Ballistic Pendulum Printer Friendly Version
In this experiment we will use a ballistic pendulum to determine the initial horizontal launch velocity of a plastic, foam dart. The first method will use conservation of momentum and conservation of energy while the second method will employ horizontal projectile motion.

In the first part of the experiment you will fire the foam dart from the dart gun so that it's suction cup allows it to stick to the side of the wooden pendulum resulting in the pendulum and its attached dart swinging back and forth. The initialy inelastic collision only conserves momentum while the pendulum's subsequent swing conserves mechanical energy.

In the second part of the experiment you will carefully discharge the dart gun to release the foam dart as a horizontal projectile.

You might need to use a level provided to insure that the gun's barrel is horizontal before firing. By measuring the dart's range and height of release you will be able to calculate the ball's flight time and its muzzle velocity.

Finally, you will be asked to calculate a percent difference between the two values for the dart's release velocity.

Part I: Pendulum Measurements

Carefully level the pendulum's rectangular bob and record the equilibrium position of the straw pointer. Standing close to the pendulum, aim and fire the dart gun so that the dart will strike the middle of the wooden bob. As shown in the picture below, measure and record the amplitude of the straw as it makes it initial swing. You will fire the dart a total of three times, each time recording the amplitude of the pendulum's vibration.

Step 1: Angle data and calculations

 amplitude trial (cm)
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 What was the value of H, the distance from the floor to the suspension points for the strings on the metal supports. Record this value in cm.

 Measure and record the value of y, the distance from the floor to the center of mass of the pendulum's wooden bob. Record this value in cm.

 What is the actual length of your pendulum? Record your value in cm.

 Using your pendulum's actual length and its average angular displacement, determine its average vertical displacement. Record your answer in cm.

Step 2: Mass data, energy and momentum calculations
 Find out from your instructor the mass of the pendulum's wooden block. Report your answer in grams.

 Measure the mass of the foam dart. Report your answer in grams.

 Calculate the potential energy, in joules, of the pendulum bob and dart when they reached maximum amplitude. Remember to show your calculations on your lab sheet.

 Using conservation of energy, calculate the velocity, in m/sec, of the pendulum bob and dart immediately after the collision. Remember to show your calculations on your lab sheet.

 Use conservation of momentum to determine the initial horizontal velocity of the dart when first released from the dart gun. Remember to show your calculations on your lab sheet.

Part II: Projectile Measurements

Carefully level the air gun on the top of a lab table. Test fire it and note where the foam dart strikes the floor and then place a meter stick near the anticipated point of contact. Measure the distance of the end of the gun's muzzle from the edge of the table and use a plumb line to record the location of the edge of the table on the floor. After firing the gun three times, measure and record each of the dart's impact positions. Note that each floor tile measures 12 inches and that there are 2.54 cm to one inch. Remember to always make sure that the gun is level before each firing.  Record your answers in the chart below.

 range trial (cm)
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 How high was the air gun's muzzle above the floor? Record you result in cm.

 How much time did each of the darts fired form the table spend in the air? Record your answer in seconds. Remember to show your calculations on your lab sheet.

 What is the average velocity of the air dart when shot from your air gun? Remember to show your calculations on your lab sheet.

Part III: Percent Difference
 What is the percent difference between your two values for the air dart's velocity?

Which value do you feel was the most accuracte?