Forces of 8N and 40N act on the ends of the lever. The length of the arm is 90 cm.

Forces of 8N and 40N act on the ends of the lever. The length of the arm is 90 cm. Where is the fulcrum if the arm is in balance?

Given:
F1 = 8 N.
F2 = 40 N.
l1 + l2 = 90 cm.
Find:
l1 -?, l2 -?.
According to the balance rule of the lever:
F1 / F2 = l2 / l1, where F1 is the force acting on the shoulder l1; F2 is the force acting on the shoulder l2.
l1 + l2 = 90 cm, therefore: l1 = 90 – l2.
F1 / F2 = l2 / (90 – l2).
8/40 = l2 / (90 – l2).
l2 = 0.2 * (90 – l2).
l2 = 18 – 0.2l2.
1.2l2 = 18; l2 = 15 cm.
l1 = 90 – l2 = 90 – 15 = 75 cm.
Answer: The fulcrum is 15 cm from the end of the arm with a force of 40 N and 75 cm from the end with a force of 8 N.