9.2:
Force and Momentum
The ease with which an object's motion can be stopped in track and field events like javelin throw and shot put can be comparatively assessed based on their momentum values.
Between the javelin and the shot, the mass of the shot is nine times greater than the mass of the javelin, whereas the shot's velocity is one-third of the javelin's velocity.
On substituting the mass and velocity values in the equation, the shot's momentum appears to be greater than that of the javelin. Therefore, it would be more difficult to stop the heavy shot despite its low velocity as compared to the javelin.
When an object's mass remains constant, then a change in momentum is expressed as a product of mass and change in velocity.
As per Newton's second law of motion, the net force equals the product of mass and acceleration.
By expressing acceleration in terms of velocity and from the definition of change in momentum of an object of constant mass, the net force becomes equal to the rate of change of momentum caused by the force. This expression is nothing but Newton's second law of motion in terms of momentum.
9.2:
Force and Momentum
Force and momentum are intimately related. Force acting over time can change momentum, and Newton's second law of motion can be stated in its most broadly applicable form in terms of momentum. Momentum can be applied to systems where the mass is changing, such as rockets, as well as to systems of constant mass. Also, momentum continues to be a key concept in the study of atomic and subatomic particles in quantum mechanics. One can consider systems with varying mass in some detail; however, the relationship between momentum and force remains useful when mass is constant, such as in the following example.
During the 2007 French Open, Venus Williams hit the fastest recorded serve in a premier women's match, reaching a speed of 58 m/s (209 km/h). What is the average force exerted on the 0.057 kg tennis ball by Venus Williams' racquet, assuming that the ball's speed just after impact is 58 m/s, that the initial horizontal component of the velocity before impact is negligible, and that the ball remained in contact with the racquet for 5.0 ms (milliseconds)?
To determine the change in momentum, substitute the values for the initial and final velocities into the equation below:
Now, the magnitude of the net external force can be determined by using
where only two significant figures were retained in the final step.