# A balanced lever has two weights on it, the first with mass #8 kg # and the second with mass #24 kg#. If the first weight is # 2 m# from the fulcrum, how far is the second weight from the fulcrum?

Since the lever is balanced, the sum of torques is equal to 0

Answer is:

Since the lever is balanced, the sum of torques is equal to 0:

About the sign, obviously for the lever to be balanced if the first weight tends to rotate the object with a certain torque, the other weight will have opposite torque. Let the masses be:

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To find the distance of the second weight from the fulcrum, use the formula for a balanced lever: ( \text{mass}_1 \times \text{distance}_1 = \text{mass}_2 \times \text{distance}_2 ). Substitute the given values and solve for ( \text{distance}_2 ).

( 8 \times 2 = 24 \times \text{distance}_2 )

( \text{distance}_2 = \frac{8 \times 2}{24} )

( \text{distance}_2 = \frac{16}{24} )

( \text{distance}_2 = \frac{2}{3} ) 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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