- Investigation 2 Predict The Velocity Of The Marble In A Ballistic Pendulum The Video Below Shows An Apparatus Called 1 (296.73 KiB) Viewed 16 times
#1 Using conservation of mechanical energy, derive an expression for the initial velocity of the marble + pendulum system as it starts to move.
#2 Now use conservation of momentum to analyze the perfectly inelastic collision of the marble and the pendulum mass. Find an expression for the velocity of the marble before it collides with the initially motionless pendulum (show your work).
✓ Investigation 2: Predict the Velocity of the Marble in a Ballistic Pendulum The video below shows an apparatus called a ballistic pendulum. Historically, it was used to measure the speeds of bullets before fast electronic timing devices were developed. The marble launcher on the left is powered by compressed air. You can see a burst of air propelling the marble as it is ejected from the launcher. The marble hits and embeds into soft putty on the face of the pendulum. The pendulum is made of a very light carbon fiber rod with a massive bob attached to the bottom of the rod. For this experiment, we will assume that all the mass of the (rod + bob) pendulum is located at the crosshairs on the mass - the center of mass. The impact of the marble causes the pendulum to swing upwards. By measuring the swing angle and knowing parameters like the mass of the marble and the mass and length of the pendulum, we can determine what the velocity of the marble must have been. This video shows two trials recorded at normal speed, showing the marble colliding with the pendulum. Note that you must complete this section -- your theoretical prediction before you measure the velocity in the next section. pivot TRIAL Trial 1 2 K✔ 1. We can use conservation of momentum principles to compare the velocity of the marble before the collision to the velocity of the pendulum bob (with embedded marble) after the collision. After the collision, we can use conservation of energy principles to compare the initial kinetic energy of the (marble + pendulum) system with its potential energy when the pendulum reaches a maximum swing angle. Analyze the problem "backwards." Start with the motion of the (marble + pendulum) system after the inelastic collision. Using conservation of mechanical energy, derive an expression for the initial velocity of the marble + pendulum system as it starts to move Change motalmtagh, or = v₁ = √2gh. Using trigonometry, you should be able to show that h= L-Leos. Before Collision By conservation of mechanical energy, we can see that the kinetic energy immediately after the collision equals the change in gravitational potential energy from this moment to the maximum height. Therefore, Thus, the speed after the collision, V₁, is BIU = √/2g(L-Lcose) Score: 0/5 where L is the length of the ballistic pendulum, and is the maximum angle reached by the pendulum after the impact (show your work). BIU Score: 0/5 Immediately after Collision % e At maximum height %#! ● 2. Now use conservation of momentum to analyze the perfectly inelastic collision of the marble and the pendulum mass. Find an expression for the velocity of the marble before it collides with the initially motionless pendulum (show your work). Hint: mey=(m+ M)v 3. Select Trial 1 in the video and measure the total length of the ballistic pendulum and the maximum angle reached by the ballistic pendulum after the impact. Use these values to estimate the initial velocity of the marble. The marble mass is m = 10±0.1g. the mass of the ballistic pendulum is M=578±0.1g. Report your answer including +/- uncertainty in your result.