Find the lowest energy level for a particle in a box if the particle is a billiard ball (m=0.200 kg) and the box has a width of 1.5 m, the size of a billiard table. (assume that the billiard ball slides without friction rather than rolls. that is, ignore the rotational kinetic energy.)

since the energy in part (a) is all kinetic, to what speed does this correspond?

how much time would it take at this speed for the ball to move from one side of the table to the other?

what is the difference in energy between the n = 2 and n = 1 levels?

are quantum-mechanical effects important for the game of billiards?

As part of your daily workout, you lie on your back and push with your feet against a platform attached to two stiff springs arranged side by side so that they are parallel to each other. when you push the platform, you compress the springs. you do an amount of work of 79.0 j when you compress the springs a distance of 0.230 m from their uncompressed length. (a) what magnitude of force must you apply to hold the platform in this position? (b)how much additional work must you do to move the platform a distance 0.230 m farther? (c) what maximum force must you apply to move the platform a distance 0.230 m farther?