Physics for Scientists and Engineers, Vol. 1
6th Edition
ISBN: 9781429201322
Author: Paul A. Tipler, Gene Mosca
Publisher: Macmillan Higher Education
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Chapter 9, Problem 75P
To determine
Speed of the car as it hits the water.
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Vlad needs to draw water from a deep well. He is using a bucket that is connected by rope (negligible mass) to a wooden axle at the top of the well. By cranking a handle at the end of the axle, Vlad is able to unwind the rope around the axle and move the bucket downward. The radius of the axle is R = 30 cm. The bucket is traveling downward at speed vi = 25 cm/s when the handle slips out of Vlad’s hand. As the rope unwinds and the bucket falls downward, the axle spins freely with an angular acceleration whose magnitude is α = 4.5 rad/s^2. The bucket falls through a distance of d = 7.0 m before crashing into the water.
1. What is the angular speed ωf of the axle when the bucket first hits the water?
2. As d → 0, what limit does ωf approach and why?
2. A cylindrical plug A of mass ma = 0.5
B
kg is released from rest at point B and
slides down smooth circular guide with a
radius r= 2 m, as shown in the Figure.
The plug strikes the block C of mass mc
= 1.2 kg and becomes embedded in it.
After the impact plug-block system
-
travel a rough surface S with coefficient
of kinetic friction uk = 0.3. Neglect the
air friction for the following calculations.
(a)
Calculate the work done on the plug due to the displacement in the circular
path.
(b)
Calculate the velocity of the plug-block system just after the strike.
(c)
Before coming to rest how much distance the block and plug will travels. Also
calculate the deceleration rate in this distance.
A 15.0 kg bucket of water is suspended by a very light rope wrapped around a solid uniform cylinder 0.300 m in diameter with mass 12.0 kg. The cylinder pivots on a frictionless axle through its center. The bucket is released from rest at the top of a well and falls 10.0 m to the water. (a) What is the tension in the rope while the bucket is falling? (b) With what speed does the bucket strike the water? (c) What is the time of fall? (d) While the bucket is falling, what is the force exerted on the cylinder by the axle?
Chapter 9 Solutions
Physics for Scientists and Engineers, Vol. 1
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- 2. A cylindrical plug A of mass ma = 0.5 kg is released from rest at point B and slides down smooth circular guide with a radius r= 2 m, as shown in the Figure. The plug strikes the block C of mass mc = 1.2 kg and becomes embedded in it. After the impact plug-block system travel a rough surface S with coefficient of kinetic friction Hk = 0.3. Neglect the air friction for the following calculations. (a) path. Calculate the work done on the plug due to the displacement in the circular (b) Calculate the velocity of the plug-block system just after the strike. (c) Before coming to rest how much distance the block and plug will travels. Also calculate the deceleration rate in this distance.arrow_forwardA 15.0-kg bucket of water is suspended by a very light rope wrapped around a solid uniform cylinder 0.300 m in diameter with mass 12.0 kg. The cylinder pivots on a frictionless axle through its center. The bucket is released from rest at the top of a well and falls 10.0 m to the water. (a) What is the tension in the rope while the bucket is falling? (b) With what speed does the bucket strike the water? (c) write the kinetic equation as the bucket sink into the water, suppose the resistance force is proportional to the speed, the volume of bucket is V, and draw the free-body diagram.arrow_forwardA yo-yo is constructed of three disks: two outer disks of mass MM, radius RR, and thickness dd, and an inner disk (around which the string is wrapped) of mass mm, radius rr, and thickness dd. The yo-yo is suspended from the ceiling and then released with the string vertical (see figure below). Calculate the tension in the string as the yo-yo falls. Note that when the center of the yo-yo moves down a distance y, the yo-yo turns through an angle y/r, which in turn means that the angular speed ω is equal to Vcm/r. Use the following as necessary: M, R, d, m, r, and g for the acceleration due to gravity.)arrow_forward
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