• Before understanding Newton’s second law of motion, let understand one important physical quantity momentum.• Suppose two vehicles, one light(light bicycle) and one heavy (like truck) are moving with equal velocities. Our experience says that we have to use less force to stop bicycle where as for truck we need to apply more force to stop.• You might have burst balloons using a gun in a fair.• In gun small green gram is used.• Why did it burst with the gun only?• Why did it happen?• Due to the velocity of the thing which is been fired from the gun?• The physical quantity relating to mass of body and its velocity is momentum.
MOMENTUM• Momentum: The product of mass of an object and its velocity of an object is called momentum of the object.• Momentum=mass x velocity i.e. p=mv• It is in vector quantity. Its direction is in the direction of velocity. Its SI unit is kg m/s.• Suppose you are driving a car and you apply brakes less then car will stop slowly while if it is applied more then it will stop soon.• It is related to momentum and time taken.
FORMULA• The rate of change in momentum is directly proportional to the resultant of external force and change in momentum is in the direction of the resultant external force.• Initial momentum of the object p=mu• Find momentum of the object p=mu• The change in momentum in time t• P=Pf – Pi• f oc p/t i.e. oc Pr-pi /t i.e. oc mv/m/t• F=K m(v-u)/t• But according to the definition of acceleration,• (v- u) / t=a• F=ma• Thus force= mass x acceleration.
FORCE• External force acting on a body is equal to product of mass and acceleration of the body.• U of force=m x a• 1 newton=1kg x 1m/second s q• The force which can produce acceleration of 1m/second s q in a body of mass 1 kg is called 1 newton force.• Its CGS nit is g cm/second s q.• When external force acting on the body is F=0, so acceleration is also zero.
ILLUSTRATION• S of car= 90 km/h & M=1000 kg• S of truck= 18 km/h & M=6000 kg• Momentum=m x v/s• Momentum of truck• 18 x 1000m/3600s = 5 m/s• P=mv• =1000 x 25= 25000 kg m/s
ILLUSTRATIONS• Momentum of car.• Momentum= m x v• =90 x 1000m x 3600s= 25• P=mv• 6000 x 5• =30,000 kg m/s
ILUSTRATIONS• To calculate the force of a body required to increase the velocity of the body of mass 50 kg which increases from 2m/s to 10m/s in 4s?• M= 50 kg, u=2m/s & v=10m/s t= 4s• F=ma• =[v-u/t] = 50 [10-2/4]= 100N
Impulse of Force• Product of force and the time period for which force is acting is called impulse of force.• If an object of force acts for the time• Impulse of force= force x time