NEWTON'S LAWS OF
MOTION
CKMB
FORCE
A Force is a push or a pull on an object. Force is a vector quantity because the applied force has
direction.The SI unit of force is the newton (N). 1N= 1Kg m/s2.
Forces can be categorised as contact and field forces.
Contact forces are forces that are as a result of physical contact between two objects. E.g a pull
on a string, a force used to kick the ball
Field forces are do not involve any physical contact. E.g weight, electric force,gravitational
force
FORCE TYPES
The common force we encounter are;
1. Tension; Tension is the pull on objects through cables, springs, bars etc.
2. Friction; is the force which causes resistance to motion or opposes motion
between surfaces that are in contact.
3. Viscosity; viscosity is the fluids resistance to flow or resistance to objects
passing through it.
4. Attractive or repulsive forces include gravity, magnetic and electrical forces
5. Compression; Forces involve interaction of rigid objects which support weight
e.g Fluid pressure in brake systems or in the collision of objects.
EFFECTS OF FORCES
Force is an action that can change motion.
• A force has the ability to change an object’s motion.
• Forces can cause acceleration.
• Force can cause deceleration.
• Force can change the direction of an object.
• Force can deform an object and change its shape.
• Force can cause an object to start moving .
• Force can cause a moving object to stop.
• Forces can hold a body in a stable position or equilibrium
NEWTON’S FIRST LAW OF MOTION
A body continues in its state of the rest or of uniform motion in a straight line
unless it is compelled by an external force that changes its state. Newton’s law
is also known as the law of ‘inertia’
INERTIA AND MASS
▪ Inertia is athe tendency of an object to resist a change in its state of motion.
▪ Newton's first law of motion is also called the law of inertia
▪ The concept of inertia is about the ability of objects to resist forces tending to
change the state of motion.
▪ Mass is used to quantify inertia. The more the mass an object has, the more is its
inertia.
▪ An object with a lot of inertia takes a lot of force to start or stop; an object with a
small amount of inertia requires a small amount of force to start or stop.
NEWTON’S SECOND LAW
Newton’s second law states that;
The acceleration of an object is directly proportional to the net force acting on it and inversely
proportional to its mass
𝐹
𝑎∝
𝑚
When a body is acted upon by an external force, the rate of change of momentum is
proportional to the force and takes place in the direction of the force.
𝑚𝑣 − 𝑚𝑢 𝑣−𝑢
𝐹= =𝑚 = 𝑚𝑎
𝑡 𝑡
𝐹𝑛𝑒𝑡 = 𝑚𝑎
Momentum - is the product of the mass and velocity of a body.
𝑃 = 𝑚𝑣
NEWTON'S SECOND LAW
The equation for Newton’s second law can be extended to 3-dimension
space along each coordinate axis as follows
𝐹𝑥−𝑛𝑒𝑡 = 𝐹 = 𝑚𝑎𝑥
𝐹𝑦−𝑛𝑒𝑡 = 𝐹 = 𝑚𝑎𝑦
𝐹𝑧−𝑛𝑒𝑡 = 𝐹 = 𝑚𝑎𝑧
EXAMPLE
A 1000kg car accelerates from rest to 10 m/s in 7s along a straight stretch of
the road. How large is the force required to achieve this velocity?
Solution
𝐹𝑛𝑒𝑡 = 𝑚𝑎
𝑣 − 𝑢 10 − 0 𝑚
𝑎= = = 1.43 2
𝑡 7 𝑠
𝑚
𝐹𝑛𝑒𝑡 = 1000𝑘𝑔 × 1.43 2 = 1430𝑁
𝑠
EXAMPLE
A 900kg car accelerates from rest to 12 m/s in 8.00 s along a straight stretch
of the road. How large is the force required?
EXAMPLE
Two forces are acting on a 5kg mass as shown in the diagram, 4N along the 𝑥 −
𝑎𝑥𝑖𝑠 and 3N along the y-axis. What is the magnitude of the acceleration produced
by these forces.
y
4N
3N
5kg x
Since the forces are at right angles to each other, hence the resultant of the two
forces is
𝐹𝑛𝑒𝑡 5𝑁
2 2
𝐹𝑛𝑒𝑡 = (3𝑁) +(4𝑁) = 5 𝑁 𝑎= = = 1.0 𝑚/𝑠 2
𝑚 5𝑘𝑔
NEWTON’S THIRD LAW
Newton's third law states that:
For every action force, there is a reaction force that is equal in strength (magnitude) and opposite in direction.
Newton’s third law is sometimes referred to as action-reaction law.
The force F12 exerted by object 1 on object 2 is equal in magnitude and opposite in direction to the force F21 exerted by object 2 on
object 1. The force Fhn exerted by the hammer on the nail is equal in magnitude
and opposite to the force Fnh exerted by the nail on the hammer
The action force is equal in magnitude to the reaction force and opposite in direction. In all cases, the action and reaction forces act
on different objects and must be of the same type.
ACTION AND REACTION
• Action and reaction forces act on different objects, not on the same object. The forces cannot cancel
because they act on different objects.
• Newton’s third law states that for every action force there has to be a reaction force that is equal in
strength and opposite in direction.
The action force is equal in magnitude to the reaction force and opposite in direction. In all cases, the action and
reaction forces act on different objects and must be of the same type.
ONE BLOCK PUSHES ANOTHER
Consider a case in which one block pushes another block as shown below with
applied external force, F.
𝐹𝑥 𝑠𝑦𝑠𝑡𝑒𝑚 = 𝐹 = (𝑚1 + 𝑚2 )𝑎𝑥
𝐹
𝑎𝑥 =
𝑚1 + 𝑚2
σ 𝐹𝑥 = 𝑃12 = 𝑚2 𝑎𝑥
𝑚2
𝑃12 = 𝑚2 𝑎𝑥 = 𝐹
𝑚1 +𝑚2
EXAMPLE :ONE BLOCK PUSHES ANOTHER
Two blocks A and B are in contact on a frictionless horizontal surface and
have masses of 2.0 kg and 4.0 kg respectively. A force of 12 N is applied to
block A.
i) Find the force block A exerts on block B
ii) If the same force is applied to block B, what is the force block B exerts
on block A?
EXAMPLE
A man of mass 75 kg and a woman of mass 55 kg stand facing each other on ice
rink, both wearing ice skates. The woman pushes the man with a horizontal force
of 85.0 N in the positive 𝑥 − 𝑑𝑖𝑟𝑒𝑐𝑡𝑖𝑜𝑛.
Assume the ice is frictionless.
(a) What is the man’s acceleration
(b) What is the reaction force acting on the woman?
(c) Calculate the woman’s acceleration
SOLUTION
(a) What is the man’s acceleration
𝐹 = 𝑚𝑎𝑚𝑎𝑛
𝐹 85.0 𝑁
𝑎𝑚𝑎𝑛 = = = 1.13 𝑚/𝑠 2
𝑚 75.0 𝑘𝑔
(a) What is the reaction force acting on the woman?
𝑅 = −𝐹 = −85𝑁
(a) Calculate the woman’s acceleration
𝑚𝑎𝑤𝑜𝑚𝑎𝑛 = 𝑅 = −𝐹
𝐹 −85.0 𝑁
𝑎𝑤𝑜𝑚𝑎𝑛 = = = −1.55 𝑚/𝑠 2
𝑚 55.0 𝑘𝑔
