Rotational and Translational Motion

In summary: F=maand realizing that the torque is also equal to the tension times the radius of the cylinder. Therefore, you can set those two torque formulas equal to each other and solve for the tension.
  • #1
doopokko
4
0

Homework Statement



A bucket of water of mass 14.2 kg is suspended by a rope wrapped around a windlass, that is a solid cylinder with diameter 0.350 m with mass 12.1 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 a distance 11.0 m to the water. You can ignore the weight of the rope.

Solve for:
1) tension in the rope
2) time before the bucket hits the water
3) speed at which the bucket hits the water
4) force exerted on the cylinder by the axle during the fall

Homework Equations



Torque=R*F*sin(phi)
Torque=I*alpha
I=(M*R^2)/2

The Attempt at a Solution



M=12.1 kg (mass of cylinder)
R=0.175 (radius of cylinder)
m=14.2 (mass of bucket)

Torque = 0.175 * Tension = 1/2 * 12.1 * 0.175^2 * alpha

Torque = 0.175 * Tension = 0.18528125 * alpha

1.05875 * alpha = Tension

Weight = 14.2 * 9.8 = 139.16

ForceNet (on bucket) = Weight - Tension = m*a
ForceNet = 139.16 - Tension = 14.2 * a
139.6 - 1.05875*alpha = 14.2 * a

Tension = (1/2) * M * a

Tension = 41.57619

But I've been told that this isn't the correct answer. Can somebody set me straight, please?
 
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  • #2
There shouldn't be problems, as long as the rope is assumed to be wrapped on the rim of the cylinder throughout the whole process.
 
  • #3
doopokko said:

Homework Statement



A bucket of water of mass 14.2 kg is suspended by a rope wrapped around a windlass, that is a solid cylinder with diameter 0.350 m with mass 12.1 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 a distance 11.0 m to the water. You can ignore the weight of the rope.

Solve for:
1) tension in the rope
2) time before the bucket hits the water
3) speed at which the bucket hits the water
4) force exerted on the cylinder by the axle during the fall

Homework Equations



Torque=R*F*sin(phi)
Torque=I*alpha
I=(M*R^2)/2

The Attempt at a Solution



M=12.1 kg (mass of cylinder)
R=0.175 (radius of cylinder)
m=14.2 (mass of bucket)

Torque = 0.175 * Tension = 1/2 * 12.1 * 0.175^2 * alpha

Torque = 0.175 * Tension = 0.18528125 * alpha

1.05875 * alpha = Tension

Weight = 14.2 * 9.8 = 139.16

ForceNet (on bucket) = Weight - Tension = m*a
ForceNet = 139.16 - Tension = 14.2 * a
139.6 - 1.05875*alpha = 14.2 * a

Tension = (1/2) * M * a

Tension = 41.57619

But I've been told that this isn't the correct answer. Can somebody set me straight, please?

It looks pretty good to me. I think you've got it right.

edit: Worked it out, got the same answer. Can't see why it would be wrong...:confused:
 
Last edited:
  • #4
Hahaha, I went through again and it turns out that that really was the right answer after all. I think there are just some wires crossed in my brain.

Thanks to everyone who looked this over, though.
 
  • #5
Hey guys, why is the tension 1/2 * M * a ? Am a bit confused about that..
 
  • #6
Dupain said:
Hey guys, why is the tension 1/2 * M * a ? Am a bit confused about that..
That fact can be deduced by combining these formulas (plus one other):
doopokko said:
Torque=R*F*sin(phi)
Torque=I*alpha
I=(M*R^2)/2
 

1. What is the difference between rotational and translational motion?

Rotational motion refers to the movement of an object around an axis, while translational motion refers to the movement of an object from one point to another in a straight line.

2. How are rotational and translational motion related?

Rotational motion can cause translational motion and vice versa. For example, when a wheel rotates, it also moves forward in a straight line, causing translational motion. Similarly, when an object is pushed in a straight line, it can also cause rotational motion if there is a pivot point.

3. What is angular velocity?

Angular velocity is a measure of how fast an object is rotating around an axis. It is measured in radians per second (rad/s) or degrees per second (deg/s).

4. How is rotational inertia different from mass?

Rotational inertia, also known as moment of inertia, is a measure of an object's resistance to change in its rotational motion. It depends on the distribution of mass around an object's axis of rotation, whereas mass is a measure of the amount of matter in an object.

5. What is torque and how does it affect rotational motion?

Torque is a measure of the force that causes an object to rotate around an axis. It is calculated by multiplying the force applied to an object by the distance from the axis of rotation. The greater the torque, the greater the rotational acceleration of an object.

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