ZIMSEC A Level Mechanics Paper 4 November 2010

Section b

Section b, Question 12

[2 marks]Projectiles

A stone is projected from a point A on level ground with a speed of 20 ms

^{-1}

at an angle of 30° to the horizontal, towards a pole standing 30 m away. Find the time, in seconds, at which the stone is level with the pole. Give your answer correct to 3 significant figures.

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[3 marks]Projectiles

A stone is projected from a point A on level ground with a speed of 20 ms

^{-1}

at an angle of 30° to the horizontal, towards a bird standing on a pole 2,5 m above the level ground and 30 m from A. Taking

g=9,81

^{-2}

and assuming the path is not impeded, find how far vertically above the bird the stone passes. Give your answer in metres.

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Section b, Question 13

[3 marks]Friction on an inclined plane

A block of weight 20 N rests on a rough plane inclined at an angle

\beta

to the horizontal, where

\sin\beta=\dfrac{4}{5}

, and is on the point of slipping down the plane. A horizontal force of P N acts on it, and the coefficient of friction between block and plane is

\dfrac{1}{4}

. Find the value of P, in newtons, needed to prevent the block from slipping.

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[2 marks]Friction on an inclined plane

A block rests on a rough inclined plane and is on the point of slipping downwards while a horizontal force pushes it towards the slope. In which direction does the frictional force on the block act, and what is its size?

AUp the plane, but smaller than $\mu R$ .
BUp the plane, at its limiting value $\mu R$ .
CHorizontally, opposing the applied force, at its limiting value $\mu R$ .
DDown the plane, at its limiting value $\mu R$ .

[1 marks]Friction on an inclined plane

A plane is inclined at an angle

\beta

to the horizontal, where

\sin\beta=\dfrac{4}{5}

. Find the value of

\cos\beta

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Section b, Question 14

[1 marks]Kinematics

A particle starts from rest and moves in a straight line with acceleration

a=3

^{-2}

for

0\le t\le2

and

a=-3

^{-2}

for

2<t\le8

, where

t

is in seconds. Write down the velocity of the particle, in ms

^{-1}

, when

t=2

Answer this when you sit the paper.

[1 marks]Kinematics

A particle starts from rest and moves in a straight line with acceleration

a=3

^{-2}

for

0\le t\le2

and

a=-3

^{-2}

for

2<t\le8

, where

t

is in seconds. Write down the velocity of the particle, in ms

^{-1}

, when

t=8

Answer this when you sit the paper.

[1 marks]Kinematics

A particle starts from rest and moves in a straight line with acceleration

a=3

^{-2}

for

0\le t\le2

and

a=-3

^{-2}

for

2<t\le8

, where

t

is in seconds. At what time, in seconds, is the particle momentarily at rest again?

Answer this when you sit the paper.

[3 marks]Kinematics

A particle starts from rest and moves in a straight line with acceleration

a=3

^{-2}

for

0\le t\le2

and

a=-3

^{-2}

for

2<t\le8

, where

t

is in seconds. Find the total distance, in metres, travelled by the particle in the interval

0\le t\le8

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Section b, Question 15

[2 marks]Connected particles

Masses of 2 kg and 5 kg are connected by a light inextensible string hanging vertically on either side of a smooth pulley, and the system is released from rest. Find the acceleration of the particles in terms of

g

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[1 marks]Connected particles

Masses of 2 kg and 5 kg hang on either side of a smooth pulley on a light inextensible string and are released from rest, so that the system accelerates at

\dfrac{3g}{7}

. Taking

g=9,81

^{-2}

, find the tension in the string, in newtons, correct to 3 significant figures.

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[2 marks]Connected particles

Masses of 2 kg and 5 kg are connected by a light inextensible string over a smooth pulley and released from rest, both 2,5 m above the ground. Taking

g=9,81

^{-2}

, find the velocity, in ms

^{-1}

, of the 5 kg mass as it hits the ground. Give your answer correct to 3 significant figures.

Answer this when you sit the paper.

[2 marks]Connected particles

Masses of 2 kg and 5 kg are connected by a light inextensible string over a smooth pulley and released from rest, both 2,5 m above the ground. The 5 kg mass hits the ground at 4,58 ms

^{-1}

and does not rebound. Taking

g=9,81

^{-2}

, find the greatest height above the ground, in metres, reached by the 2 kg mass, assuming it does not hit the pulley.

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Mechanics Paper 4 November 2010

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The questions

Section b

Section b, Question 12

Section b, Question 13

Section b, Question 14

Section b, Question 15

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The answers, and why they are the answers

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