Practice Paper 4 (Mechanics) (CIE AS Maths: Pure 1)

Practice Paper Questions

1a
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3 marks

Two objects A and B have masses 0.6 kg and 1.4 kg respectively. They are moving towards each other in opposite directions in a straight line on a smooth horizontal plane. The objects collide directly and coalesce to form an object C. Immediately before the collision, A is moving with speed 8 m s-1 and B is moving with speed 6 m s-1.

By modelling the objects as particles, find the speed and direction of motion of C after the collision.

1b
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1 mark

At the instance that object C is moving with speed u space m space s to the power of negative 1 end exponent, the magnitude of its momentum is 13 N s.

Find the value of u.

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2a
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5 marks

A bus of mass 2400 kg moves forwards on a straight horizontal road, and it travels with its maximum speed of 30 m s-1.  There is a constant resistive force of 2000 N acting on the bus.  

Find the maximum power that the engine of the bus can produce.

2b
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3 marks

Find the maximum acceleration of the bus at the instant when it is travelling at a speed of 10 m s-1.

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3a
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3 marks

The following force diagram shows three forces acting on a particle:

FRVC2wU4_3-3-q-2-e-a-level-maths-mechanics

Show that the resultant force on the particle in the horizontal direction is zero.

3b
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3 marks

Given that the particle is in equilibrium, find the exact value of F.

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4a
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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.

4b
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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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5a
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3 marks

A child has connected two toy wagons together with a light horizontal rod and is pushing them along a horizontal level track.  Each wagon has a mass of 11.2 space kg, and the resistance to motion of each wagon is modelled as a constant force of P N.

The child pushes on the rearmost wagon with a constant horizontal force of space 16.6 space straight N spaceand the wagons experience a forward acceleration of 0.25 space straight m space straight s to the power of negative 1 end exponent.

Find:

the value of the constant P

5b
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2 marks

the thrust in the connecting rod.

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6a
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2 marks

A box of mass 4 kg slides down the line of greatest slope on a ramp inclined at alpha degree to the horizontal with constant acceleration 2 m s-2.  Two markers on the ramp are set 7 metres apart and the box slides past the second marker exactly 2 seconds after sliding past the first.  


Show that the box passes the first marker with speed 1.5 m s-1 and find the speed of the box as it passes the second marker.

6b
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5 marks

The work done against friction on the box as it slides between the two markers is 84 J.  Find, 

i)
the magnitude of the frictional force,

ii)
the value of the angle, alpha,

iii)
the work done against gravity during this period of time.  

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7a
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7 marks

A particle of mass m kg is projected up a rough plane which is inclined at an angle of theta degree to the horizontal.  It is projected up the line of greatest slope with an initial velocity of begin mathsize 20px style u end style metres per second, and it comes to instantaneous rest in t subscript 1 seconds after moving a distance of begin mathsize 20px style s end style metres up the slope. The coefficient of friction between the particle and the slope is mu.

Show that:

(i)
t subscript 1 space equals space fraction numerator u over denominator g space open parentheses sin space theta space plus space mu space cos space theta close parentheses end fraction
(ii)
s space equals space fraction numerator u squared over denominator 2 space g space open parentheses sin space theta space plus space mu space cos space theta close parentheses end fraction
7b
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4 marks

After coming to instantaneous rest, the particle begins to slide back down the slope, and after t2 seconds it has returned to its starting point.

Find an expression for t2 in terms of u space comma space g space comma space mu space and space theta.

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