Work/ energy on a rigid body (mechanics)

[smruthi92]

pls see attached file for the question.

so W = change in T + change in V_e + 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 V_e = 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)?

im so sorry, i just have no idea about this one.

 

[Doc Al]

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 V_e = 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?

 

[smruthi92]

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]

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?

 

[Doc Al]

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?

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?)

 

[smruthi92]

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 V_g, then its mg h, where h = the height you find forming a triangle?

 

[smruthi92]

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 V_g, 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