1. Newton’s Laws of Motion
Indus International School, Bangalore

2. Newton’s First Law Newton’s First Law of Motion
An object at rest will remain at rest and an object in motion will continue moving at a constant velocity unless acted upon by a net force.

3. Newton’s First Law Newton’s First Law of Motion Inertia
“Law of Inertia”
Inertia
tendency of an object to resist any change in its motion
increases as mass increases

4. Equilibrium
Static equilibrium: If a body is in the state of rest and the net force acting on it is zero, then the body is said to be in Static equilibrium.
Example: Book resting on a table
Dynamic equilibrium: If a body is moving with a constant velocity and the net force acting on it is zero, then the body is said to be in dynamic equilibrium.

5. Example of static equilibrium
forces acting on an
object that
are opposite in direction
and equal in size.
The book does not move.

6. Example of dynamic equilibrium
If forces acting on an object are opposite in direction and equal in size, then there is
no change in velocity

7. F = ma Newton’s Second Law Newton’s Second Law of Motion
The acceleration of an object is directly proportional to the net force acting on it and inversely proportional to its mass.
F = ma

8. F = ma F m a Newton’s Second Law F m F: force (N) m: mass (kg)
a: acceleration
(m/s2)
1 N = 1 kg ·m/s2
F = ma

9. Newton’s Second Law Linear momentum p=mass(m) x velocity(v) F = ∆p/∆t
F = ∆(mv)/∆t
F = m(∆v/∆t)
F = ma

10. A single fixed pulley Forces affecting m1: forces affecting m2:
                    
forces affecting m2:
and adding the two previous equations
we obtain
                                ,
and at last
                  

11. Fixed Pulley
To evaluate tension we substitute the equation for acceleration in either of the 2 force equations.
For example substituting into m1a = N − m1g, we get
The tension can be found in a similar manner from m2a = m2g − N

12. Newton’s Third Law Newton’s Third Law of Motion
When one object exerts a force on a second object, the second object exerts an equal but opposite force on the first.

13. Newton’s Third Law Problem:
How can a horse pull a cart if the cart is pulling back on the horse with an equal but opposite force?
Aren’t these “balanced forces” resulting in no acceleration?
NO!!!

14. Newton’s Third Law Explanation:
forces are equal and opposite but act on different objects
they are not “balanced forces”
the movement of the horse depends on the forces acting on the horse

15. Newton’s Third Law Action-Reaction Pairs
The hammer exerts a force on the nail to the right.
The nail exerts an equal but opposite force on the hammer to the left.

16. Newton’s Third Law Action-Reaction Pairs FG FR
The rocket exerts a downward force on the exhaust gases.
The gases exert an equal but opposite upward force on the rocket. FG FR

17. Newton’s Third Law F m Action-Reaction Pairs Both objects accelerate.
The amount of acceleration depends on the mass of the object. F m
Small mass  more acceleration
Large mass  less acceleration

18. Impulse – Momentum theory
When a force is applied to an object, it occurs over a finite time. (golf ball being struck below)
Concepts of impulse & momentum are needed to describe the force being applied.
© John Wiley and Sons, 2004

19. Impulse – Momentum theory
This graph shows the magnitude of the force applied to a baseball when hit by a bat.
Time interval is very short but the imparting of the force is not constant!
At t0 the ball first strikes bat F =0
At Tf ball leaves bat F = 0
© John Wiley and Sons, 2004

20. Impulse – Momentum theory
Spreading impulse out over a longer time means
that the force will be less
© John Wiley and Sons, 2004

21. Impulse – Momentum theory
The Impulse J of a force is the product of the average force F and the time interval t during which the force acts.
Impulse is a vector quantity and acts in the same direction as the force.
SI Units Newton second (Ns)

22. Impulse – Momentum theory
A large impulse produces a large response on the ball.
Experience tells us that the larger the mass of the ball, the slower its velocity will be after being struck with a given impulse.
The same impulse for a tennis ball and a football will result in a greater velocity for the tennis ball as its mass is smaller.

23. Impulse – Momentum theory
We introduce the concept of momentum to allow us to relate the mass and the resultant velocity of an object after being struck. (i.e. compare the velocity of a tennis ball and football after being struck with the same force).
Also what is the velocity before & after impact?
© John Wiley and Sons, 2004

24. Impulse – Momentum theory
The linear momentum of an object p is the product of the objects mass m and velocity v
SI units = kg.m/s
When a net force acts on a body, the impulse of the force equals the change in momentum of the object!!
Prove this in the next slide.

25. Impulse – Momentum theory
Newton’s 2nd law X
Impulse
Final momentum
Initial momentum
© John Wiley and Sons, 2004

26. Impulse – Momentum theory
Example:A baseball (mass= 0.14 kg) has an initial velocity of –38m/s as it approaches the bat. After being struck by the bat it now has a velocity of 58m/s. Determine the impulse and force exerted on the ball by the bat.
© John Wiley and Sons, 2004

27. Momentum conservation
Consider this mid-air collision between two masses m1 and m2 with velocities v01 and v02 initially.
Assume no outside influence (only internal forces & no external forces – (no gravity))
Newton’s 3rd law gives
F12=-F21
© John Wiley and Sons, 2004

28. Momentum conservation
Apply Impulse – momentum theory to each object.
Adding together for the whole system

29. Momentum conservation
The Principle of conservation of linear momentum states -
The total linear momentum of an isolated system remains constant (is conserved).
An isolated system is a system where the sum of the average external forces is zero.

30. Momentum conservation example
Train carriages are joined together. Carriage 1 has a mass of 65,000kg and a velocity of +0.8m/s. Carriage 2 has a mass of 92,000kg and a velocity of +1.3m/s.
Find the velocity when they are joined
© John Wiley and Sons, 2004

31. Momentum conservation example
Two skaters push off against one another from rest. masswoman = 54kg and massman =88kg. If the woman’s velocity is +2.5m, what is the velocity of the man?
© John Wiley and Sons, 2004