# A balanced lever has two weights on it, the first with mass #14 kg # and the second with mass #9 kg#. If the first weight is # 2 m# from the fulcrum, how far is the second weight from the fulcrum?

A moment is the product of force and the distance over which the force acts.

In a balanced lever, both moments are equal to each other, so

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Using the principle of torque balance for a balanced lever, the torque exerted by the first weight (14 kg) equals the torque exerted by the second weight (9 kg).

Torque = force × distance from fulcrum

For the first weight: Torque1 = (14 kg) × (9.8 m/s^2) × (2 m)

For the second weight: Torque2 = (9 kg) × (9.8 m/s^2) × (x m)

Setting Torque1 equal to Torque2: (14 kg) × (9.8 m/s^2) × (2 m) = (9 kg) × (9.8 m/s^2) × (x m)

Solving for x:
(14 kg) × (2 m) = (9 kg) × (x m)
28 kg*m = 9 kg * x
x = (28 kg*m) / (9 kg)
x ≈ 3.11 m

Therefore, the second weight is approximately 3.11 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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