1. As a demonstration of lab safety violations, a stainlesssteel water bottle is filled with a small amount of liquidnitrogen, and then the cap is sealed on the bottle (don’t ever dothis – you could get seriously hurt). The bottle is laid on itsside on the edge of the roof of the library building, which is 14meters above the street below. When the bottle explodes, the 240gram bottle flies back onto the roof and you measure its initialvelocity to be 6.1 m/s. You can clearly see this velocity isinitially completely horizontal. The 20.0 gram cap flies off theroof also with an initial velocity that is completely horizontal.How far away from the edge of the building does the cap land? Youcan assume air resistance is negligible.

2. You get a summer job testing springs at a manufacturingplant. Every 50th spring is taken off the line and is pushed with aforce sensor a certain distance to make sure the spring constant iswithin specifications. The force sensor quits working. You devise amethod using a flat track to push a 500 gram calibration mass alongthe track and then up a ramp angled at 20°. You cover the ramp andtrack with lubrication to make it nearly frictionless, but run outbefore you can coat the entire thing, leaving a 25 cm length on theflat part of the track with friction. Using a spring with a knownspring constant of 150 N/m, you compress the spring 10 cm with themass. You release the mass and measure it to go 23.0 cm along theangled part of the ramp when it stops. (a) What is the coefficientof friction of the patch left unlubricated? (b) If the springs youare currently manufacturing are supposed to be 400 N/m constantsand you compress it 5 cm with the calibration mass, how far alongthe angled ramp should the calibration mass slide, assuming thefriction is still present?

3. You set up a small ramp in your house to do some physicsexperiments. It is a smooth metal sheet and you are using an icecube as a way to slide without friction. Your sheet is 1.42 meterslong and you prop it up at an angle of 27°. You make a large icecube of 250 grams for your experiment. a. If you allow the ice cubeto slide from the top of the ramp, how fast is it going at thebottom? b. If the ice cube falls off the top of the ramp over theedge (instead of sliding down the ramp), how fast is it going whenit hits the ground? c. If you wanted to slide the cube from thebottom of the ramp to the top, how much work would you do pushingit, assuming the speed at the bottom of the ramp and top of theramp is zero? d. How much work does gravity do during the push frompart (c)?