0.18 Phy1160: force and motion -- momentum, impulse, and conservation  (Page 5/14)

A walk through the gym

Assume that you, as a blind student are walking through a gym that contains a punching bag of the type described above. Because of the void, you may not detect the presence of thepunching bag with your cane and you might walk directly into the punching bag.

A force over a short period of time

Unlike a solid wall, the punching bag probably wouldn't stop your forward progress instantly. Instead, there would probably be a period of time duringwhich the bag would exert a force on you and you would exert an equal but opposite force on the bag.

Initially, both you and the heavy punching bag would probably move in the direction that you are walking. Shortly thereafter, your forwardvelocity would probably go to zero.

Then the punching bag would probably push you backwards giving you a negative velocity as the bag swings like a pendulum. However the collision plays itself out, you would experience an impulse thatwould change your momentum and the momentum of the punching bag as well.

An ideal assumption

If we assume (ideally) that the force exerted on you by the bag is constant at ten newtons for a total of five seconds, the impulse would be equalto 50*N*s.

(In reality, the force would vary during the time interval and the computation of the impulse would be somewhat more complicated. For atime-varying force, the impulse is the area under a graph of force versus time. The average of the force over the given time interval cal also be used tocompute the impulse when the force is not constant.)

The effect of the time interval

The impulse, or the change in momentum, is equal to the product of the force and the time. Therefore, a large force over a short period of time can producethe same change in momentum as is produced by a smaller force over a longer period of time.

The effect on the object experiencing the change in momentum can be quite different for the two cases. This is particularly true when the human bodyexperiences a change in momentum. Among other things, air bags in cars are designed to lengthen the time over which the change in momentum occurs for ahuman body involved in a collision. In addition, the air bag can also spread the force over a larger portion of the body, which can reduce the damage to the bodycaused by the change in momentum.

Another representation of units

In any event, if we substitute the units for the newton in the above expression, we get

50*N*s = 50*(kg*m/s^2)*s = 50*kg*m/s

Two ways to represent the units of an impulse

Therefore, we can represent the units for an impulse as either N*s or as kg*m/s. You should recognize the latter as the product of mass and velocity,which are the same units as momentum.

In a collision, the impulse experienced by an object is always equal to the change in momentum experienced by the object.

A Super Ball

Consider the case of a Super Ball bouncing off of a solid concrete floor. (Super Ball is a brand name and registered trademark of Wham-O Incorporated.)

The main characteristic of a Super Ball is its ability to bounce almost as high as the height from which it was released when dropped onto a solid surface.As a result, when the Super Ball collides with the floor, it demonstrates a strong rebound effect . The greater the rebound effect, the greater will be the acceleration, momentum change, and impulse in acollision.