A balanced lever has two weights on it, the first with mass #7 kg # and the second with mass #30 kg#. If the first weight is # 7 m# from the fulcrum, how far is the second weight from the fulcrum?

Question

A balanced lever has two weights on it, the first with mass #7 kg # and the second with mass #30 kg#.  If the first weight is # 7 m# from the fulcrum, how far is the second weight from the fulcrum?

Isabella Alvarez · Accepted Answer

The distance is #=1.63m#

The first mass is #M_1=7kg#

The distance #a=7m#

The second mass is #M_2=30kg#

Taking moments about the fulcrum

#M_2xxb=M_1xxa#

The distance

#b=(M_1xxa)/(M_2)=(7*7)/30=1.63m#

Isabella Alvarez · Answer

undefined Using the principle of moments in a balanced lever, we can calculate the distance of the second weight from the fulcrum using the equation:

$$ \text{Moment}_1 = \text{Moment}_2 $$

Where:
- Moment 1 is the moment created by the first weight,
- Moment 2 is the moment created by the second weight,
- Moment is calculated as the product of mass and distance from the fulcrum.

Given:
- Mass of the first weight (m1) = 7 kg,
- Distance of the first weight from the fulcrum (d1) = 7 m,
- Mass of the second weight (m2) = 30 kg,
- Distance of the second weight from the fulcrum (d2) = unknown.

We can set up the equation:

$$ m_1 \times d_1 = m_2 \times d_2 $$

$$ 7 \times 7 = 30 \times d_2 $$

$$ 49 = 30 \times d_2 $$

$$ d_2 = \frac{49}{30} $$

$$ d_2 = 1.63 \, \text{m} $$

So, the second weight is approximately 1.63 meters from the fulcrum.