the position

of the particle, r metres, is given by the equation

r= (3t2 kt+ 2) i+ (kt

2+ 4t k)j

where kis a positive constant.

(a)

Find the velocity of Pin terms of k.

(2)

(b) Hence find the acceleration of Pin terms of k.

(1)

(c)

Given that the magnitude of Fis 50N, calculate the value of k.

(4)

The particle is moving in a direction parallel tojwhen t= T.

(d) Find the value of T.

(2)

(e)

Hence find, to the nearest 0.1, the angle that the position vector makes with thedirection of iwhen t= T.

(4)

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___________________________________________________________________________ Q4

(Total 13 marks)

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5. A car of mass 850 kg is travelling along a road that is straight but not level.

On a horizontal section of the road, the car develops a constant power of 25 kW and there

is a constant resistance of 800 N to its motion.

(a)

Calculate the maximum possible steady speed of the car.

(3)(b) Find the driving force and acceleration of the car when its speed is 10 ms

1.

(4)

When the car is travelling at 20 ms1up a constant slope inclined at an angle to the

horizontal, where20

1sin , the engine stops. Subsequently, the resistance to the

motion of the car remains constant at 800 N.

(c) Using the work-energy principal, calculate the speed of the car when it has travelled

a further 105 m up the slope.

(6)

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(Total 13 marks)

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6. A particle Aof mass m, moving with speed uon a smooth horizontal surface, collides

directly with a stationary particle Bof mass 4m. The coefficient of restitution between A

and Bis e. The direction of motion of Ais reversed by the collision.

(a)

(i)

Find, in terms of eand u, the speed of Bimmediately after the collision.

(ii) Show that the speed of Aimmediately after the collision is )14(5

eu .

(7)

Subsequently, Bhits a smooth wall at right angles to the direction of motion of Aand B.

The coefficient of restitution between Band the wall is4

3. After Brebounds from the

wall, there is another collision between Aand B.

(b) Show that the speed of Bimmediately after hitting the wall is )1(20

3e

u .

(2)

(c) Show that13

7

4

1 e .

(5)

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___________________________________________________________________________ Q6

(Total 14 marks)

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7.

A ballP is kicked from a pointA, which is 9 m vertically above a point Oon the ground,

with a speed of 40 ms-1

which is modelled as a particle moving freely under gravity, hits the ground atB.

(a)

Calculate the maximum vertical height ballP can reach aboveA.

(3)(b)

(i)

Show that, t seconds after being kicked, the vertical height of ballP aboveAis

2

220 t

gt metres.

(2)

(ii)

Hence calculate the time ballP will take to reachB.

(2)

(c)

State an additional physical factor which may be taken into account in a refinement

of the above model to make it more realistic.

(1)Subsequently, another ball Q is kicked from the same point, speed and angle of elevation

as that of ballP, and moves freely under gravity. Its vertical height aboveAis

2)2(

2)2(20 t

gt metres t seconds after ballPis kicked.

(d)

How many seconds after kicking ballP is ball Qkicked?

(1)

(e)

Hence calculate how far ballPis horizontally fromA when ball Qis kicked.

(2)

The vertical height of both balls aboveAis the same 49

2

3 seconds after ballPis kicked.

(f)

State, giving a reason, whether the balls will collide or not.

(2)

at an angle of elevation of 30 above the horizontal. The ball,

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Question 7 continued

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Question 7 continued

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TOTAL FOR PAPER: 75 MARKS

END

Q7

(Total 13 marks)

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