Examkin

Question

Difficulty: Very hardLevers and Fulcrums

A specialized industrial press uses a compound lever system composed of two uniform steel bars to compress a heavy coil spring.

- Lever A (Top handle): is 20 inches20\text{ inches} long, weighs 10 lbs10\text{ lbs}, and pivots on a fulcrum at its left end. A vertical rigid connecting link is attached to Lever A at a point 5 inches5\text{ inches} from its fulcrum.
- Lever B (Bottom pressing bar): is 30 inches30\text{ inches} long, weighs 30 lbs30\text{ lbs}, and pivots on a fulcrum at its left end. The connecting link from Lever A attaches to the far right end of Lever B (30 inches30\text{ inches} from its fulcrum). A heavy coil spring is placed under Lever B, located 6 inches6\text{ inches} from Lever B's fulcrum.

If a worker applies a 40 lb40\text{ lb} downward force at the far right end of Lever A (20 inches20\text{ inches} from its fulcrum), what is the total downward compressive force (in lbs) exerted on the spring?

*Assume both levers are horizontal, the connecting link is perfectly vertical, and the system is in static equilibrium.*

Answer: 975 lbs

Answer

975 lbs
In static equilibrium, the sum of clockwise and counterclockwise torques about any pivot point must be exactly zero. By calculating the torques step-by-step through the compound system—incorporating both the applied forces and the center of gravity of each uniform bar—we find the final compressive force transmitted to the spring is 975 lbs.

Step-by-Step Solution

1
Calculate total clockwise torque on Lever A
900 lb-in
The worker's force (40 lbs at 20 inches) and the lever's own uniform weight (10 lbs at its 10-inch center of gravity) both create clockwise rotation around the fulcrum.
2
Determine the force transmitted through the connecting link
180 lbs
The link must balance the 900 lb-in torque at a distance of 5 inches (900 / 5 = 180 lbs). This 180 lbs force is transmitted downward to Lever B.
3
Calculate total clockwise torque on Lever B
5850 lb-in
The downward force from the link (180 lbs at 30 inches) and Lever B's uniform weight (30 lbs at its 15-inch center of gravity) create clockwise rotation around Lever B's fulcrum.
4
Calculate the final compressive force applied to the spring
975 lbs
The spring must balance Lever B's total 5850 lb-in torque at a distance of 6 inches (5850 / 6 = 975 lbs).

Key Concept

Torque Equilibrium in Compound and Uniform Levers
Rate this question

Topics

Levers and Fulcrums

More questions from this topic