Kinetics of a rigid body (conservation of energy)

[sseebbeekkk]

Homework Statement

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Homework Equations

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(1) (pink) Is it vertical displacement ?
* 4 - 2 (unstretched length of the spring) ?

(2) (blue) What does it mean ?
* I was thinking that maybe they used The Pythagorean theorem (6²+4²)=7,2 ≅ 7) but I'm not sure. Besides I don't understand why they used it.

3. Attempt

My reasoning: In general I think they are using this formula,

where in that case the left side is the initial state - the right side - the final state of the spring.

 

[Dr. Courtney]

I recommend setting it up carefully in terms of conservation of energy, expressing T and V in terms of all the relevant quantities (leaving as symbols), making simplifications, solving for the unknown (with symbols), and plugging in numbers at the end.

 

[haruspex]

The 4-2 and 7-2 are both calculations of spring extension. In each case, 2 is the relaxed length. At the horizontal position, the total length is 4, so the extension is 4-2. After rotating 30 degrees, the total length is 4+6 sin(30)=7.
I don't like the way they divide the mass by 32.2 in the KE terms. It seems more natural to me to multiply by 32.2 in the other terms - it comes to the same thing, of course. Maybe their way is standard in this non-metric system. I have no background in it.

 

[Dr. Courtney]

The English (Imperial) unit of mass is slugs. One obtains mass by dividing weight (lbs) by the acceleration of gravity (32.2 ft/s/s) to obtain the mass in slugs.

I thought ballistics was the last holdout still using English units for real physics.

https://en.wikipedia.org/wiki/English_Engineering_units

 

[haruspex]

The English (Imperial) unit of mass is slugs. One obtains mass by dividing weight (lbs) by the acceleration of gravity (32.2 ft/s/s) to obtain the mass in slugs.

I thought ballistics was the last holdout still using English units for real physics.

https://en.wikipedia.org/wiki/English_Engineering_units

Ok, thanks.

 

[sseebbeekkk]

Thank you for help.

Dr. Courtney - is this equation correct ?

 

[Dr. Courtney]

Is the only potential energy due to the spring?

 

[sseebbeekkk]

If a spring is not stretched or compressed, then there is no elastic potential energy stored in it.

However in this case at the beginning the spring was stretched 2 metres (4-2=2), hence 1/2*k*s1^2

At the end, the spring was stretched 5 meters (7-2=5), hence 1/2*k*s2^2

'W' stands for: work of a weight -> WΔy= 50 * (1.5)

 

[Dr. Courtney]

Gravity?

 

[sseebbeekkk]

I think the only potential energy is due to the spring. If the spring lies the ground then mgh=0

 

[haruspex]

I think the only potential energy is due to the spring. If the spring lies the ground then mgh=0

The massive bar is rotating in a vertical plane. Are you saying its centre of gravity does not change in height?

 

[sseebbeekkk]

Ok, it does. Thanks.