# A balanced lever has two weights on it, the first with mass 1 kg  and the second with mass 7 kg. If the first weight is  3 m from the fulcrum, how far is the second weight from the fulcrum?

Feb 25, 2017

Solve using torque: The distance is $\frac{3}{7}$m

#### Explanation:

Torque ($\tau$) is defined as force times distance (regarding rotation).

So in this case, the lever is balanced so the summation of the torque should be zero.

So the clockwise torque should be equal and opposite to the counter clockwise torque.

It should look something like this:

(1kg) <-------3m------->$\Delta$<---$x$m--->(7kg)

Remember that the force of gravity on Earth is $m g$.

${\tau}_{\text{left" =tau_"right}}$

${F}_{1} {d}_{1} = {F}_{2} {d}_{2}$

${m}_{1} g {d}_{1} = {m}_{2} g {d}_{2}$

$3 g = 7 g {d}_{2}$

$3 = 7 {d}_{2}$

${d}_{2} = \frac{3}{7}$ m