You accidentally knock a full bucket of water off the side of the well shown in the figure. The bucket plunges a distance L to the bottom of the well. Attached to the bucket is a light rope that is wrapped around the crank cylinder. The mass of the bucket plus water within it is M. The crank is a solid cylinder which has a radius of R and mass of m. The moment of inertia of a solid cylinder through its long axis is I = mR². (Assume the small handle's inertia is negligible in comparison with the crank cylinder.) a) Set up the energy equation for when the bucket hits the bottom. Find an expression for how fast the bucket moves as it hits the bottom of the well. Your expression may contain the variables, m, M, R, L and any constants needed. b) How fast is the handle turning when the bucket hits the bottom? Your expression may contain the variables, m, M, R, L and any constants needed. c) If the mass of the bucket plus water is M = 10.1 kg, the radius of crank cylinder R = 0.0800 m, the mass of crank cylinder is m = 3.80 kg and the bucket plunge L = 15.0 m to the bottom of the well, find how fast the handle is turning when the bucket hits the bottom. Enter your answer in units of rad/s with 3 sig figs.
You accidentally knock a full bucket of water off the side of the well shown in the figure. The bucket plunges a distance L to the bottom of the well. Attached to the bucket is a light rope that is wrapped around the crank cylinder. The mass of the bucket plus water within it is M. The crank is a solid cylinder which has a radius of R and mass of m. The moment of inertia of a solid cylinder through its long axis is I = mR². (Assume the small handle's inertia is negligible in comparison with the crank cylinder.) a) Set up the energy equation for when the bucket hits the bottom. Find an expression for how fast the bucket moves as it hits the bottom of the well. Your expression may contain the variables, m, M, R, L and any constants needed. b) How fast is the handle turning when the bucket hits the bottom? Your expression may contain the variables, m, M, R, L and any constants needed. c) If the mass of the bucket plus water is M = 10.1 kg, the radius of crank cylinder R = 0.0800 m, the mass of crank cylinder is m = 3.80 kg and the bucket plunge L = 15.0 m to the bottom of the well, find how fast the handle is turning when the bucket hits the bottom. Enter your answer in units of rad/s with 3 sig figs.
Principles of Physics: A Calculus-Based Text
5th Edition
ISBN:9781133104261
Author:Raymond A. Serway, John W. Jewett
Publisher:Raymond A. Serway, John W. Jewett
Chapter10: Rotational Motion
Section: Chapter Questions
Problem 75P: A wad of sticky clay with mass m and velocity vi is fired at a solid cylinder of mass M and radius R...
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Transcribed Image Text:You accidentally knock a full bucket of water off the side of the well shown in the
figure. The bucket plunges a distance L to the bottom of the well. Attached to the
bucket is a light rope that is wrapped around the crank cylinder. The mass of the
bucket plus water within it is M. The crank is a solid cylinder which has a radius of R
and mass of m. The moment of inertia of a solid cylinder through its long axis is
I =
mR. (Assume the small handle's inertia is negligible in comparison with the
crank cylinder.)
a) Set up the energy equation for when the bucket hits the bottom. Find an
expression for how fast the bucket moves as it hits the bottom of the well. Your
expression may contain the variables, m, M, R, L and any constants needed.
b) How fast is the handle turning when the bucket hits the bottom? Your expression
may contain the variables, m, M, R, L and any constants needed.
c) If the mass of the bucket plus water is M = 10.1 kg, the radius of crank cylinder R =
0.0800 m, the mass of crank cylinder is m = 3.80 kg and the bucket plunge L = 15.0
m to the bottom of the well, find how fast the handle is turning when the bucket hits
the bottom. Enter your answer in units of rad/s with 3 sig figs.
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