CALC A block with mass m is revolving with linear speed υ 1 in a circle of radius r 1 on a frictionless horizontal surface (see Fig. E10.40). The string is slowly pulled from below until the radius of the circle in which the block is revolving is reduced to r 2 . (a) Calculate the tension T in the string as a function of r , the distance of the block from the hole. Your answer will be in terms of the initial velocity υ 1 and the radius r 1 . (b) Use W = ∫ r 1 r 2 T → ( r ) • d r → to calculate the work done by T → when r changes from r 1 to r 2 . (c) Compare the results of part (b) to the change in the kinetic energy of the block.
CALC A block with mass m is revolving with linear speed υ 1 in a circle of radius r 1 on a frictionless horizontal surface (see Fig. E10.40). The string is slowly pulled from below until the radius of the circle in which the block is revolving is reduced to r 2 . (a) Calculate the tension T in the string as a function of r , the distance of the block from the hole. Your answer will be in terms of the initial velocity υ 1 and the radius r 1 . (b) Use W = ∫ r 1 r 2 T → ( r ) • d r → to calculate the work done by T → when r changes from r 1 to r 2 . (c) Compare the results of part (b) to the change in the kinetic energy of the block.
CALC A block with mass m is revolving with linear speed υ1 in a circle of radius r1 on a frictionless horizontal surface (see Fig. E10.40). The string is slowly pulled from below until the radius of the circle in which the block is revolving is reduced to r2. (a) Calculate the tension T in the string as a function of r, the distance of the block from the hole. Your answer will be in terms of the initial velocity υ1 and the radius r1. (b) Use
W
=
∫
r
1
r
2
T
→
(
r
)
•
d
r
→
to calculate the work done by
T
→
when r changes from r1 to r2. (c) Compare the results of part (b) to the change in the kinetic energy of the block.
In a popular amusement park ride, a rotating cylinder of radius 3.00 m is set in rotation at an angular speed of 5.00 rad/s, as in Figure P7.75. The floor then drops away, leaving the riders suspended against the wall in a vertical position. What minimum coefficient of friction between a rider’s clothing and the wall is needed to keep the rider from slipping? Hint: Recall that the magnitude of the maximum force of static friction is equal to μsn, where n is the normal force—in this case, the force causing the centripetal acceleration.
A yo-yo-shaped device mounted on a horizontal frictionless axis is used to lift a 37 kg box as shown in the figure. The outer radius R of the device is 1.0 m, and the radius r of the hub is 0.33 m. When a constant horizontal force F→app of magnitude 160 N is applied to a rope wrapped around the outside of the device, the box, which is suspended from a rope wrapped around the hub, has an upward acceleration of magnitude 0.98 m/s2. What is the rotational inertia of the device about its axis of rotation?
A conical pendulum is formed by attaching a ball of mass m to a string of length L, then allowing the ball to move in a horizontal circle of radius r. The string traces out the surface of a cone, hence the name.
Find an expression for the tension T in the string (expressing the answers in terms of the variables L, m, r). Find an expression for the ball's angular speed (in terms of the variables L and r). Lastly, what is the tension for a 500 gg ball swinging in a 20-cmcm-radius circle at the end of a 1.0-mm-long string?
Given the peculiar circumstances, I was forced to self-teach this material and I am incredibly confused as to how to approach these problems. Can you please help me?
Thank you :)
Chapter 10 Solutions
University Physics with Modern Physics (14th Edition)
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