A force of 45 pounds is exerted along a rope attached to a crate at an angle of 30 degrees above the horizontal. The crate is moved 22 feet. How much work has been accomplished?
To calculate the work done, you need to use the formula:
Work = Force × Distance × cos(angle)
In this case, the force is 45 pounds, the distance is 22 feet, and the angle is 30 degrees.
First, convert the force to the standard unit of measurement, which is the pound-force (lbf). Since 1 pound-force is equal to the force exerted by gravity on a mass of 1 pound, we can simply use 45 lbf as the force value.
Next, convert the angle from degrees to radians. Radians are the standard unit of measurement for angles when dealing with trigonometric functions. To convert from degrees to radians, you use the formula:
radians = (π/180) × degrees
In this case, the angle in radians is:
radians = (π/180) × 30 = π/6
Now, plug the values into the formula:
Work = 45 lbf × 22 ft × cos(π/6)
Use a calculator to find the cosine of π/6, which is √3/2.
Work = 45 lbf × 22 ft × √3/2
Multiply the values together:
Work = 45 lbf × 22 ft × √3/2 ≈ 871.78 ft lbf
So, approximately 871.78 foot-pounds of work has been accomplished.