This preview shows page 1. Sign up to view the full content.
Unformatted text preview: Dr. Galeazzi [1.] PHY205 Test #2 March 7, 2010 This problem has five multiple choice questions. Circle the best answer in each case. . What is the [1A.] The drag force on a parachute jumper of mass m is given by maximum speed the jumper can reach? Maximum speed for 0 0 [1B.] A toy train with mass m moves at constant speed on a circular track of radius R. If the train completes one lap in a time T, what is the magnitude of the net force acting on the train? 2 2 4 [1C.] A ball with mass m is hanging from a chain with mass m/2, which, in turn, is connected to the ceiling. What are the magnitudes of the tension at the top and bottom of the chain respectively? At the top: At the bottom: 0 0 [1D.] A cart with mass m is initially moving on a horizontal plane at speed v. A force which increases with distance as is then applied to the cart until, after a distance L, its speed doubles. If the coefficient of kinetic friction of the cart is , find the net work on the cart from where the force is first applied, to the distance L. Work energy theorem: 2 [1E.] If you are in the seat of a ferris wheel and, at the top of the wheel, you feel weightless, which of the following statements must be true: To feel weightless the ferris must be moving, therefore the seat is moving of circular motion (not necessarily uniform). Therefore the seat (and yourself) is accelerating (centripetal acceleration). 2 Dr. Galeazzi PHY205 Test #2 March 7, 2010 [2.] A horizontal spring with coefficient k is initially compressed a length L and "loaded" with a block of mass m, which is not attached to the spring. Spring and block are sitting on a horizontal surface which is frictionless in the area of the spring.
[a] Calculate the work done by the spring once it is released. [b] Find the speed of the block right when it is released by the spring. . How [c] After the mass in released, it enters a rough region with coefficient of kinetic friction far will the block travel in this region before it stops? Write your results in terms of k, L, m, each answer. , and g. Remember to check the dimensions/units for [a] Setting the origin where the spring is not compressed, we get: 1 2 1 2 OK . Check units: k, multiplied by a distance, gives a force; its units are Work is a force multiplied by a distance, its units are [b] In the area of the spring, the only force producing work is that of the spring (weight and normal force are perpendicular to the displacement). Using the work energy theorem: 1 2 Check units: 2 2 1 2 OK [c] Once the block is released by the spring the only force acting on it is friction, which is constant and has value . If the block travels a distance d before stopping, its work is Using the work energy theorem: 1 2 Where we used the fact that, when the block stops, its kinetic energy is zero. It follow that 1 1 1 2 2 2 2 Check units: OK 3 Dr. Galeazzi PHY205 Test #2 March 7, 2010 [3.] An amusement park ride consists of small cars of mass m attached to steel cables of length L (cable 1). The cables have negligible mass and are attached to a spinning post (see figure). A second horizontal cable of negligible mass (cable 2) connects the cars to the post and, when fully stretched, limits the maximum angle of the top cable to a value . of the ride to fully stretch the cable 2? [a] What is the minimum angular velocity (HINT: the minimum angular velocity is the one for which cable 2 is fully stretched, but has not tension) [b] If the ride is spinning with angular velocity , what is the tension in cable 2? in cable 1? [c] For the same angular velocity of part [b], what is the tension Write your results in terms of m, L, , each answer. , and g. Remember to check the dimensions/units for [a] Using Newton's second law in the x and y directions, we get: sin cos sin 0 cos Check units: OK cos [b, c] Adding the tension in cable 2, we get: sin cos Check units: [b] [c] sin 0 sin cos OK OK cos sin 4 Dr. Galeazzi PHY205 Test #2 5 is given by sin , March 7, 2010 [4.] The position of a particle with mass with [a] [b] [c] 4 and . Find the force acting on the particle as a function of time, . Find the force acting on the particle as a function of the particle's position Find the net work done on the particle between 0 and . . Write your results in terms of the quantities (and units) given. [a] 20 sin sin 5 [c] At At 0, , 0 0, 0 sin 5 ; ; cos 0. cos ; sin . and . sin , we get 5 4 sin sin , [b] Comparing Integrating: 5 40 . 16 Also, using the workenergy theorem: 0 5 16 40 . 5 Dr. Galeazzi PHY205 Test #2 March 7, 2010 [5.] Block A in the figure has mass and coefficient of static friction with respect to the incline's surface. The masses of both the cable and the pulley are negligible. [a] What is the minimum value of mass so that the two masses do not move? so that the two masses do not move? [b] What is the maximum value of mass [c] If the two blocks are initially at the same height, and the cable is cut, which block will reach the surface of the table underneath with the higher speed? Explain. Write your results in terms of each answer. , , , and . Remember to check the dimensions/units for [a] Using Newton's first law for block B, the magnitude of the tension in the string is given by: . Choosing the xaxis parallel to the incline, and the yaxis perpendicular to it, the forces acting on block A are weight, tension, normal force, and static friction. The maximum value the static friction can have is , and it may point up the incline or down the incline. The minimum value of is determined when the static friction is equal to the maximum value and it is pointing up. Newton's second law for the x and y directions then becomes: sin cos Check units: 0 0 OK sin cos sin cos is determined when the static friction is equal to the maximum [b] The maximum value of value and it is pointing down. Newton's second law for the x and y directions then becomes: sin cos Check units: 0 0 OK sin cos sin cos [c] Both blocks travel the same vertical displacement, so the work done by gravity is the same. However, block A is also subject to friction, which produces negative work. The work energy theorem therefore predicts that block A will have less speed, or block B will be faster. 6 ...
View
Full
Document
This note was uploaded on 01/08/2012 for the course PHYSICS 205 taught by Professor Galeazzi during the Fall '11 term at University of Miami.
 Fall '11
 Galeazzi
 Force, Mass

Click to edit the document details