ZIMSEC A Level Mechanics Paper 4 November 2011

Section b

Section b, Question 12

[3 marks]Resultant of two forces

Two forces have magnitudes

P

and

Q

and the acute angle between them is

\theta

, so their resultant has magnitude

R

where

R^{2}=P^{2}+Q^{2}+2PQ\cos\theta

. Two forces of magnitudes 5 N and 8 N act at an angle of

60^{\circ}

to each other. Find the magnitude of their resultant, in newtons, correct to 3 significant figures.

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Section b, Question 13

[2 marks]Friction on an inclined plane

A body of mass 5.2 kg is held in equilibrium on a rough plane by a force

P

N acting up the line of greatest slope. The plane is inclined at an angle

\theta

to the horizontal where

\cos\theta=\dfrac{4}{5}

. Take

g=9.81

m s

^{-2}

. Find the normal reaction, in newtons, between the body and the plane, correct to 3 significant figures.

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[3 marks]Friction on an inclined plane

A body of mass 5.2 kg is held in equilibrium on a rough plane by a force

P

N acting up the line of greatest slope. The plane is inclined at an angle

\theta

to the horizontal where

\cos\theta=\dfrac{4}{5}

. Take

g=9.81

m s

^{-2}

. When

P

is 19.2 N the body is about to slide down the plane. Find the value of

\mu

, the coefficient of friction between the body and the plane, correct to 2 significant figures.

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Section b, Question 14

[2 marks]Projectiles

A particle is projected vertically upwards from a point A on level ground with initial speed

U

m s

^{-1}

, and

g

is the acceleration due to gravity. Write down, in terms of

U

and

g

, the time taken for the particle to reach its greatest height.

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[2 marks]Projectiles

Two particles are projected at the same instant from points A and B on level ground. The first is projected vertically upwards from A with initial speed

U

m s

^{-1}

, and the second is projected from B towards A with initial speed

V

m s

^{-1}

at an angle

\alpha

to the horizontal. They collide when both are at their greatest height above AB. Which relation must therefore hold?

A $V\sin\alpha=U\cos\alpha$
B $V\sin\alpha=U$
C $V\cos\alpha=U$
D $V=U$

[3 marks]Projectiles

Two particles are projected at the same instant from points A and B on level ground 150 m apart. The first is projected vertically upwards from A with initial speed

U

m s

^{-1}

, and the second is projected from B towards A with initial speed

V

m s

^{-1}

at an angle

\alpha

to the horizontal. They collide when both are at their greatest height, which gives

\tan\alpha=\dfrac{U^{2}}{150g}

. Taking

U=21

m s

^{-1}

and

g=9.81

m s

^{-2}

, find

\alpha

correct to the nearest degree.

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Section b, Question 15

[1 marks]Kinematics

Two vehicles moving in the same direction pass the point O on a straight road at time

t=0

. Vehicle A moves at a constant velocity of 11 m s

^{-1}

. Vehicle B has a constant acceleration of 2 m s

^{-2}

and has a velocity of 3 m s

^{-1}

as it passes O. Find the time, in seconds, at which the two vehicles have the same velocity.

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[3 marks]Kinematics

Two vehicles moving in the same direction pass the point O on a straight road at time

t=0

. Vehicle A moves at a constant velocity of 11 m s

^{-1}

. Vehicle B has a constant acceleration of 2 m s

^{-2}

and has a velocity of 3 m s

^{-1}

as it passes O. Find the distance, in metres, of B from O when its speed is 21 m s

^{-1}

Answer this when you sit the paper.

[3 marks]Kinematics

Two vehicles moving in the same direction pass the point O on a straight road at time

t=0

. Vehicle A moves at a constant velocity of 11 m s

^{-1}

. Vehicle B has a constant acceleration of 2 m s

^{-2}

and has a velocity of 3 m s

^{-1}

as it passes O. Find the time, in seconds, at which B overtakes A.

Answer this when you sit the paper.

[2 marks]Kinematics

Two vehicles moving in the same direction pass the point O on a straight road at time

t=0

. Vehicle A moves at a constant velocity of 11 m s

^{-1}

. Vehicle B has a constant acceleration of 2 m s

^{-2}

and has a velocity of 3 m s

^{-1}

as it passes O. B overtakes A after 8 s. Find the distance, in metres, from O travelled by A before it was overtaken by B.

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Mechanics Paper 4 November 2011

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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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