A bucket of water of mass 14.7kg is suspended by a rope wrapped around a windlas
ID: 1289450 • Letter: A
Question
A bucket of water of mass 14.7kg is suspended by a rope wrapped around a windlass, that is a solid cylinder with diameter 0.310m with mass 11.5kg . The cylinder pivots on a frictionless axle through its center. The bucket is released from rest at the top of a well and falls a distance 10.6m to the water. You can ignore the weight of the rope.
1.
What is the tension in the rope while the bucket is falling?
Take the free fall acceleration to be g = 9.80m/s2 .
2.
With what speed does the bucket strike the water?
Take the free fall acceleration to be g = 9.80m/s2 .
3.
What is the time of fall?
Take the free fall acceleration to be g = 9.80m/s2 .
4.
While the bucket is falling, what is the force exerted on the cylinder by the axle?
Take the free fall acceleration to be g = 9.80m/s2 .
Explanation / Answer
on bucket :
14.7g - T =14.7a
on cy;ionder :
T x r = (mr^2/2) x (a/r)
T = 11.5a/2 = 5.75a
add them,
14.7g = (14.7 + 5.75)a
a =7.04 m/s2
T = 5.75 a =40.51 N
2. v^2- u ^2 = 2ad
v^2 - 0 = 2x 7.04 x 10.6
v = 12.22 m/s
3. v = u +at
t = (12.22 - 0) / 7.04 =1.74 sec
4. F = T = 40.51 N
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