F.4PHY moment10marks!!!

chi ming

2010-02-21 9:18 pm

When ball bearings are manufactured, it is important that they have the correct mass.The diagram illustrates a device for doing this. A uniform beam AB is pivoted at its centre O. It has a weight W of 1 N placed at end B , and a container of negligible weight placed at X. When the container is filled with 100 ball bearings, the beam should balance if the ball bearings have the correct mass. Assume that a mass of 1kg has a weight of 10N.
a) What is the moment of the weight W about the pivot?
b) Calculate the weight (in newtons) of the ball bearings in the container at X.
c) What is the average mass(in grams) of one ball bearings?
d) If the container was filled with 100 ball bearings of identical size but lower density, would the end A of the beam tip up or down?Give a clear reason for your answer.

回答 (1)

天同

2010-02-22 12:42 am

✔ 最佳答案

Since you did not give the diagram, and I guess some data are given on that diagram, I need to use symbols to represent these data.

Let d be the distance from the end B (where the weight W is palced) to the pivot, and L be the distance of point X (where the box of ball bearings is placed) from the pivot.

(a) Momentum = 1 x d = d N-m
(b) Take moment about the pivot,
d = Wb x L
i.e. Wb = d/L (unit in N)
where Wb is the weight of the ball bearings

(c) Mass of all 100 number of ball bearings = Wb/10 (unit in kg)
Mass of a ball bearing = (Wb/10)/100 (unit in kg)

(d) The end A would tip up.
Ball bearing of identical size but lower density means the mass of ball bearing is smaller than before. Hence, the moment given by the lower density ball bearings is no longer sufficient to balance the moment given by the weight at end B.

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