PHYSICS 203 & 213 EXPERIMENT 9 FALL 2007

CONSERVATION OF MOMENTUM

PRE-LAB EXERCISE (5 POINTS)

1. A ball is hurled horizontally from a table top with an unknown initial speed v₀. It lands on the floor a horizontal distance of four meters from the launch position. If the balls initial vertical position on the table top is 1.2 meters above the floor, find v₀.

2. A thang is dangling from a string just above the table top. It is struck by a big baseball bat giving it an initial velocity v_thang. If the thang swings to a maximum height above the table top of .2 meters, find the initial velocity v_thang.

3. An auto weighing 4000 lbs and traveling at a velocity of 75 mi/hr collides head on with a smaller auto weighing 2500 lbs and traveling 60 mi/hr and the two vehicles lock together. Find the resultant velocity (speed and direction) of the two after impact.

Introduction

Definition: Momentum (p) of a body with mass (m) and velocity (v ) is p = mv.

Definition: Total momentum of a system of bodies is the sum of their momenta.

The Law of Conservation of Momentum says if two bodies collide, the total momentum before collision P_i = p_1i + p_2i is the same as the total momentum after collision P_f = p_1f + p_2f.

Objective

In this experiment the ballistic pendulum device will be used to determine if the momentum is conserved in a perfectly inelastic collision. A perfectly inelastic collision is one in which the two bodies stick together upon collision.

Using this device a steel ball will be fired by a gun into a cup. The momenta before and after the collision will be determined and compared to see if momentum is conserved in a perfectly inelastic collision.

References

Serway & Faughn's College Physics, Chapter 6

Serway's Physics for Scientists and Engineers, Chapter 9

Apparatus

Ballistic Pendulum device-cab 6 D, Meter stick - corner by cab 6, carbon paper - top drawer of file cab.

Procedure

PART I. FINDING INITIAL MOMENTUM

Since the total momentum of the system before collision P_i is the momentum of the ball just as it leaves the firing rod, (since the cup is stationary at this time), and p = mv, you must find the initial velocity of the ball v_bi as it just leaves the rod. You will accomplish this by raising the cup onto the rack out of the way, and firing the ball from the table top onto the floor, thus obtaining experimentally the horizontal range (R) of the ball from its initial position (0,y_o). To obtain y_o measure the distance from the bottom of the ball while on the firing rod to the floor. Measure the range R from the point on the floor directly below the midpoint of the ball as it sits on the firing rod in the release position. Take the average of 5 trials. Mark the locations where the ball strikes the floor by taping a piece of paper to the floor in the approximate location of the landings, and place a piece of carbon paper over it. (Also place a piece of scrap paper over the carbon paper to keep it from being torn by impact.) Using these values of R and y₀ and the kinematic equations of motion, you should be able to find the v_xo = v_bi, and hence P_i = m_b v_bi.

PART II. FINDING FINAL MOMENTUM.

For this part of the experiment you will need the mass of the ball and cup together. THIS IS STATED ON THE APPARATUS. Do NOT remove the cup from the apparatus to weigh it !

Next you will lower the cup into the vertical position and fire ball into the cup. The final momentum of the system just after collision is what carries the cup and ball up to the rack. Since this final momentum equals the total mass of ball, cup and pendulum rod combined (m_T) times the velocity immediately after collision (v_f), you must find this velocity. You will accomplish this by means of the law of conservation of energy. This law says E_o = E_f, where E = mgy + .5mv². In this experiment E_o is the total energy just after collision, and E_f is total energy after the ball and cup come to rest on the rack. The location of the position of the center of mass of the ball- cup- pendulum rod combination is indicated by the pointer on the side of the cup. Let the height of this pointer in the vertical position be y_o = 0. To obtain the final height of the pointer (y_f), measure the height of the pointer above the platform with the pendulum in the vertical position and subtract from the height of the pointer in the average rack position after firing. Take the average of 5 trials.

By substituting the appropriate values into the equation E₀ = E_f you should be able to find v_f. Finally, you will use this value of v_f to obtain P_f = m_T v_f, and compare this statistically to P_i = m_b v_bi.

INSTRUCTIONS:

State your objectives and procedures, present all data obtained, and calculations therefrom, give percent difference between the two momentums calculated and give reasons for the discrepancy.

QUESTIONS.

1. Suppose your apparatus were tilted so that the gun released the ball at an angle of 30^o above the horizontal. Calculate the range R for your gun. Repeat for 45^o and 60^o.

2. If you had fired the gun vertically upward, how high would the ball have gone ?

3. Find the position and velocity of the ball in question 2 one second after firing.

4. 5 POINTS BONUS ! A machine gun fires 500 bullets/minute. If each bullet has a mass of 30 grams and a muzzle velocity of 5000 cm/s, find the average reaction force of the gun on its support.

************************************************************