Momentum & Impulse
1. Newton’s 2nd Law Reprise
The second Newton’s law states that if an unbalanced force acts upon an object, the object changes its velocity (i.e. accelerates).
An important characteristic of the objects is their momentum.
From the formulation follows:
1) The unit that measures the momentum is kg.m/s.
1 kg.m/s is the momentum of an object with mass 1kg, than is moving with velocity 1 m/s.
2) The momentum is a vector quantity. The mass is always positive; therefore the direction of the momentum has the same direction as the velocity.
3) If the velocity changes in time, the momentum changes, as well.
This means that there is dependence between the forces acting upon the object, which are reason for its motion (acceleration), and the change in the momentum.
Or we can write it as follow:
Where is the net force (the sum of all forces acting on the object)
is the change of the momentum
is the time interval
From the definition for momentum:
Therefore, the change in momentum of an object for a very short time interval equals the momentum of the force, acting upon the object for that certain interval of time. We call the momentum of the force - impulse
(The latter is equivalent formulation of the second Newton’s law)
3. Momentum and impulse – units
- symbol: ; units: kg.m/s (kilograms –meter per second)
- symbol - ; units : N.s (Newton-second)
Sample problem: Golf ball momentum.
• Mass of golf ball m= 0.0459kg
• Speed of the golf ball leaving tee on drive v=70m/s
1) What is the momentum of the golfball
2) If the golf club is in contact with the ball for 0.5 ms (1ms=0.001s), what is the average force exerted on the ball by the club?
(Momentum =mass x velocity)