Question

Prelab 2: Write an expression for the conservation of energy for the system that you considered in Prelab 1. You may consider the system to be frictionless. The equations should include the change in gravitational potential energy of the falling mass (), the change in kinetic energy of the falling mass ) and the change in rotational kinetic energy of the platter (K-12l Prelab 3: In the following apparatus, the auxiliary platter is dropped onto the main platter Auxiliary Platter Spindle The m ain platter has a rotational inertia 4e and an initial angular velocity ω0. The auxiliary platter has a rotational inertia la and is initially not spinning a.) Explain why the two platters will have the same final angular velocity b.) Show that by using the conservation of angular momentum equation, the expression for the final angular velocity of the system (assuming the two carts have the same final velocity ) is described below c.) Using your answer to Part (b) above, show that the ratio of final kinetic energy to initial kinetic energy is given by the expression below Do this by noting that and that K-1/2lYou will use this result in Part III of the lab.

Answer 1

Prelab 2 cannot be solved as it refers to Prelab 1.

Here is Prelab 3

(a) when the auxillary platter falls on an already rotating main platter, there is an inelastic collision between two and they both start moving at the same velocity.

(b) using conservation of angular momentum, we have

I_MW_O + I_A*0 = (I_M + I_A) W_FINAL

I_MW_O  = (I_M + I_A) W_FINAL

W_FINAL = I_MW_O / I_M + I_A

(C) Final Kinetic Energy = 1/2*(I_M + I_A) * W_FINAL²

Final Kinetic Energy = 1/2*(I_M + I_A) * ( I_MW_O / I_M + I_A)²

Final Kinetic Energy = 1/2 * ( I_MW_O)² / I_M + I_A

Initial Kinetic Energy = 1/2 * I_M* W_O²

Divide final by initial, we get

1/2 * ( I_MW_O)² / I_M + I_A / 1/2 * I_M* W_O²

K_f / K_o = I_M / I_M + I_A