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A balanced lever has two weights on it, the first with mass #4 kg # and the second with mass #2 kg#. If the first weight is # 3 m# from the fulcrum, how far is the second weight from the fulcrum?

Answer 1

Leo Abeyta

The distance is #=6m#

The mass #M_1=4kg#

The mass #M_2=2kg#

The distance #a=3m#

Taking moments about the fulcrum

#M_1xxa=M_2xxb#

#b=(M_1xxa)/(M_2)=(4*3)/(2)=6m#

The distance #b=6m#

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Answer 2

Parker Abbott

To find the distance of the second weight from the fulcrum, we can use the principle of moments, which states that the total clockwise moment is equal to the total anticlockwise moment about the fulcrum.

Let's denote the distance of the second weight from the fulcrum as (x).

The moment exerted by the first weight is (4 , \text{kg} \times 3 , \text{m}), and the moment exerted by the second weight is (2 , \text{kg} \times x).

Since the lever is balanced, these moments are equal:

[4 , \text{kg} \times 3 , \text{m} = 2 , \text{kg} \times x]

[12 , \text{kg} \cdot \text{m} = 2 , \text{kg} \times x]

To find (x), divide both sides by (2 , \text{kg}):

[x = \frac{12 , \text{kg} \cdot \text{m}}{2 , \text{kg}}]

[x = 6 , \text{m}]

So, the second weight is (6 , \text{m}) from the fulcrum.

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