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3. The pendulum will start to swing upwards. At the beginning of its swing, what kind of energy does the pendulum have? It will swing up to a certain angle where it will temporarily stop. What kind of energy does the pendulum have at the top of its swing? Draw a diagram of the pendulum, showing the pendulum at the bottom (where it starts) and also draw a diagram when it has been displaced to its maximum angle. Use the diagrams to find the vertical height difference between the pendulum's initial position and ation =rgy = + P²₂ final position. At the beginning of its swing, the pendul has kinetic energy At the top of its swing, Start Pendulum has Potenti vertical height difference= h=1-1c05d2 Th=/(1-Cos 0 4. With your height difference from number 3, you're ready to use the conservation of energy. Since the energy at the bottom of the swing must equal the energy at the top of the swing, use that fact to find the velocity of the pendulum in terms of the length of the pendulum, the acceleration of gravity g, angle 0, and the masses. maximum angles

3. The pendulum will start to swing upwards. At the beginning of its swing, what kind of energy does the pendulum have? It will swing up to a certain angle where it will temporarily stop. What kind of energy does the pendulum have at the top of its swing? Draw a diagram of the pendulum, showing the pendulum at the bottom (where it starts) and also draw a diagram when it has been displaced to its maximum angle. Use the diagrams to find the vertical height difference between the pendulum's initial position and ation =rgy = + P²₂ final position. At the beginning of its swing, the pendul has kinetic energy At the top of its swing, Start Pendulum has Potenti vertical height difference= h=1-1c05d2 Th=/(1-Cos 0 4. With your height difference from number 3, you're ready to use the conservation of energy. Since the energy at the bottom of the swing must equal the energy at the top of the swing, use that fact to find the velocity of the pendulum in terms of the length of the pendulum, the acceleration of gravity g, angle 0, and the masses. maximum angles

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Conservation of energy = + P₁= K₂ + P²₂ N 3. The pendulum will start to swing upwards. At the beginning of its swing, what kind of energy does the pendulum have? It will swing up to a certain angle where it will temporarily stop. What kind of energy does the pendulum have at the top of its swing? Draw a diagram of the pendulum, showing the pendulum at the bottom (where it starts) and also draw a diagram when it has been displaced to its maximum angle. Use the diagrams to find the vertical height difference between the pendulum's initial position and final position. At the beginning of its swin has kinetic energy At the top of its swing, pe Start U maximum angle. 2 Jello Pendulum has gro Potentiale vertical he difference= h=1-1 cose d 4. With your height difference from number 3, you're ready to use the conservation of energy. Since the energy at the bottom of the swing must equal the energy at the top of the swing, use that fact to find the velocity of the pendulum in terms of the length of the pendulum, the acceleration of gravity g, angle 0, and the masses. 11/9/22, 7:56 AB 2 h=((1-cos) ball of the masses.
Transcribed Image Text:Conservation of energy = + P₁= K₂ + P²₂ N 3. The pendulum will start to swing upwards. At the beginning of its swing, what kind of energy does the pendulum have? It will swing up to a certain angle where it will temporarily stop. What kind of energy does the pendulum have at the top of its swing? Draw a diagram of the pendulum, showing the pendulum at the bottom (where it starts) and also draw a diagram when it has been displaced to its maximum angle. Use the diagrams to find the vertical height difference between the pendulum's initial position and final position. At the beginning of its swin has kinetic energy At the top of its swing, pe Start U maximum angle. 2 Jello Pendulum has gro Potentiale vertical he difference= h=1-1 cose d 4. With your height difference from number 3, you're ready to use the conservation of energy. Since the energy at the bottom of the swing must equal the energy at the top of the swing, use that fact to find the velocity of the pendulum in terms of the length of the pendulum, the acceleration of gravity g, angle 0, and the masses. 11/9/22, 7:56 AB 2 h=((1-cos) ball of the masses.
Lab 8- The Ballistic Pendulum A ballistic pendulum is an object that can measure the velocity of a projectile by using the conservation of energy and momentum. It is a different way of measuring velocity since it does not involve a time measurement. Although modern projectile velocities are measured using optical chronographs (which involves a time measurement), the ballistic pendulum remains an instructive method of measuring a velocity. It was invented in 1742 by an English mathematician (Benjamin Robins) who used a heavy iron pendulum to make his measurements. His rather involved calculations used the period of the oscillations induced by the projectile's impact. Our experimental devices will allow for the use of simple conservation of energy and momentum calculations to obtain the velocity of the projectile. For our device, the ball will be launched by a horizontal spring launcher (see diagram) toward the catcher which is attached to the end of a rod that can swing upward (i.e., the pendulum). When the ball is caught, it will cause the pendulum to swing upward. We can measure the angle to which the rod swings when it reaches its maximum height. Equipment Steel projectile, spring launcher & pendulum system (the rod and "catcher" in the diagram below), triple beam mass balances, meter stick launcher 0010 axle rod Dhara Patel catcher Prediction In this lab we will measure the deflection angle of a ballistic pendulum. Derive an equation for the velocity of the projectile given the masses of the projectile and pendulum, the length of the pendulum, and the deflection angle. The pre-lab is designed to help you come up with this prediction. 11/9/22, 7:56 AM 11/9/22, 7:56 AM
Transcribed Image Text:Lab 8- The Ballistic Pendulum A ballistic pendulum is an object that can measure the velocity of a projectile by using the conservation of energy and momentum. It is a different way of measuring velocity since it does not involve a time measurement. Although modern projectile velocities are measured using optical chronographs (which involves a time measurement), the ballistic pendulum remains an instructive method of measuring a velocity. It was invented in 1742 by an English mathematician (Benjamin Robins) who used a heavy iron pendulum to make his measurements. His rather involved calculations used the period of the oscillations induced by the projectile's impact. Our experimental devices will allow for the use of simple conservation of energy and momentum calculations to obtain the velocity of the projectile. For our device, the ball will be launched by a horizontal spring launcher (see diagram) toward the catcher which is attached to the end of a rod that can swing upward (i.e., the pendulum). When the ball is caught, it will cause the pendulum to swing upward. We can measure the angle to which the rod swings when it reaches its maximum height. Equipment Steel projectile, spring launcher & pendulum system (the rod and "catcher" in the diagram below), triple beam mass balances, meter stick launcher 0010 axle rod Dhara Patel catcher Prediction In this lab we will measure the deflection angle of a ballistic pendulum. Derive an equation for the velocity of the projectile given the masses of the projectile and pendulum, the length of the pendulum, and the deflection angle. The pre-lab is designed to help you come up with this prediction. 11/9/22, 7:56 AM 11/9/22, 7:56 AM
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