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Review. A piece of putty is initially located at point A on the rim of a grinding wheel rotating at constant angular speed about a horizontal axis. The putty is dislodged from point A when the diameter through A is horizontal. It then rises vertically and returns to A at the instant the wheel completes one revolution. From this information, we wish to find the speed v of the putty when it leaves the wheel and the force holding it to the wheel. (a) What analysis model is appropriate for the motion of the putty as it rises and falls? (b) Use this model to find a symbolic expression for the time interval between when the putty leaves point A and when it arrives back at A, in terms of v and g. (c) What is the appropriate analysis model to describe point A on the wheel? (d) Find the period of the motion of point A in terms of the tangential speed v and the radius R of the wheel. (e) Set the time interval from part (b) equal to the period from part (d) and solve for the speed v of the putty as it leaves the wheel. (f) If the mass of the putty is m, what is the magnitude of the force that held it to the wheel before it was released?
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Chapter 6 Solutions
Physics for Scientists and Engineers
- A small particle of mass m is pulled to the top of a friction less half-cylinder (of radius R) by a light cord that passes over the top of the cylinder as illustrated in Figure P7.15. (a) Assuming the particle moves at a constant speed, show that F = mg cos . Note: If the particle moves at constant speed, the component of its acceleration tangent to the cylinder must be zero at all times. (b) By directly integrating W=Fdr, find the work done in moving the particle at constant speed from the bottom to the top of the hall-cylinder. Figure P7.15arrow_forwardA 0.50-kg object moves in a horizontal circular track with a radius of 2.5m. An external force of 3.0N, always tangent to the track, causes the object to speed up as it goes around. The work done by the external force as the mass makes one revolution is: 0. 47J 59J 94J O 122Jarrow_forwardThe figure shows a thin rod, of length L = 2.20 m and negligible mass, that can pivot about one end to rotate in a vertical circle. A heavy ball of mass m = 8.10 kg is attached to the other end. The rod is pulled aside to angle 00 = 8° and released with initial velocity V 0. (a) What is the speed of the ball at the lowest point? (b) Does the speed increase, decrease, or remain the same if %3D the mass is increased? 3.arrow_forward
- The figure below shows a block of mass 0.5 kg moving on the inside surface of a vertical circular track of radius R = 1 m. The block has a speed vB = when it is at point B at the bottom of the circular track. The track is not smooth and a force of kinetic friction 12 m/s of magnitude 7.0 N acts on the block while it slides around the track. The frictional force on the block is always tangent to the track. Find the speed of the block when it is at point T at the top of the track. (Hint: the circumference of the circular track is 2nR.) T R® Barrow_forwardTo test the speed of a bullet, you create a pendulum by attaching a 5.80 kg wooden block to the bottom of a 1.60 m long, 0.800 kg rod. The top of the rod is attached to a frictionless axle and is free to rotate about that point. You fire a 10 g bullet into the block, where it sticks, and the pendulum swings out to an angle of 39.0°. What was the speed of the bullet?arrow_forwardA 10.0-kg bob is attached to a rod whose length is 10.0 m. The right end of the rod is fixed, and the bob is released from rest. a) Determine the speed of the bob when it is below the pivot point (vertical angle is zero). b) Determine the tension in the rod when the bob is below the pivot point. hint: to determine the speed of the bob when it is below the pivot point, you will need to use Calculus.arrow_forward
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- A cord is wrapped around a pulley that is shaped like a disk of mass mand radius r. The cord's free end is connected to a block of mass M. The block starts from rest and then slides down an incline that makes an angle 0 with the horizontal as shown in Figure P10.48. The coefficient of kinetic friction between block and incline is u. (a) Use energy methods to show that the block's speed as a function of position d down the incline is 4Mgd(sin 0 – µ cos 0) т+ 2M (b) Find the magnitude of the acceleration of the block in terms of µ, m, M, g, and 0. m M Figure P10.48arrow_forwardThe puck in the figure below has a mass of 0.260 kg. Its original distance from the center of rotation is 40.0 cm, and it moves with a speed of 90.0 cm/s. The string is pulled downward 15.0 cm through the hole in the frictionless table. Determine the work done on the puck. (Hint: Consider the change of kinetic energy of the puck.)arrow_forwardA playground ride consists of a disk of mass M=48 kg and radius R=1.6 m mounted on a low-friction axle (see figure below). A child of mass m=22 kg runs at speed v=2.8 m/s on a line tangential to the disk and jumps onto the outer edge of the disk. What is the change in the kinetic energy of the child plus the disk?arrow_forward
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