# A balanced lever has two weights on it, one with mass #4 kg# and one with mass #2 kg#. If the first weight is # 9 m# from the fulcrum, how far is the second weight from the fulcrum?

To balance the lever, the torque about the fulcrum must be zero.

In this question, we have

#M_1 = 4 "kg"# #a = 9 "m"# #M_2 = 2 "kg"#

We want to find

Therefore,

#(4 "kg") * (9 "m") = (2 "kg") * b#

#b = frac{(4 "kg") * (9 "m")}{2 "kg"}#

#= 18 "m"#

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To find the distance of the second weight from the fulcrum, we can use the principle of moments. The principle states that the moment (torque) produced by each weight is equal when the lever is balanced.

The moment produced by a weight is calculated by multiplying its mass by its distance from the fulcrum. Therefore, the moment produced by the 4 kg weight is (4 , \text{kg} \times 9 , \text{m}).

Since the lever is balanced, the moment produced by the 2 kg weight must be equal to the moment produced by the 4 kg weight. So, we can set up the equation:

(4 , \text{kg} \times 9 , \text{m} = 2 , \text{kg} \times \text{distance of the second weight from the fulcrum})

Solving for the distance of the second weight from the fulcrum:

(2 \times \text{distance of the second weight from the fulcrum} = \frac{4 \times 9}{2} )

(\text{distance of the second weight from the fulcrum} = \frac{4 \times 9}{2 \times 2})

(\text{distance of the second weight from the fulcrum} = \frac{36}{4})

(\text{distance of the second weight from the fulcrum} = 9 , \text{m})

So, the second weight is 9 meters from the fulcrum.

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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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