A Lab Without A Point

PURPOSE: To estimate the speed of an object by applying conservation of momentum to an inelastic collision.

DISCUSSION: If you catch a heavy ball while standing motionless on a skateboard, the momentum of the ball is transferred to you and sets you in motion. If you measure your speed and the masses of the ball, skateboard, and yourself, then you know the momentum of everything after the ball is caught. But this is equal to the momentum of the ball just before you caught it, from the law of conservation of momentum. To find the speed of the ball just before you caught it, divide the momentum by the mass of the ball. A similar technique is used to determine the speed of high-speed bullets in the laboratory. In this experiment you will find the speeds of a toy dart before and after it collides with a toy car.

PROCEDURE:

Tailgate car with dart

Step 1. Construct a straight line track with hot-wheels track or meter sticks. Your car must be able to coast for a long enough distance so that it comes to a stop naturally due to friction. The dart must fully leave the dart gun before it sticks the car. Place the gun so that the dart just leaves the end of the gun before it hits the car. Practice shooting the dart onto the back end of the car. The dart should stick to the car, the car should travel in as straight a line as possible and coast to a stop. Place the gun about 10 cm from the back of the car.

Step 2. Find the mass of the car and find the mass of the dart. Write these once in data lines.

Step 3. a) Make a data table with a column for trial, coasting distance "d", coasting time "t", average speed of car after impact "v_avg", speed of car just at impact "v_ci", speed of dart and car right after impact "v_f" ,and initial speed of dart "v_di". Also include a column for "P_ti" the total momentum before the dart hits the car and "P_tf", the total momentum of the car & dart after they stick together. You will calculate "v_avg", "v_f" , "v_di", "P_ti", "P_tf"and as you go through the experiment

b) Measure the distance and time that the car coasts after it is hit by the dart, until it comes to a stop. Record your data in a Data Table.

c) Repeat for four more trials for a total of five trials.

Calculations (Show all work in 5-steps for trial 1!...write in data table for ALL trials))

1) Calculate the average speed of the car after impact for the five trials and record in your data table ("v_avg").

2) Calculate the speed of car and dart RIGHT AFTER impact. Hint: v_avg = (v_f+v_i)/2....since v_f = 0, v_avg = v_i/2...find v_i). ("v_f" since it's right AFTER collision)

3) Calculate the initial velocity of the dart BEFORE impact. Hint: Use sticky collision equation. ("v_di")

4) Calculate the total initial momentum of the dart and car. Hint: Only the dart had momentum. ("P_ti")

5) Calculate the total final momentum of the dart and car. Hint: The car and dart are stuck together so add their masses for m. ("P_tf")

Questions:

Q1) What is the relationship between the momentum of the dart before the impact and the combined momentum of the dart and car just immediately after the impact?

Q2) Was the speed of the car constant as it coasted? Explain.

Q3) If the retarding force on the car is assumed to be nearly constant, how does the speed of the car immediately after impact compare with the average speed?

Q4) Is the momentum of the tailgated car constant the whole time it is moving? Explain.

CER

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