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FORCES
Force: A force is a push, pull or twist.
Effects of forces
 Can change the shape and size of an object.
 Can change the state of motion of an object/body.
EFFECTS OF FORCE ON SHAPE AND SIZE.
Hooke’s Law
The force applied on an elastic material is directly proportional to the extension it causes
provided the elastic limit or limit of proportionality is not exceeded.
F = ke
Where e = extension
where F = applied force
where k = force or spring constant
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The force constant is the amount of force that is required to cause a unit extension in an
elastic material. Each elastic material has its own spring constant.
If the elastic limit of the material is exceeded the object gets a permanent extension or
breaks/snaps/gets damaged.
The extension vs load graph for a material that obeys Hooke’s Law is always a diagonal
line.
The elastic limit of the spring will be the point where the spring stops being a straight
line.
The spring used in graph above has an elastic limit of ______ N and has gained a
permanent extension of ______cm.
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Classwork
1.
A spring of natural length 5 cm is extended by 1 cm when a load of 2N is suspended on
it.
Calculate
(a)
force constant of the spring
(b)
force if extension is 3cm
(c)
total length of spring if force is 6N.
2.
The diagram below shows the same spring with different loads suspended on it.
Calculate
(a)
force X
(b)
length Y
(c)
original length of spring.
3.
The diagram below shows the same spring with different masses suspended on it
(a)
(b)
(c)
What is the extension on the spring when the mass is increased from 50g to 100g?
Determine the spring constant in N/cm
What is the original length of the spring?
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Series and Parallel Spring Combinations
A 3 cm long spring extends by 1 cm when a 2N force is suspended on it as shown below.
Series Combinations
In a series combination each of the springs individually obeys Hooke’s law. i.e each spring
extends as if the force was placed only on it.
The total extension is the sum of the individual spring extensions. The spring shown above is
connected in series with another identical spring as shown below.
Each spring extends individually, and the total extension = 1 cm + 1 cm = 2 cm.
Parallel Combinations
If springs are arranged in parallel then they share the extension that would have caused on one
spring. Thus the total extension of a parallel combination is the “extension on one spring”
divided by the number of springs in the parallel combination.
The spring show above is connected in parallel with another identical spring as shown below
The extension e on each spring in the combination is 1 cm [ the extension on one spring] divided
by 2[the number of springs in the combination] = 1 cm / 2 = 0.5 cm.
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EFFECTS OF FORCE ON MOTION
A force can cause changes in the state of motion of a body. In other words a force can cause
acceleration and deceleration.
Newton’s Laws of Motion
Newton’s 1st Law of Motion
A body at rest or already moving with a steady velocity, stays in that state of motion unless an
unbalanced force acts on it.
Newton’s 2nd Law of Motion
For a body to accelerate there must be an unbalanced force acting on it. This unbalanced force is
called the resultant force R.
The resultant force on a body is directly proportional to the acceleration it causes such that
R = ma
Where R = resultant force.
m = mass
a = acceleration.
If there is only one force F acting on an object, then
F=R
and as such
F = ma
Where F = applied force
ma = resultant force.
If an opposing force f is acting on a body at the same time as force F, then R =F- f
so that F = R + f
and as such
F = ma + f
Where F = applied force
f = opposing force
ma = resultant force.
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Centripetal Force
A body that moves in a circular path is found to be accelerating at all times. This is because even
if the size of the velocity is NOT changing, the direction of the velocity is changing. [The
direction of the velocity is always tangential to the circular motion].
The force that causes objects in circular motion to accelerate is called the centripetal force. This
force acts towards the centre of the circular motion. [The direction of the acceleration is also
towards the centre of the circular motion and it is called centripetal acceleration}.
The magnitude[size] of the centripetal force depends on;
 Radius, r, of the circular motion.
 Velocity, v, of the rotating body.
 Mass, m, of the body.
Classwork
1.
A car of mass 2 500kg is pushed forward by a force of 1500N. If the road has a friction of
300N, calculate the acceleration of the car.
2.
A 5 kg trolley has an acceleration of 2 m/s2. What is the resultant force on the trolley?
3.
The diagram below shows four forces acting on a 12kg box.
(a)
(b)
(c)
Find the resultant force on the box.
In which direction does the box move?
Determine the acceleration of the box.
4.
A 900 kg car travelling at 25 m/s comes to a halt in 5 seconds. Calculate
(a)
acceleration of the car
(b)
average braking force of the car.
5.
A 2 ton truck starts from rest and reaches 20 m/s in 5 seconds. If it experiences air
friction of 20N, calculate
(a)
acceleration of the truck
(b)
applied force.
6.
A 10 000 kg truck moving at 25 m/s comes to a stop in 12.5 seconds. If there is an
opposing force of 200N, calculate
(a)
acceleration of the truck
(b)
average braking force.
(c)
braking distance
Newton’s 3rd Law of Motion
If body A exerts a force on body B, then body B exerts an equal but opposite force on body A.
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MOMENT OF FORCE (turning effects of a force).
A moment of force is its turning effect about a point called the pivot (fulcrum).
Moment of force is the product of the force and its perpendicular distance from pivot.
Moment = force x distance
M = Fd
Where F= applied force
d = perpendicular distance from pivot.
Moment of force is measured in Newton-metres (Nm).
Example
Find the moment of the 150 N force about the pivot.
Moment of force
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=
=
=
Fxd
150 N x 20 cm
3 000 N
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Principle of moments
For a system to be in equilibrium, the sum of the clockwise moments should be equal to the sum
of the anticlockwise moments.
F1d1 + F2d2 = F3d3 + F4d4
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Classwork
1.
The system below is in equilibrium.
Calculate force F.
2.
The diagram below shows a balanced metre rule which has been pivoted at the 40cm
mark. Weights are attached at the 10 cm, 25cm, 65cm and 85cm marks on the rule.
Ignoring the weight of the ruler calculate the weight W that is attached at the 65 cm mark
3.
The diagram below shows a man playing with his children on a see-saw. The distance of
the children and their father from the pivot is indicated.
If the see saw is in equilibrium, calculate the mass m of the child closer to the pivot.
4.
The diagram shows a uniform metre rule pivoted at the 20cm mark. The rule is balanced
horizontally by a mass of 100g suspended at the 5cm mark.
Calculate the mas of the rule.
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Parallel Forces
When several parallel force act on a body such that it is in equilibrium, then the following
conditions prevail:
 Upward forces should be equal to downward forces
 The principle of moments should be obeyed.
Classwork
5.
The diagram below shows a plank resting on two trestles M and N.
6.
If the mass of the plank is 1kg, calculate the upward forces P and Q.
Mr Bean is standing on a uniform plank of weight 200N. The plank is supported by two
ropes A and B. He has a mass of 80kg and is carrying a load of mass 60kg.
(a)
(b)
Which rope has more tension? Explain your answer.
Calculate the tensions in ropes A and B.
Couples
Couples are a pair of forces which are equal in magnitude but opposite in direction. Couples
cause rotation and they can NOT be replaced with a single.
Example
The diagram below shows two forces acting on a steering wheel.
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The steering wheel has a diameter of 42cm. Two 30N forces act in opposite as shown.
Moment of force
= 30N x 21cm + 30N x 21cm
= 630Ncm + 630Ncm
= 1260Ncm
NB: Multiplying one of the two forces by the diameter should give
30N x 42cm = 1260Ncm
Thus;
Moment of a couple = One of the forces multiplied by the perpendicular distance between
them.
Scalars and Vectors
Scalars:
Vectors:
A scalar is a physical quantity which is fully described by its magnitude only.
Examples include, mass, temperature, energy, speed, distance.
A vector is a physical quantity which is fully described by its magnitude and
direction. Example include, forces, velocity, acceleration, displacement.
Adding Vectors
Addition of vectors is done in several ways. This include
(i)
Use of parallelogram laws
If two vectors acting at a point are represented in size and direction by the sides of a
parallelogram drawn from the point, their resultant is represented in size and direction by
the diagonal of the parallelogram drawn from the point.
(ii)
Use of trigonometry rules
The following rules of trigonometry can be used to add vectors.
(iii)
1.
a
b
c


sin A sin B sin C
2.
a2 = b2 + c2 – 2bc Cos A
Use of Pythagoras rule
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a2 = b2 + c2
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