Question 3 **Projectiles and Pendulums: Inelastic Collisions**1. **In an inelastic collision, what is conserved and what is not conserved? Explain.**2. **Use \( m_1 \) for the mass of the ball, \( m_2 \) for the mass of the pendulum, \( v_1 \) for the velocity of the ball, and \( v_2 \) for the velocity of the ball and pendulum together.** a. For the drawings above, assuming a completely inelastic and instantaneous collision, derive an equation for the momentum of the system at the instant just before the collision. *A completely inelastic collision often refers to a collision where the two objects stick together.* b. Derive an equation for the final velocity of the ball and bob immediately after collision. *Show how you arrived at this.* c. Derive an equation for the total mechanical energy of the ball and bob combination immediately after collision.---**Apparatus:**- Ballistic Pendulum apparatus- Ruler, meter stick, and two-meter stick- Catch boards- Tape- Metal Ball**Part L-1:**Now we will continue from where you left off in the prelab by examining what happens after the collision. We will now use the relationships derived in the prelabs to perform the measurements. Spend some time in your groups checking your answers to the prelab.3. After the collision, the combination will reach some maximum height. Derive an equation for the total energy at this point.*Mass of Ball and Pendulum Arm:*In a portion of this lab, you may decide you need the mass of the Ball and Pendulum arm. When taking the pendulum arm off the apparatus to measure it is easy to accidentally damage the arm. Therefore, we are providing you with the mass of the arm (245.53g) and cup (65.85g).---**Graph/Diagram Explanation:**The image shows a sequence of diagrams illustrating a collision scenario. The first diagram depicts a ball moving towards a pendulum, and the second shows the ball and pendulum moving together after collision, highlighting a completely inelastic collision where the objects stick together.

An inelastic collision is a type of collision where the total kinetic energy is not conserved. For a perfectly inelastic collision, the two colliding bodies stick to each other, and hence the coefficient of restitution is 0. The total mechanical energy of the system is conserved and the momentum is also conserved. Let the mass of the ball be m1 and the block be m2 and the initial velocity of the ball be v1 and the final velocity of the ball block together be v2. After the collision, the ball and block will stick together. Applying the conservation of momentum for the first and second diagrams m20+m1v1=m1+m2v2 From here we can calculate v2=m1v1m1+m2 Now in the second diagram, the total energy is purely kinetic energy as the height is 0 at the mean position of the pendulum. Therefore from the diagram at the mean position TE=12m1+m2v22=12m1+m2m1v1m1+m22=m12v122m1+m2 The system will move with this kinetic energy and this kinetic energy will be converted into potential energy. At a certain maximum height h the total energy will be purely potential energy. Thus the total energy at the height h will be TE=m1+m2gh To find this value of h we can use conservation of energy m12v122m1+m2=m1+m2gh⇒h=m12v122m1+m22g Answer: The total energy at the height h is m1+m2gh

Answered: 3. After the collision, the combination…

Science

Advanced Physics

3. After the collision, the combination will reach some maximum height. Derive an equation for the total energy at this point.