Read 125 Physics Projects for the Evil Genius Online
Authors: Jerry Silver
When objects collide, they either bounce off each other or they stick together.
Figure 53-1
Inelastic collision with one or both carts initially moving. Courtesy PASCO
.
The experimental setup is shown in
Figure 53-1
. (This actually shows a motion sensor at
both
ends. The previous procedure uses only one motion sensor, but this can easily extended to include both carts in motion. For simplicity, we will start out with one of the carts stationary.)
The momentum of
both carts before
the collision should equal the momentum of
both carts after
the collision.
Before the collision, one of the carts is stationary, which means it has no momentum, so the moving cart is the only one with momentum before the collision.
After the collision, both carts stick together and move off with the same velocity. The combined mass of the two carts together times their combined velocity is the momentum after the collision.
Figure 53-2
shows the position versus the time graph before and after the collision obtained by a motion sensor. Notice how the slope of the line abruptly drops, indicating the collision.
Figure 53-3
shows the velocity versus time graph before and after the collision. The velocity before and after can be determined directly from the graph. You can notice a slight downward slope indicating some slowing of the carts due to friction. This is not a showstopper for the experiment, but it shows the extent to which an air track can improve the overall results.
The most reliable velocity measurement is immediately before the collision. The collision shows some bouncing around and variability in the velocity for a short period until the two carts stick together and move as one. This provides some insight into the nature of inelastic collisions, which result in the loss of kinetic energy (but not linear momentum). The most reliable postcollision velocity to use is the point where a new horizontal line begins. The results should be fairly accurate, but some losses due to friction may be encountered without an air track. Also, excessive mass can load down the wheel bearing and increase the losses to friction.
Figure 53-2
Motion sensor measurement of distance versus time for an inelastic collision between a moving car and a stationary cart
.
Figure 53-3
Motion sensor measurement of velocity versus time for an inelastic collision between a moving car and a stationary cart
.
The total momentum before an inelastic collision equals the total momentum after.
However, unlike an elastic collision, the kinetic energy for an inelastic collision is less after the collision.
In an elastic collision, the objects bounce off each other in such as way that linear momentum and kinetic energy are conserved. This is true to the extent that no external force occurs during the collision.
In an inelastic collision, the objects interact in such a way that linear momentum is conserved (as long as no forces affect the collision). However, kinetic energy is not conserved in an inelastic collision. In a perfectly inelastic collision, the objects stick together and move after the collision as if they were a single object.
Figure 53-4
Motion sensor measurement of velocity versus time for an inelastic collision between a moving cart and a second moving cart
.
What do you think will happen if you throw a raw egg as hard as you can at a blanket held vertically? There is really only one way to find out. This experiment gives you an opportunity to explore the relationship between momentum and impulse.
1. Hold the blanket vertically, with the bottom edge curled out to form an overhang, as shown in
Figure 54-1
. This requires at least two people.
Figure 54-1
Throwing a raw egg at a blanket
.
Expected Results2. The third person throws the egg at the blanket. Don’t hold back. Give it a good shot. You can throw as hard as you can without having the egg break in your hands as you throw.
You know what will happen if you throw a raw egg against a cinder-block wall. However, if the egg is stopped by the blanket, the deceleration occurs over a sufficiently long time, which prevents the egg from breaking.
Momentum is changed by a force exerted over time. The ability to change an object’s momentum is called
impulse
, which is defined as the force exerted multiplied by the time. Anytime an object is brought to rest, the change in momentum equals the momentum the object had to start, applied in the opposite direction. The impulse to bring that object to rest can come from any combination of force and time, which when multiplied, equal the momentum change.