Collisions

Theory

The law of conservation of linear momentum states that the total momentum of a system is conserved. For two objects that collide, the law takes the form of the following equation:

Equipment

Gliders

Use the same gliders in this experiment. Weight one of them and accept that the weight is the same for both gliders.

Notice that the gliders have two different bumpers, a spring, and a Velcro bumper.

• Spring bumpers are used to study elastic collisions (Video 1 and Video 3 below). Notice that the gliders might be equipped with different bumpers depending on the supplier. Watch the videos below to get familiar with the spring bumpers.

• Velcro bumpers are designed for modeling inelastic collisions (Video 2 and Figure 2 below).

Photogates

We use a set of two Vernier photogates in this experiment (Figure 4). Use clamps to mount the photogate on a stand (Figure 5).

Connect both photogates to the LabQuest interface. Use digital ports (Figure 6).

The photogates measure the time of a glider's flag blocking the beam when passing through. In order to get correct measurements, set it to “Mode: Photogate Timing" and "Timing: Gate" (Figure 7).

When the mode is set properly, go to the data collection screen. Use the green arrow to initiate data collection. The arrow will be replaced with a red square, which indicates that the data is being recorded (Figure 8).

The time intervals are displayed in the third column of the data collection screen (Figure 9).

The first column presented in Figure 9 shows the timeline of events. Columns 2 and 3 show the history of changes in the photogates state. The 4th column is used in this experiment to collect data. In Figure 9, we can see that the first photogate was blocked for 0.146717 s and, later on, for 0.085291 s. Knowing the length of the flag that blocked the photogate, we can calculate the velocity of the glider.

If the flag is 10.0 cm long, the velocity of the glider passing under the photogate for the first time is

v₁ = (0.100 m)/(0.146717 s) = 0.682 m/s

The velocity of the glider passing under the photogate for the second time is

v₂ = (0.100 m)/(0.085291 s) = 1.172 m/s

Attention!

Do not use the velocity calculated by the photogate. The calculation can be misleading if yo did not enter the length of the flag.

The second photogate measures the time of the second glider passing under after the collision.

Experimental procedure

The investigation focuses on linear momenta before and after the collision. With known masses, we need to find the velocities of the gliders. The only known velocity is that of the second glider, stationary before the collision.

• Before the collision: v₁ = unknown, v₂ = 0

• After the collision: v₁ = unknown, v₂ = unknown

Test conservation of linear momentum in all fours scenarios:

A. Elastic collisions. The same gliders’ masses

Use two identical gliders. Set both in a way that they collide with the elastic bumpers (Video 4 below). What happens with the first glider after it transfers its momentum to the second one? Make a prediction and observe the phenomenon of transferring momentum.

B. Elastic collisions. Different gliders’ masses

Continue with the same gliders. Add mass to the second glider. What happens with the first glider after it transfers its momentum to the second one? Does it transfer all its momentum? Why?

C. Inelastic collisions. The same gliders’ masses

Set both gliders in a way that they collide with the Velcro bumpers. After the collision, both gliders will join and move together under the second photogate (Video 6 below). How will you calculate the velocity then? What mass will you use to calculate momentum?

D. Inelastic collisions. Different gliders’ masses

The last part is similar to Part C. The only difference is to adjust calculations to use proper lengths and masses (Video 7).

Write down your observations in the laboratory worksheet.