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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
EBK PHYSICS FOR SCIENTISTS AND ENGINEER
- 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_forwardTo form a pendulum, a 0.050 kg ball is attached to one end of a rod of length 1.2 m and negligible mass, and the other end of the rod is mounted on a pivot. The rod is rotated until it is straight up, and then it is released from rest so that it swings down around the pivot. When the ball reaches its lowest point, what are (a) its speed and (b) the tension in the rod? Next, the rod is rotated until it is horizontal, and then it is again released from rest. (c) At what angle from the vertical does the tension in the rod equal the weight of the ball? (d) If the mass of the ball is increased, does the answer to (c) increase, decrease, or remain the same? (a) Number i 4.8e0 (b) Number i 1.4e0 (c) Number i 19. (d) increase Units Units Units m/s N °(degrees)arrow_forwardA puck of mass m = 47.0 g is attached to a taut cord passing through a small hole in a frictionless, horizontal surface (see figure below). The puck is orbiting with initial speed vi = 1.60 m/s in a circle of radius ri = 0.310 m. The cord is then slowly pulled from below, decreasing the radius of the circle to r = 0.130 m. How much work is done (in J) by the hand in pulling the cord so that the radius of the puck's motion changes from 0.310 m to 0.130 m?arrow_forward
- A uniform thin rod of length 0.310 m and mass 5.74 kg is suspended freely from one end. It is pulled to the side an angle 51.0 degrees and released. If friction can be ignored, what is the speed of its free end (in m/s), at the lowest point?arrow_forwardYou push a .50kg block against a spring (k=3100 N/m),compressing it by .12m. The block is then released from rest and the spring pushes the block away. The spring and the block lose contact and the block collides with a second block of twice the mass. The two blocks slide together down a frictionless track consisting of a flat straightaway and a vertical, semi-circle of radius 40cm. What is the speed of the blocks when they have travelled halfway up the semicircle part of the track? What is the magnitude of the normal force on the two blocks at that same location?arrow_forwardTo form a pendulum, a 0.092 kg ball is attached to one end of a rod of length 0.84 m and negligible mass, and the other end of the rod is mounted on a pivot. The rod is rotated until it is straight up, and then it is released from rest so that it swings down around the pivot. When the ball reaches its lowest point, what are (a) its speed and (b) the tension in the rod? Next, the rod is rotated until it is horizontal, and then it is again released from rest. (c) At what angle from the vertical does the tension in the rod equal the weight of the ball? (d) If the mass of the ball is increased, does the answer to (c) increase, decrease, or remain the same? (a) Number i (b) Number (c) Number (d) Units Units Units #arrow_forward
- A porter governor, its central load is 18 kg and the weight of each ball is 2 kg. The top arms are 25 cm while the bottom arms are each 30 cm long and all arms pivoted on the axis of rotation. The friction of the sleeve is 14 N. If the top arms make 45 ° with the axis of rotation in equilibrium position, find the speed of the governor at that position.arrow_forwardTo form a pendulum, a 0.024 kg ball is attached to one end of a rod of length 0.70 m and negligible mass, and the other end of the rod is mounted on a pivot. The rod is rotated until it is straight up, and then it is released from rest so that it swings down around the pivot. When the ball reaches its lowest point, what are (a) its speed and (b) the tension in the rod? Next, the rod is rotated until it is horizontal, and then it is again released from rest. (c) At what angle from the vertical does the tension in the rod equal the weight of the ball? (d) If the mass of the ball is increased, does the answer to (c) increase, decrease, or remain the same? (a) Number i Units (b) Number i Units (c) Number i Unitsarrow_forwardThe 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_forward
- An amusing trick is to press a finger down on a marble on a horizontal table top, in such a way that the marble is projected along the table with an initial linear speed v and an initial backward rotational speed ω about a horizontal axis perpendicular to v. The coefficient of sliding friction between marble and top is constant. The marble has radius R. If the marble skids to a stop and then starts returning toward its initial position, with a final constant speed of 0.620v, what was ω in terms of v and R? Hint for part (b): When the marble rolls without slipping, the relationship between speed and angular speed is v = ωR.arrow_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 group of engineering students constructs a sun-powered car and tests on a circular track of 300-meter radius. The car with a mass of 210 kg including the passenger and the driver, starts from rest. The total tangential components of force on the car is EF, = 125 – 2.50D, where D is the distance the car travels along the track from the point where it starts. a. When D=30m, compute the work done by the car. b. When D=30m, compute for its velocity. c. What is the magnitude of the total horizontal force exerted on the car by the road when the car travels D=30m?arrow_forward
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