# Work/ energy on a rigid body (mechanics)

• smruthi92
In summary, the conversation discusses how to find the velocity, stretch of a spring, and gravitational potential energy of a bar that is rotating. The bar is treated as having purely rotational kinetic energy and starts and stops at rest. The stretch of the spring can be found using geometry and comparing the length of the spring in different positions. The gravitational potential energy can be calculated by finding the height of a triangle formed by the bar's rotation.
smruthi92
pls see attached file for the question.

so W = change in T + change in Ve + change in g

T = 1/2 mv2 + 1/2 I (w1^2 - w2^2), but how do u find the velocity, shouldn't it be 0 since it starts/stops at v=0.

for Ve = 1/2 kx2, how do u know how far it stretches once the moment is applied? :O :(

and for Vg = mgh, is it mg (1.458)?

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smruthi92 said:
T = 1/2 mv2 + 1/2 I (w1^2 - w2^2), but how do u find the velocity, shouldn't it be 0 since it starts/stops at v=0.
You can treat the bar as have purely rotational KE about its pivot; it's initial speed is zero since it's released from rest.

for Ve = 1/2 kx2, how do u know how far it stretches once the moment is applied? :O :(
I suspect that you are supposed to figure out its initial stretch and its final stretch (using a bit of geometry).

and for Vg = mgh, is it mg (1.458)?
How does the position of the center of mass change as the bar moves?

Doc Al said:
You can treat the bar as have purely rotational KE about its pivot; it's initial speed is zero since it's released from rest.

I suspect that you are supposed to figure out its initial stretch and its final stretch (using a bit of geometry).

How does the position of the center of mass change as the bar moves?

oh awesome! so T would essentially just = 1/2 I (w2^2).

so W = 0,
1/2 I (w2^2) + 1/2 k (x2^2-x1^2) = 0?

i guess if it comes back to rest, x1 = 0. but i still don't know how to figure out that extended length using geometry? coz when ur rotating the rod by 69 degrees, could u maybe do 69/360 * length of spring to find it? :S its a bit odd.

smruthi92 said:
oh awesome! so T would essentially just = 1/2 I (w2^2).

so W = 0,
1/2 I (w2^2) + 1/2 k (x2^2-x1^2) = 0?

i guess if it comes back to rest, x1 = 0. but i still don't know how to figure out that extended length using geometry? coz when ur rotating the rod by 69 degrees, could u maybe do 69/360 * length of spring to find it? :S its a bit odd.

sorry i made a mistake. um so what i have is. to find x I am creating an arc with 69 degrees + tan inverse (1.458/1.8), so then i would find the extension to be 2 x pie x 1.8 x 108/230. minus that from the original length and then use the eqn above. but this is all assuming, its rotated about the point where the rod connects to the surface?

smruthi92 said:
oh awesome! so T would essentially just = 1/2 I (w2^2).
Yes.

so W = 0,
1/2 I (w2^2) + 1/2 k (x2^2-x1^2) = 0?
What happened to gravity?

smruthi92 said:
sorry i made a mistake. um so what i have is. to find x I am creating an arc with 69 degrees + tan inverse (1.458/1.8), so then i would find the extension to be 2 x pie x 1.8 x 108/230. minus that from the original length and then use the eqn above. but this is all assuming, its rotated about the point where the rod connects to the surface?
Not sure what you're saying here. In any case, you need to compare how the stretch of the spring changes. Figure out the length of the spring in each position. (When the bar is horizontal, how much of the spring's 1.458 m length is the stretch from its unstretched position?)

Doc Al said:
Yes.

What happened to gravity?

Not sure what you're saying here. In any case, you need to compare how the stretch of the spring changes. Figure out the length of the spring in each position. (When the bar is horizontal, how much of the spring's 1.458 m length is the stretch from its unstretched position?)

ok as I am assuming that they are rotating it at the end of the bar connected to the spring, and not say, the centre of mass?

so if we include Vg, then its mg h, where h = the height you find forming a triangle?

Doc Al said:
Yes.

What happened to gravity?

Not sure what you're saying here. In any case, you need to compare how the stretch of the spring changes. Figure out the length of the spring in each position. (When the bar is horizontal, how much of the spring's 1.458 m length is the stretch from its unstretched position?)

smruthi92 said:
ok as I am assuming that they are rotating it at the end of the bar connected to the spring, and not say, the centre of mass?

so if we include Vg, then its mg h, where h = the height you find forming a triangle?

OOOOHHH I WORKED IT OUT! THANKYOU SO MUCH FOR UR HELP! :d:d:d:d

## 1. What is work in mechanics?

Work is a measure of the energy transferred to or from an object by a force acting on the object. In mechanics, work is typically measured in joules and is calculated by multiplying the magnitude of the force by the distance the object moves in the direction of the force.

## 2. What is a rigid body in mechanics?

A rigid body is an object that does not deform or change shape when subjected to external forces. This means that all points in the body maintain their relative positions to each other. In mechanics, rigid bodies are often used as simplified models for real-world objects, such as a baseball or a car.

## 3. How is energy related to work on a rigid body?

Energy and work are closely related in mechanics. Energy is the ability to do work, and work is the transfer of energy from one object to another. In the case of a rigid body, energy can be transferred to or from the body by the application of external forces, resulting in work being done on the body.

## 4. What is the difference between kinetic and potential energy?

Kinetic energy is the energy an object possesses due to its motion, whereas potential energy is the energy an object possesses due to its position or configuration. In the context of a rigid body, kinetic energy can be thought of as the energy of the body's overall motion, while potential energy can be thought of as the energy of the body's internal forces and interactions.

## 5. How is the conservation of energy applied to work on a rigid body?

The principle of conservation of energy states that energy cannot be created or destroyed, only transferred from one form to another. In the case of work on a rigid body, this means that the total amount of energy in the system must remain constant. This can be used to analyze the motion and interactions of a rigid body, as energy can be transferred between different forms (such as kinetic and potential) but the total energy of the system will always remain the same.

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