Forces and Motion
Newton’s First Law
A body will remain at rest, or will continue to move with a constant velocity, unless the external forces
acting on it have a non-zero resultant. i.e. For a body to change its velocity an unbalanced force must
act on the body.
Newton’s Second Law
When a force F newtons acts on an object of mass m kg, the acceleration a ms-2 is given by
F = ma
Example
A car of mass 1200 kg is pushed with a force of 150 N. Calculate the acceleration of the car, and find
how long it will take to reach 1.5 ms-1 from rest.
Example
A curling stone of mass 18kg is launched across ice with a speed of 2 ms-1, and goes a distance of 30
metres before coming to rest. Calculate the deceleration, and find the frictional force between the stone
and the ice.
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Example
A truck of mass 3.2 tonnes is pulled by a horizontal cable. Find the tension in the cable when the truck
is:
a) accelerating at a constant rate of 1.6 ms-2.
b) moving at a constant speed of 58 kmh-1.
Example
A box of mass 3.5 kg is being acted on by a single force
newtons. Find:
a) The vector acceleration of the box
b) The magnitude of the acceleration
CUP Ex 21A 1a 2d 3 5 6 8 9
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Forces acting together
The resultant force or net force = total of all forces
(remember that force is a vector so direction is important and some forces will be negative)
If an object remains at rest or moving at constant velocity then the forces in each direction balance, they
are in equilibrium.
Equilibrium: Resultant force = 0
Acceleration = 0
Velocity is constant
Example
Two forces act on a particle P as shown. Find the direction and magnitude of the resultant force.
Example
Three forces acting together on an object.
and the angle it makes with the horizontal direction.
. Find the magnitude of the resultant force
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Example
Two children are pulling a box of mass 8 kg. One pulls with a force of 26 N and the other pulls with a
force of 18.8 N in the opposite direction.
a) Find the acceleration of the box.
b) A third child joins in pulling with a force F. The acceleration of the box is now 0.75ms-2 in the
direction of the 26 N force. Fin the magnitude of F.
Example
A particle is subject to 3 forces
Given that the particle moves with constant velocity, find F3.
CUP Ex 21B 1c 2c 3c 4c 5b 6cd 8 9
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Types of force
Tension
Driving force
Braking force
Thrust (Compressive force)
Weight
Air resistance
Contact force is a force that acts between an object and the surface it is in contact with. It is considered
in two parts and is the resultant of the two forces.
Normal contact force
Friction
acts to oppose motion and is between an object and a surface.
Smooth surface:
If a surface is said to be smooth then friction is considered
to be zero (it is a good modelling assumption if friction
would be very small).
Rough surface:
If the surface is said to be rough then friction has to
included.
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Example
a) A car moves under the action of a driving force of 1740N. The total resistance to motion equals
600N. Given that the acceleration of the car is 1.2 ms-2, find its mass.
b) The car starts to brake and decelerates at 2.5 ms-2. Assuming that the total resistance force
remains the same, find the magnitude of the braking force.
Example
A box of mass 24 kg moves on a rough horizontal floor under the action of a constant horizontal force
(16i + 11j) N. Find, in vector form, the frictional force acting on the box when its acceleration is (0.7i –
1.1j) ms-2.
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Example
A small toy of mass 250g moves along the floor with an initial speed of 8 ms-1.
a) The contact between the toy and the floor is modelled as smooth, Predict the time it would take
the toy to travel 6m.
b) The toy actually takes 0.82 seconds to travel 6m. Find the magnitude of the frictional force
assuming it is constant.
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Example
A boy is using a light horizontal stick to pull a toy box of mass 3.2 kg across rough carpet. The tension
in the stick is 18 N and the frictional force is 7 N.
a) Find the acceleration of the box, and the time it takes for it to accelerate from rest to 2.1ms-1?
b) Assuming that the frictional force remains the same, what tension is required for the box to
maintain the constant speed of 2.1ms-1?
The boy now makes the box slow down by applying a different constant force through the stick, and the
box comes to rest after travelling 0.8 metres. The frictional force remains the same.
c) Find the magnitude of the force in the stick, and state whether it is tension or thrust.
CUP Ex 21C
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CUP Ex 21E
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Weight
Weight is the force of gravity with which the earth attracts a mass.
Units mass kilograms (kg)
weight in Newtons (N)
From Newton’s second law F = ma
weight = mg
Example
mg
An injured seaman is being winched up to a rescue helicopter. The mass of the seaman is 55 kg.
Find the tension in the cable when the seaman is being raised:
a. At a steady speed of 4 ms-1.
b. With an acceleration of 0.8 ms-1.
Example
A ball falling through the air is subject to a constant resistance force of magnitude 0.3N. The ball starts
from rest and takes 1.6 seconds to fall 12 metres. Find the mass of the ball.
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Example
Machinery of total mass 280 kg is being lowered to the bottom of a mine by means of two ropes
attached to a cage of mass 20 kg.
For the first 3 seconds of the descent the tension in each rope is 870 N.
Then for a further 16 seconds the tension in each rope is 1470 N.
For the final 8 seconds the tension in each rope is 1695 N.
Find the depth of the mine.
CUP Ex 21D
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CUP Ex 21E
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