Problem 1 The system shown below has frictionless pulleys and the strings have negligible mass. The system is initially at rest when the lower string
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1 Problem 1 The system shown below has frictionless pulleys and the strings have negligible mass. The system is initially at rest when the lower string is cut. For y = 2 m, what is the speed of the objects when they are at the same height?
2 Problem 2 A 1383 kg roller coaster car starts from rest at a height H = 24 m (see figure) above the bottom of a 15.0 m diameter loop. If friction is negligible, determine the downward force of the rails on the car when the upside-down car is at the top of the loop.
3 Problem 2 (cont.)
4 Problem 3 The 2 kg block slides down a frictionless curved ramp, starting from rest at a height of h = 4 m. The block then slides d = 10 m on a rough horizontal surface before coming to rest. (a) What is the speed of the block at the bottom of the ramp?
5 Problem 3 (cont. (b) What is the energy dissipated by friction? (c) What is the coefficient of friction between the block and the horizontal surface?
6 Problem 4 In the figure below, the coefficient of kinetic friction between m1 = 3.8 kg and the shelf is (a) Find the energy dissipated by friction when the block of mass m2 = 2.2 kg falls a distance. (b) Find the change in the mechanical energy Emech of the two-block-earth system during the time it takes the block of mass m2 falls a distance y. (c) If they started from rest, use your result for Part (b) to find the speed of either block after the block of mass m2 falls a distance y = 2 m.
7 Problem 4 (cont.)
8 Problem 5 Starting from rest, a mass m = 13 kg is pulled along a horizontal floor with NO friction for a distance d = 8.5 m. Then the mass is pulled up an incline that makes an angle θ = 25 with the horizontal and has a coefficient of kinetic friction μk = The entire time the massless rope used to pull the block is pulled parallel to the incline at an angle of θ = 25 (thus on the incline it is parallel to the surface) and has a tension T = 51 N. (a) What is the work done by tension before the block goes up the incline? (On the horizontal surface.) (b) What is the speed of the block right before it begins to travel up the incline?
9 Problem 5 (cont.) (c) What is the work done by friction after the block has traveled a distance x = 3.6 m up the incline? (Where x is measured along the incline.) (d) What is the work done by gravity after the block has traveled a distance x = 3.6 m up the incline? (Where x is measured along the incline.)
10 Problem 5 (cont.) (e) How far up the incline does the block travel before coming to rest? (Measured along the incline.)
11 Problem 5e (cont.)
12 Problem 6 You plan to take a trip to the moon. Since you do not have a traditional spaceship with rockets, you will need to leave the earth with enough speed to make it to the moon. Some information that will help during this problem: mearth = x kg rearth = x 10 6 m mmoon = 7.36 x kg rmoon = x 10 6 m dearth to moon = x 10 8 m (center to center) G = x N*m 2 /kg 2 (a) On your first attempt you leave the surface of the earth at v = 5534 m/s. How far from the center of the earth will you get?
13 Problem 6 (cont.) (b) Since that is not far enough, you consult a friend who calculates (correctly) the minimum speed needed as vmin = m/s. If you leave the surface of the earth at this speed, how fast will you be moving at the surface of the moon? Hint carefully write out an expression for the potential and kinetic energy of the ship on the surface of earth, and on the surface of moon. Be sure to include the gravitational potential energy of the earth even when the ship is at the surface of the moon!
14 Problem 6 (cont.) (c) A change in which of the following would change the minimum velocity needed to make it to the moon? 1) the mass of the earth 2) the radius of the earth 3) the mass of the spaceship
15 Problem 7 A dumbbell consisting of two balls of mass m connected by a massless 0.96mlong rod rests on a frictionless floor against a frictionless wall until it begins to slide down the wall, as in the figure below. Find the speed of the bottom ball at the moment when it equals the speed of the top ball. (Treat the dumbbell as two point-like particles separated by a massless 0.96m rod. Also assume that the initial state of the dumbbell is vertical and that image shows the dumbbell some time after it has fallen.)
16 Problem 7 (cont.)
17 Problem 7 (cont.)
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