An object with a mass of m = 4.65 kg is attached to the free end of a light stri

Question

An object with a mass of m = 4.65 kg is attached to the free end of a light string wrapped around a reel of radius R = 0.270 m and mass of M = 3.00 kg. The reel is a solid disk, free to rotate in a vertical plane about the horizontal axis passing through its center as shown in the figure below. The suspended object is released from rest 6.70 m above the floor.

(a) Determine the tension in the string.
N

(b) Determine the magnitude of the acceleration of the object.
m/s2

(c) Determine the speed with which the object hits the floor.
m/s

(d) Verify your answer to part (c) by using the isolated system (energy) model. (Do this on paper. Your instructor may ask you to turn in this work.)

Explanation / Answer

Tension in string = T

for the body, mg - T = ma
for the disc, Tr = Ia/r => TTr^2 = Ia

mg - Ia/r^2 = ma
mg - 0.5ma =ma
g/1.5 = a
a = 6.533 m/s/s

a. T = m(g-a) = 15.19 N
b. a = 6.533 m/s/s
c. 2*6.7*6.533 = v^2
   v = 9.356 m/s

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects