If you run the simulation a few times, you should see that for this particular pair of block and disc the block's position has the same numerical value as the disc's angular position, and the block's velocity has the same numerical value as the disc's angular velocity. Which of the following pairs of quantities must also have the same numerical values for the block and disc (assuming we use standard meter-kilogram-second units)? Select all that apply.

a. The work done by the force on the block and the work done by the torque on the disc.
b. The acceleration of the block and the angular acceleration of the disc.
c. The mass of the block and the mass of the disc.
d. The translational kinetic energy of the block and the rotational kinetic energy of the disc.
e. The momentum of the block and the angular momentum of the disc

Amass m = 74 kg slides on a frictionless track that has a drop, followed by a loop-the-loop with radius r = 18.4 m and finally a flat straight section at the same height as the center of the loop (18.4 m off the ground). since the mass would not make it around the loop if released from the height of the top of the loop (do you know why? ) it must be released above the top of the loop-the-loop height. (assume the mass never leaves the smooth track at any point on its path.) 1. what is the minimum speed the block must have at the top of the loop to make it around the loop-the-loop without leaving the track? 2. what height above the ground must the mass begin to make it around the loop-the-loop? 3. if the mass has just enough speed to make it around the loop without leaving the track, what will its speed be at the bottom of the loop? 4. if the mass has just enough speed to make it around the loop without leaving the track, what is its speed at the final flat level (18.4 m off the ground)? 5. now a spring with spring constant k = 15600 n/m is used on the final flat surface to stop the mass. how far does the spring compress?