Lab 10 – BALLISTIC PENDULUM

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Lab 10 – BALLISTIC PENDULUM

THEORY:

A projectile launcher can repeatedly launch an object with a constant initial speed. The object can then collide with, and become attached to, a ballistic pendulum undergoing a completely inelastic collision. In this type of collision, linear momentum is conserved, but total mechanical energy is not conserved. After the collision, as the pendulum arm swings upwards, the total mechanical energy of the system is also conserved if neglecting resistive forces.

Consider the initial state of the system where the object (small sphere) with mass m is launched at a large mass M connect to one or more strings of length L as in the figure below:

Figure 1. Sphere launched towards Ballistic Pendulum Block at rest.

The mass M is initially at rest, and the mass m has an initial velocity that is unknown. An inelastic collision then occurs between the sphere and the block and the sphere becomes imbedded in the block. Immediately after the collision, the block and sphere have a velocity that is determined by momentum conservation. See figure 2.

Figure 2. Sphere and Block immediately after collision.

The Ballistic Pendulum will then swing up conserving Mechanical Energy and converting its kinetic energy into potential energy. The Ballistic Pendulum will reach a maximum height h before swinging down again. See Figure 3.

Figure 3. Ballistic Pendulum at its maximum swing position.

1. Initial Calculations:

a. Given a maximum height h attained by the Ballistic Pendulum swing, use Conservation of Energy to derive an expression for the velocity of the Ballistic Pendulum immediately after the collision.

Determine this velocity for the case where .

b. Given a velocity for the Ballistic Pendulum immediately after the collision, use Conservation of Momentum to derive an expression for the initial velocity of the sphere before the collision. Using the numerical values for Question 1 above, determine the initial velocity of the sphere for this case.

c. This is an inelastic collision and in an inelastic collision kinetic energy is not conserved. Determine the difference in the kinetic energy of the system immediately before the collision to that immediately after the collision. What happens to this energy?

2. Lab Activity:

Open the following link for a simulation of the Ballistic Pendulum: https://ophysics.com/e3.html

a. Set the initial parameters for the simulation of

Measure the maximum height reached by the Ballistic Pendulum. Compare this with what you would predict from theory. Show calculation of the percent error PE value the height reached.

b. For a initial mass of the sphere and Ballistic Pendulum of ; what initial velocity of the sphere results in a maximum height of ? Show a calculation for your prediction, and test your result using the Simulation.

c. Increasing the mass of the Ballistic Pendulum to ; what initial velocity now results in the same maximum height for the Ballistic Pendulum, ? Show your calculation and test your prediction.

d. Take the Ballistic Pendulum Quiz at the following link: https://ophysics.com/e4.html

Set the mass of the sphere and Ballistic Pendulum to Adjust the initial velocity bar until the Ballistic Pendulum reaches a maximum height of Compute the initial velocity value and enter it into the box and see if you are correct.

3. Reflection on the result

The Ballistic Pendulum makes use of an inelastic collision between the sphere and the Ballistic Pendulum. If it were to be an elastic collision between the sphere and the Pendulum block, would the Ballistic Pendulum rise higher or lower than for the inelastic collision? Show a calculation to justify your answer using,

Conclusion: