a man pushes a lawnmower 50ft in 5s by exerting a force of 30lb at an angle of 53degrees with the horizon. find the work done and the average power expended in horsepower. Answer Please need help
To find the work done and the average power expended, we can use the formulas:
1. Work = force × distance × cos(angle)
2. Power = work ÷ time
Let's calculate the values step by step.
1. Work:
Work = force × distance × cos(angle)
Given: force = 30 lb, distance = 50 ft, angle = 53 degrees
First, convert the force from pounds (lb) to pounds-force (lbf). The conversion factor is 1 lb = 1 lbf.
Therefore, force = 30 lb = 30 lbf.
Now, calculate the work done:
Work = 30 lbf × 50 ft × cos(53 degrees)
Using a calculator, find the cosine of 53 degrees and multiply it by 30 lbf and 50 ft. Let's denote the value as W.
W = 30 lbf × 50 ft × cos(53 degrees) ≈ 1083 ft-lbf
Therefore, the work done is approximately 1083 foot-pounds (ft-lbf).
2. Average Power:
Power = work ÷ time
Given: time = 5 seconds
Let's convert the time from seconds (s) to hours (hr). The conversion factor is 1 hour = 3600 seconds.
Therefore, time = 5 s ÷ 3600 = 0.00139 hr
Now, calculate the average power:
Power = 1083 ft-lbf ÷ 0.00139 hr
Using a calculator, divide 1083 ft-lbf by 0.00139 hr to find the average power. Let's denote the value as P.
P = 1083 ft-lbf ÷ 0.00139 hr ≈ 779560 horsepower (ft-lbf/hr)
Therefore, the average power expended is approximately 779560 horsepower (ft-lbf/hr).
Please note that the unit "horsepower (ft-lbf/hr)" is a non-standard unit used for comparison purposes. In practice, power is usually measured in watts (W) or horsepower (hp).