Question

Two boxes on opposite ends of a massless board that is 3.0 m long. The board is supported in the middle by a fulcrum. The box on the left has a mass (m1) of 25 kg, and the box on the right has a mass (m2) of 15kg. How far should the fulcrum be positioned from the left side of the board in order to balance the masses horizontally?

a. 0.38 m
b. 1.1 m
c. 0.60 m
d. 1.9 m

Answer 1

b. 1.1 m

Step-by-step explanation:

It is given that the total distance between the masses is equal to the length of the board, which is 3 m. Therefore,

`s_(1) + s_(2) = 3\ m\\\\s_(2) = 3\ m - s_(1)\ --------- eqn(1)`

where,

s₁ = distance of fulcrum from left mass

s₂ = distance of fulcrum from right mass

In order to achieve balance, the torque due to both masses must be equal:

`T_(1) = T_(2)\\m_(1)s_(1) = m_(2)s_(2)\\(25\ kg)(s_(1)) = (15\ kg)(s_(2))\\\\(15\ kg)/(25\ kg)(s_(2)) = s_(1)\\\\using\ eqn(1):\\(0.6)(3\ m - s_(1)) = s_(1)\\1.8\ m = 1.6\ s_(1)\\s_(1) = (1.8\ m)/(1.6)`

s₁ = 1.1 m

Hence, the correct option is:

b. 1.1 m