Name Period Date Review #1 DUE: Wednesday, April 23 [1] The 100-kg box is being pulled in the x-direction by a student. The box slides across a rough surface, and its position varies with time, t, according to the equation: x=0.5t 2 + 2t, where x is in meters and t is in seconds. (a) Determine the speed of the box at time t=0. (b) Determine the following as a function of t: i. The Kinetic energy of the box. ii. The net force acting on the box. iii. The power being delivered to the box. (c) Calculate the net work being done on the box from t=1 to t=2 seconds. (d) Indicate below whether the work done on the box by the student would be greater than, less than or equal to the answer to part (c). Greater Than Less Than Equal to Justify your answer answer. [2] An apparatus to determine coefficients of friction is shown above. The box is slowly rotated counterclockwise. When the box makes an angle θ with the horizontal, the block of mass m just starts to slide, and at this instant the box is stopped from rotating. Thus at angle θ, the block slides a distance d, hits the spring of force constant k, and compresses the spring a distance x before coming to rest. In terms of the given quantities, derive an expression for each of the following. a. µ s the coefficient of static friction. b. ΔE, the loss in total mechanical energy of the block-spring system from the start of the block down the incline to the moment at which it comes to rest on the compressed spring. c. µ k, the coefficient of kinetic friction. Review #1 1 4/21/14
[3] Two gliders move freely on an air track with negligible friction, as shown. Glider A has a mass of 0.90 kg and glider B has a mass of 0.60 kg. Initially, glider A moves toward glider B, which is at rest. A spring of negligible mass is attached to the right side of glider A. Strobe photography is used to record successive positions of glider A at 0.10 s intervals over a total time of 2.00 s, during which time it collides with glider B. The following diagram represents the data for the motion of glider A. Positions of glider A at the end of each 0.10s interval are indicated by the symbol A against a metric ruler. The total elapsed time t after each 0.50 s is also indicated. a. Determine the average speed of glider A for the following time intervals. i. 0.10 s to 0.30 s ii. 0.90 s to 1.10 s iii. 1.70 s to 1.90 s b. On the axes below, sketch a graph, consistent with the data above, of the speed of glider A as a function of time t for the 2.00 s interval. c. i. Use the data to calculate the speed of glider B immediately after it separates from the spring. ii. On the axes below, sketch a graph of the speed of glider B as a function of time t. Review #1 2 4/21/14
A graph of the total kinetic energy K for the two-glider system over the 2.00 s interval has the following shape. K o is the total kinetic energy of the system at time t = 0. d. i. Is the collision elastic? Justify your answer. ii. Briefly explain why there is a minimum in the kinetic energy curve at t = 1.00 s. Review #1 3 4/21/14
[4] A cloth tape is wound around the outside of a uniform solid cylinder (mass M, radius R) and fastened to the ceiling as shown in the diagram above. The cylinder is held with the tape vertical and then released from rest. As the cylinder descends, it unwinds from the tape without slipping. The moment of inertia of a uniform solid cylinder about its center is 1 2 MR2. a. On the circle draw vectors showing all the forces acting on the cylinder after it is released. Label each force clearly. b. In terms of g, find the downward acceleration of the center of the cylinder as it unrolls from the tape. c. While descending, does the center of the cylinder move toward the left, toward the right, or straight down? Explain. [5] A small block of mass m slides on a horizontal frictionless surface as it travels around the inside of a hoop of radius R. The coefficient of friction between the block and the wall is µ; therefore, the speed v of the block decreases. In terms of m, R. µ, and v, find expressions for each of the following. a. The frictional force on the block b. The block's tangential acceleration dv/dt c. The time required to reduce the speed of the block from an initial value v0 to vo/3 Review #1 4 4/21/14
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