Part A. When the disk has moved a distance of 5.3m , determine how fast it is mo
ID: 1323258 • Letter: P
Question
Part A.
When the disk has moved a distance of 5.3m , determine how fast it is moving.
Express your answer using two significant figures.
Part B.
How fast it is spinning (in radians per second).
Express your answer using two significant figures.
Part C.
How much string has unwrapped from around the rim?
Express your answer using two significant figures.
A solid uniform disk of mass 21.0 kg and radius 85.0 cm is at rest flat on a frictionless surface. The figure(Figure 1) shows a view from above. A string is wrapped around the rim of the disk and a constant force of 35.0 N is applied to the string. The string does not slip on the rim. Part A. When the disk has moved a distance of 5.3m , determine how fast it is moving. Express your answer using two significant figures. Part B. How fast it is spinning (in radians per second). Express your answer using two significant figures. Part C. How much string has unwrapped from around the rim? Express your answer using two significant figures.Explanation / Answer
1) F = ma
35.0 N = (21.0 kg)(a)
a = 35.0 N/21.0 kg
a = 1.67 m/s^2
Vf^2 - Vi^2 = 2ad
Vf^2 = 2ad (because Vi = 0 since the disk initially was at rest)
Vf = sqrt[2ad]
Vf = sqrt[2(1.67 m/s^2)(5.3 m)
Vf = 4.203 m/s --> answer
2) ?= I?, where ? is torque, I is moment of inertia, and ? angular
acceleration.
Fr = [(1/2)Mr^2]?
? = Fr/[(1/2)Mr^2]
? = (35.0N)(0.85m)/[(1/2)(21.0kg)(0.85m)^2]
? = 3.92 rad/s^2
a = (Vf - Vi)/t
t = (Vf - Vi)/a = (4.203 m/s - 0)/1.67m/s^2
= 2.52 s
?f = ?i + ?t
?f = 0 + (3.92 rad/s^2)(2.52 s)
?f = 9.88 rad/s --> answer
3) s = ?r, where ? is angular displacement, s is length of string
unwrapped from around the rim, and r is radius.
s = [(1/2)(?)(t^2)]r
s = [(1/2)(3.92 rad/s^2)(2.52 s)^2]0.850m
s = 10.58 m --->answer