1. A 37.0 kg crate is initially moving with a velocity that has magnitude 3.60 m/s in a direction 37.0 west of north.

How much work must be done on the crate to change its velocity to 5.70 m/s in a direction 63.0 south of east?

2. On an essentially frictionless, horizontal ice rink, a skater moving at 6.0 m/s encounters a rough patch that reduces her speed by 47% due to a friction force that is 23% of her weight.

Use the work-energy theorem to find the length of this rough patch. Express your answer in meters.

3. A wooden block with mass 2.00 kg is placed against a compressed spring at the bottom of a slope inclined at an angle of 32.0 (point A). When the spring is released, it projects the block up the incline. At point B, a distance of 7.95 m up the incline from A, the block is moving up the incline at a speed of 5.05 m/s and is no longer in contact with the spring. The coefficient of kinetic friction between the block and incline is k= 0.50. The mass of the spring is negligible.

Calculate the amount of potential energy that was initially stored in the spring. Express your answer in joules.

4. A small block with mass 0.0375 kg slides in a vertical circle of radius 0.475 m on the inside of a circular track. During one of the revolutions of the block, when the block is at the bottom of its path, point A, the magnitude of the normal force exerted on the block by the track has magnitude 3.80 N. In this same revolution, when the block reaches the top of its path, point B, the magnitude of the normal force exerted on the block has magnitude 0.670 N.

How much work was done on the block by friction during the motion of the block from point A to point B? Express your answer with the appropiate units.

5. An ideal spring of negligible mass is 13.00 cm long when nothing is attached to it. When you hang a 3.35 kg object from it, you measure its length to be 14.50 cm. If you wanted to store 10.0 J of potential energy in this spring, what would be its total length? Assume that it continues to obey Hooke's law. Express your answer in centimeters to three significant figures. If there is more than one answer, separate them by a comma.