1. The launcher is set to launch a projectile horizontally. Once launched, the projectile will immediately go into the pendulum (the “catcher” in the diagram), causing the pendulum to swing. Considering momentum, sum all the momenta of the situation after the ball is launched but before it goes into the pendulum. Do not consider the recoil of the launcher. 2. When the ball gets caught by the pendulum, what kind of collision is this (elastic or inelastic)? What is the momentum after the collision? Using conservation of momentum, derive an equation for the velocity of the ball/pendulum combo immediately after the ball is caught (and before the pendulum starts to swing upward). The equation can depend on the mass of the ball, the mass of the pendulum, and the initial velocity of the ball. 3. The pendulum will start to swing upwards. At the beginning of its swing, what kind ofenergy 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? Create a diagram of the pendulum, showing the pendulum at the bottom 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. 4. With your height difference from question #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, and the masses. 5. Finally, use your answer from question #2 to get the initial velocity of the ball in terms of the masses, g, length of the pendulum, and the angle.
1. The launcher is set to launch a projectile horizontally. Once launched, the projectile will immediately go into the pendulum (the “catcher” in the diagram), causing the pendulum to swing. Considering momentum, sum all the momenta of the situation after the ball is launched but before it goes into the pendulum. Do not consider the recoil of the launcher.
2. When the ball gets caught by the pendulum, what kind of collision is this (elastic or inelastic)? What is the momentum after the collision? Using conservation of momentum, derive an equation for the velocity of the ball/pendulum combo immediately after the ball is caught (and before the pendulum starts to swing upward). The equation can depend on the mass of the ball, the mass of the pendulum, and the initial velocity of the ball.
3. The pendulum will start to swing upwards. At the beginning of its swing, what kind ofenergy 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? Create a diagram of the pendulum, showing the pendulum at the bottom
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.
4. With your height difference from question #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, and the masses.
5. Finally, use your answer from question #2 to get the initial velocity of the ball in terms of the masses, g, length of the pendulum, and the angle.
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