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5 Forces
Stretching questions
Introduction
When analysing force questions it is important to be able to identify the body under consideration
and be able to draw all the forces acting on it.
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First isolate the body to be analysed.
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Draw all the forces acting on it.
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Identify a sensible direction (this may be horizontal or vertical, or parallel to a plane).
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Resolve all the forces in that direction and perpendicular to it.
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Sum the forces in each direction.
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Find the resultant force on the body.
The following questions involve sliding blocks, ropes, pulleys and inclined planes.
Questions
1 A thirty kilogram monkey hangs on a light
rope which goes over a frictionless light
pulley to a 30 kg bunch of bananas higher
up. The monkey decides to climb the rope
to reach them.
a) As it climbs, do the bananas go up,
down, or remain at rest?
b) As it climbs, does the distance between
it and the bananas increase, decrease,
or remain the same?
c) If the monkey lets go of the rope, what happens now to the distance to the bananas?
d) Before reaching the ground the monkey grabs the rope to stop. What happens to the
bananas?
© Hodder & Stoughton Limited 2015
5 Forces
Stretching questions
2 Two blocks of mass 8 kg and 6 kg are connected by a heavy uniform rope of
mass 3 kg. An upward force is applied to the upper 8 kg block as shown.
a) What is the acceleration of the system?
b) What is the tension at the top of the rope?
c) What is the tension at the mid-point of the rope?
3 Two blocks of mass 4 kg and 8 kg are connected by a string and slide down
an inclined plane at 30˚ to the horizontal (shown below). The coefficient of
sliding friction is 0.25 between the 4 kg block and the plane and 0.50
between the 8 kg block and the plane.
a) Calculate the acceleration of each block.
b) Calculate the tension in the string.
4 Two blocks are connected by a light cord which passes over a light smooth pulley at rest at the
top of two smooth inclined planes (shown below).
a) Which way will the system move?
b) What is the acceleration of the blocks?
c) What is the tension in the cord?
© Hodder & Stoughton Limited 2015
5 Forces
Stretching questions
The topic of terminal velocity is in a later chapter but the following questions can be solved using
your knowledge of Newton’s Second Law. When objects fall through a medium they experience a
retarding force, drag in a gas or a viscous force in a liquid. This force normally depends on the speed
through the medium and in a gas usually varies as the square of the speed. The resistive force grows
until it equals the weight of the object at which point the object will continue with constant velocity,
its terminal velocity.
A body falls from rest through a medium that exerts a resistive force R that varies directly as the
square of the speed v so that R  kv2 .
5 Draw a diagram showing the direction of motion and indicate all the forces acting on the body.
6 Use Newton’s Second Law and construct an equation which describes the motion. Describe the
motion in words.
7 Show that the body acquires a terminal velocity and calculate it.
8 Sketch a graph of acceleration, a, against v.
© Hodder & Stoughton Limited 2015