Question

Static Equilibrium A rod of uniform density that has a mass of 50 grams and is 80cm long has two masses hanging from either end. Mass 1 is 500grams and the fulcrum is placed 10cm from this mass. Find the other mass.

Answer 1

ocm 10 cm N Ful crum Mg ioum- 30 um 70

In static equilibrium the net Torque of the system about any point must be zero. To solve the problem easily, we take the reference point as the point of contact of fulcrum and the rod.

There are four forces acting: forces of gravity on mass $M_1$, $M_2$ and the rod; the contact force (N) by fulcrum on the rod.

In static equilibrium, the net Torque about the fulcrum due to these forces must be zero.

1Tfulerum +Trod+T2 =0

ro

where g is the gravitational acceleration; $r_1$, $r_2$ and $r_3$ are distances between fulcrum and mass $M_1$, center of mass of the rod, and mass $M_2$ respectively. The positive sign is for torque pointing out of the page, and negative signs indicates torques pointing into of the page.

Solving for $M_2$

$M_2=\frac{M_1r_1-M_{rod}r_2}{r_3}$

Using
M1500 grams
, ,
T1 10 cm
, and

We get