What condition must the height of the horizontal portion h meet for a disc sliding down a hill to cover maximum distance s?

H must equal H/2, where H is the height of the hill.

True or False: The spring constant is a measure of how much force is required to compress or extend a spring by a unit distance.

True.

A chain of length l has 1/3 of its mass m hanging off a smooth table. The kinetic energy of the chain as it slips off completely is ___.

4mg l/9.

Fill in the blank: The speed of particles P and Q when particle P reaches B is determined by the ___ of mechanical energy.

Conservation.

What is the relationship between the velocities of blocks A and B when connected by a string over a pulley?

The tension in the string must balance the forces acting on both blocks, leading to T = μmg for block B.

Riddle: I start with potential energy at height H, and as I descend, I convert to kinetic energy. What am I?

A disc sliding down a smooth hill.

Calculate the mean power developed by friction if the coefficient of friction is 0.27, mass is 1.0 kg, and initial velocity is 1.5 m/s.

The mean power is 2.0 W.

True or False: The work done by friction does not depend on the choice of the reference frame.

True.

If a particle slides down a track and reaches point B, the conservation of energy principle states that the potential energy lost equals ___ at point B.

The kinetic energy gained.

Fill in the blank: The maximum compression of a spring when a mass is released from height is found using the equation ___ = mgH.

1/2 kx².