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From Spring 1999. Note that you should also see Problem 5 from Sample Test 1.
1. (20 points) A 1.00-kg aluminum block is connected to a 10.00-kg copper block by a light string over a frictionless pulley. The blocks are allowed to move on a fixed steel block-wedge of angle 30 degrees. The 10.00-kg block moves down the incline, and therefore the 1.00-kg block moves to the right. The coefficient of kinetic friction between the 1.00-kg block and the horizontal surface is 0.30. The coefficient of kinetic friction between the 10.00-kg block and the inclined surface is 0.20. Please look carefully at the diagram below. Find the following:
(a) (12 points) the acceleration of the two blocks.
(b) ( 5 points) the tension in the string.
(c) ( 3 points) Suppose the blocks begin their motion from rest. Please find the speed of the blocks after a time of 3.00 seconds
2. (21 points)
A special ride in the Great America amusement park will consist of a car of mass 600 kg that rides on the inside of a vertical loop of radius R = 40.0 m. The car moves counterclockwise with constant speed v = 24.0 m/s. See the schematic of the ride below.
Find the magnitude N of the normal force on the car at the
(a) (14 points) bottom of the loop.
(b) (5 points) top of the loop
(c) (2 points) at point P where the car is in a horizontal position relative to the center and is moving straight up.
3. A block of mass 2.10-kg is attached to a spring of spring constant 490.0 N/m on a horizontal surface. The block is stretched a distance d from equilibrium and released from rest. The speed of the block is 0.520 m/s when it passes through the point x = 0. The coefficient of kinetic friction between the block and the surface is 0.30.
What is d?
4. Extra Credit. From Spring 2000. A block of mass m = 0.245 kg is dropped on a spring. Just before the block strikes the spring, the speed is v = 6.4 m/s. After the block strikes the spring, the spring compresses downward a maximum distance h before the mass comes momentarily to rest. Please see the diagrams below of the system just before compression and at maximum compression. The spring constant of the spring is k = 255 N/m .
What is the distance h ?