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The Ballistic Pendulum

By Ruth Porter,2014-07-09 03:30
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The Ballistic Pendulum

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Conservation of Energy and Momentum

PHYS 1313

Introduction

Today’s lab will provide you practical experience working with three important quantities associated with the motion of an object and, hopefully, you will see you how these quantities are related. These three quantities of interest are work, energy and momentum. As used by physicists, these quantities have technical meanings, which are different from their every day conversational meanings, so you need to concentrate on the technical meanings of these words as you perform the lab or you will become hopelessly confused. To help your concentration, we will concentrate mostly on the quantity energy and its conservation.

Simplified Theory

By now, you are probably familiar with the concepts of work, energy, and potential

energy. Today, we will observe the transfer of kinetic energy into potential energy. For

an object with speed v and mass m, the kinetic energy (K.E.) is given by:

12K.E. = mv (1) 2

22Notice that the units for kinetic energy are one kilogram•meter/second. This unit is

similar to that for the force but with the length unit squared. (The MKS unit for energy is the Joule.).

Recall that the work done on an object by a force F displaced an amount x, is defined as:

W = F • x (2)

or

W = Fx

if the force and the displacement are in the same direction.

The potential energy describes the amount of work necessary to move an object of a given mass from one point to another when the object is subject to forces. The difference in the potential energy between the starting point and the ending point of the object’s motion is the amount of work or energy necessary to move the object. For an object of mass m subject to a force over a distance h, the potential energy is simply:

P.E. = - mah

in our case a = g = -9.81

P.E = mgh (3)

where h is the vertical displacement between the final and initial positions.

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In the case of the “ballistic pendulum,” the apparatus we use today, a projectile is launched from a spring-loaded gun and is trapped in the base of a pendulum. From the conservation of momentum, we can calculate the speed at which the pendulum will move after trapping the ball. For a totally inelastic collision, we have

mv = (m + m) v(4) b0bp1

where m and m are the masses of the projectile ball and the pendulum, respectively, and bp

the initial speed of the ball is v. After the pendulum traps the projectile ball, both ball 0

and pendulum move with speed v. At the maximum swing height, the velocity of the 1

pendulum is zero and all of the kinetic energy has been converted to gravitational potential energy. Using the principle of conservation of energy, we can relate the maximum swing height h to the velocity, v: 1

12(m + m) v = (m + m) gh (5) bp1bp2

v = 2gh (6) 1

Combining equations (4) and (6), we can solve for the initial velocity of the launcher.

v = ((m + m) / m ) 2gh (7) 0bpb

This equation shows that by measuring the masses of the pendulum, the ball, and the height of the pendulum swing, we can determine the initial speed of the ball before the collision. The vertical displacement h is measured by measuring the height from the table

of the center of mass marked on the pendulum both before and after the collision. The difference between these is h.

Procedure:

Part One

1. Make sure the apparatus is level and clamped securely to the table. Use the leveling

screws and the bull’s eye bubble level on the apparatus base to level properly.

2. Measure the mass of the pendulum and the ball with the triple beam balance

3. Measure from the base of the apparatus to the "center of mass" line etched in the

pendulum (labeled on the pendulum shaft). Record this as y . This value should initial

be the same for each trial.

4. Make sure the pendulum is hanging vertically.

5. Place the metal ball on the front of the gun shaft and cock the gun until the shaft is

locked in position.

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6. Press back on the trigger to fire the ball.

7. After the pendulum comes to rest, record the vertical distance between the base of

the apparatus and the center of mass. Record this measurement as Y . The value of final

h is the difference between the two height measurements. ( Yy ) final - initial

8. Repeat steps 5-7, to make 5 measurements and compute the average value of h.

9. Compute the initial ball speed, v, using equation 7. USE g= + 9.81 m/sec^2 the 0

negative is already included in the formula.

Part Two

10. Reduce the gun spring tension by unscrewing the tension adjustment screw. Repeat

steps 4-7. Compute v for each repetition 0

Questions

1) Did your data fluctuate very much? What could be the primary sources of error in this experiment and explain their relevance in terms of accuracy and precision? For example, how well do you think you can measure h? Think of other sources.

) What role does friction play in this experiment? How might your results differ if there 2

were no friction in terms of calculated velocity? Would it be greater/smaller? 3) Sketch the apparatus and label the different forces at work in this experiment. 4) Why did we use the equation for momentum conservation for the collision but energy conservation for the change in pendulum height?

THE QUESTIONS.

1. From your results is it justifiable to say that energy and momentum are conserved in parts of the experiment? Explain another important result.

2. Compare your two values for v . Which one is greater? Why? 0

3. How much does v change with the decreased spring tension? 0

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Conservation of Energy and Momentum

Abstract

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Results

m= _______ m = ______ b p

Part 1

Y Y h=Yf - Yi initialfinal

h = ave

v = _________ 0

Part 2 - With reduced spring tension:

Y Y h=Yf - Yi initialfinal

h = ave

v = ________ 0

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