RolyPoly 3 years ago Q

1. RolyPoly

2. RolyPoly

First question, why is $$U_i=mgh_f$$ instead of $$U_i = mgh_i$$?

3. experimentX

that is the total energy of the system!! the energy of the system is constant if there were no other forces acting. i.e. Kinetic Energy + Potential Energy = constant = total energy now given that the pendulum starts from rest at height h_i, K.E. = 0, total energy = P.E

4. RolyPoly

But with the initial height hi, isn't the PE = $$mgh_i$$? Why is it $$mgh_f$$?

5. RolyPoly

|dw:1353427300243:dw|

6. RolyPoly

Initial PE = mg(l-lcosθi) = mgl (1-cosθi) Final PE = mg(l-lcosθf)= mgl(1-cosθf) PE loss = change in PE = mgl[(1-cosθf) - (1-cosθi)] = mgl(cosθi - cosθf) ??

7. experimentX

|dw:1353430286611:dw|

8. RolyPoly

Yup.

9. experimentX

since l is defined as the distanced from pivoted point to the center of mass ... the energy of the system is $$mgl (1 - \cos \theta)$$ ... this is the total energy of the system ... probably experiment expects you to observe until the blob halt's to move.