Newton’s Laws of Motion Indus International School, Bangalore

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.

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

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.

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

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

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

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

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

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

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

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.

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!!!

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

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.

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

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

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

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

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

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)

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.

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

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.

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

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

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

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

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.

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

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