don't know how 2 do it

2006-10-19 6:37 am
A pendulum consisting of a bob of mass m connected to a light rod of length l is stood upside-down and given a gentle push to start it moving.

(a)Find the centripetal force of the bob when the rod is (i) horizontal and (ii) at the bottom of the swing.

(b) What is the net tangential force acting on the bob when the rod is horizontal? what is the angular acceleration at this point?

Ans for 2. : 2mg 4mg mg g/r

回答 (1)

2006-10-19 6:53 am
✔ 最佳答案
A pendulum consisting of a bob of mass m connected to a light rod of length L is stood upside-down and given a gentle push to start it moving.
(a)Find the centripetal force of the bob when the rod is (i) horizontal and (ii) at the bottom of the swing.
(i)
依機械能守恒,擺錘的速度
0.5mv2 = mgh
v = √(2gh)
= √(2gL)
所以向心力為
F = mv2/L
= m(√(2gL))/L
= 2mg
(ii)
依機械能守恒,擺錘的速度
0.5mv2 = mgh
v = √(2gh)
= √(2g(2L))
= √(4gL)
所以向心力為
F = mv2/L
= m(√(4gL))/L
= 4mg

(b) What is the net tangential force acting on the bob when the rod is horizontal? what is the angular acceleration at this point?
它的轉動慣量 I = mL2
在水平的位置它所受的切向力只有 mg
所受的力矩為 mgL,即
mgL = Iα
mgL = mL2α
α = g/L


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