You have 1.5 hours to answer 5 questions on this exam. The last question is optional. Please answer each question only on the sheet provided for this problem, using the back if necessary. Please write the name and recitation section on each sheet at the top of the page.
You must indicate the reasoning and show all the steps.
If you are unable to obtain the answer to part of a problem and you need the answer to solve the subsequent parts, use an appropriate symbol for the answer to the previous part and solve in terms of that symbol.
1. (20 points) A weight w is suspended under a horizontal ceiling by two strings inside one vertical plane. The angles that the strings make with the ceiling are 30o and 45o respectively.
2. (25 points) A 10kg box is on a flat cart. A person is dragging the cart up the loading ramp. The ramp has a slope angle of 36.9o. The static friction coefficient ans the kinetic friction coefficient between the box and the cart are 0.95 and 0.8 respectively.
3. (25 points) A rock is thrown into the air from the roof with an initial velocity 10m/s and an angle 37o above the horizontal direction. The roof is 50m above the ground (ignoring air resistance).
4. (25 points) The apparent weight w' of an object is the upward force exerted by its supporting surface. A passenger on a Ferris wheel moves 3 revolutions/min in a vertical circle of radius 5m,
5. (15 points) A train moving with a constant velocity takes an emergency brake. An apple slips the table and drops on the floor at a distance 0.5m in front of the table before the train stops. The table is 1m high. Find the acceleration of the train. Ignore the friction between the apple and the table. You must give all the reasonings.