Verification: Hanging mass on cylinder. Moment of inertia

In summary: The only difference is that r^2 in the formula for the moment of inertia would be a different number.In summary, a 15.0 kg bucket of water is suspended by a very light rope wrapped around a solid cylinder 0.300 m in diameter with a mass of 12.0 kg. The cylinder pivots on a frictionless axle through its centre. The bucket is released from rest at the top of a well and falls 10.0 m to the water. The tension in the rope is 42.15N, the speed at which the bucket strikes the water is 11.8m/s, and the time of the fall is 1.69s. The force exerted on the cylinder
  • #1
pat666
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0

Homework Statement


A 15.0 kg bucket of water is suspended by a very light rope wrapped around a solid cylinder 0.300 m in diameter with a mass of 12.0 kg. The cylinder pivots on a frictionless axle through its centre. The bucket is released from rest at the top of a well and falls 10.0 m to the water.
a) What is the tension in the rope while the bucket is falling? my answer: 42.15N
b) With what speed does the bucket strike the water? my answer: 11.8m/s
c) What is the time of the fall? my answer: 1.69s
d) While the bucket is falling, what is the force exerted on the cylinder by the axle: my answer: 159.87N this is the one that i am really unsure of (and a))

Homework Equations



solved but unsure

The Attempt at a Solution



could someone who knows what there doing please check my answers, i wouldn't ask if it wasn't important.. thanks in advance.
 
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  • #2
It looks good. How did you get the force of the axle?

ehild
 
  • #3
actually that part was wrong, it is actually just F=ma and it turns out to be 105N i hope. I've actually been getting a lot of help from someone else on PF
 
  • #4
Hi, just a quick question. why do they give the radius of the cylinder if it is not needed, is there a way to solve these problems that does require the radius?
I have another very similar problem to this that i didnt use the radius for either
 
  • #5
pat666 said:
Hi, just a quick question. why do they give the radius of the cylinder if it is not needed, is there a way to solve these problems that does require the radius?
I have another very similar problem to this that i didnt use the radius for either

They could be giving you extra info for you to sift through and see what's relevant and what's not.
 
  • #6
pat666 said:
Hi, just a quick question. why do they give the radius of the cylinder if it is not needed, is there a way to solve these problems that does require the radius?
I have another very similar problem to this that i didnt use the radius for either
If the problem gave you a pulley with a moment of inertia that cannot be calculated from a formula, then you do need the radius. However, the method is the same.
 

1. What is the purpose of hanging a mass on a cylinder for verifying moment of inertia?

The purpose of hanging a mass on a cylinder is to determine the moment of inertia of the cylinder. This is a measure of how difficult it is to rotate an object around a specific axis. By hanging a mass on the cylinder, the gravitational force can be used to calculate the moment of inertia.

2. How does the mass and radius of the cylinder affect the moment of inertia?

The mass and radius of the cylinder both have a direct impact on the moment of inertia. The greater the mass and the larger the radius, the higher the moment of inertia will be. This is because there is more mass distributed further from the axis of rotation, increasing the resistance to rotation.

3. What is the equation for calculating moment of inertia using a hanging mass on a cylinder?

The equation for calculating moment of inertia using a hanging mass on a cylinder is I = mgh/k, where m is the mass of the hanging mass, g is the acceleration due to gravity, h is the distance between the center of mass of the cylinder and the axis of rotation, and k is the acceleration constant.

4. How does the angle of the cylinder affect the moment of inertia calculation?

The angle of the cylinder does not affect the moment of inertia calculation as long as the distance between the center of mass and the axis of rotation remains the same. This is because the moment of inertia is only affected by the mass distribution relative to the axis of rotation, not the orientation of the object.

5. How can the results of this verification be used in practical applications?

The results of this verification can be used in practical applications to determine the rotational stability and dynamics of various objects, such as wheels, motors, and pulleys. It can also be used in the design and analysis of mechanical systems to ensure proper balance and functioning. Additionally, the moment of inertia is an important parameter in calculating the torque needed to rotate an object, making it useful in engineering and physics calculations.

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