Inertia and force question

2010-06-05 6:23 pm

1. A thin cylinder of mass 15kg has a diameter of 300mm. Determine the moment of inertia about an axis 50mm from its centre using Parallel Axis Theorem. Given the angular momentum of inertia of thin cylinder, I = (1/2)mr^2 (Ans: 0.20625)

2.When a load of 1kg is attached to a vertical spring, it deflects by 10mm when it is in equilibrium. Determine:
a) the frequency of oscillation of the system; and (Ans: 4.985Hz)
b) the maximum restoring force in the spring when the load is displaced a further 15mm below the rest position and then released. (Ans: 14.716N)

更新1:

Questions 1 I have solved. Please teach me how to solve question 2.

更新2:

3.A thin cylinder of mass of 15kg rolls freely down a slope of 1 in 30 form rest. Determine a) its total kinetic energy after rolling 30m down the slope; and (Ans: 147.15J) b) its linear velocity, v, at that point. (Ans: 3.617m/s) I can find the answer of a part, but b part I can't find 3.617m/s.

回答 (2)

天同

2010-06-05 6:52 pm

✔ 最佳答案

2.(a) Spring constant = 1g/10 N/mm = 100g N/m
where g is the acceleration due to gravity
Frequency of socillation f = (1/2.pi) x square-root[100g/1] Hz
where pi = 3.14159
i.e. f = 4.985 Hz (taking g = 9.81 m/s2)

(b) Total extension of the spring = (10+15) mm = 25 mm = 0.025 m
Restoring force = (100g x 0.025 - 1g) N = 14.715 N

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AAA

2010-06-06 8:45 pm

Refer to
http://hk.knowledge.yahoo.com/question/question?qid=7010060600490
for question 3

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