A wagon was used to move a 90 lb rock 120yds. It took 40 sec and 70 lbs of force to do this. Find horsepower and efficiency
To find the horsepower and efficiency, let's break down the problem and use the appropriate formulas:
1. Calculate the work done.
Work = Force * Distance
Given: Force = 70 lbs, Distance = 120 yds
Work = 70 lbs * 120 yds
2. Convert units to a consistent system.
Since horsepower and efficiency are typically measured in consistent units, let's convert the units:
1 lb = 0.453592 kg (pounds to kilograms conversion)
1 yd = 0.9144 m (yards to meters conversion)
3. Calculate the work done in SI units (joules).
Work = (70 lbs * 0.453592 kg/lb) * (120 yds * 0.9144 m/yd)
Work = (70 * 0.453592) kg * (120 * 0.9144) m
4. Calculate the time in seconds.
Given: Time = 40 seconds
5. Calculate Power (in watts).
Power (P) = Work / Time
6. Convert Power to Horsepower.
1 watt = 0.00134048 horsepower
Power (in horsepower) = Power (in watts) * 0.00134048
7. Calculate Efficiency.
Efficiency = (Output Power / Input Power) * 100
Now, let's plug in the values and calculate the results:
Step 1:
Work = 70 lbs * 120 yds
Work = 8400 lbs * yds
Step 2:
Work = 8400 lbs * yds
Work = 8400 lbs * 0.453592 kg/lb * 120 yds * 0.9144 m/yd
Work = 194169.6128 kg * m
Step 3:
Power (in watts) = Work / Time
Power (in watts) = 194169.6128 kg * m / 40 s
Step 6:
Power (in horsepower) = Power (in watts) * 0.00134048
Step 7:
Efficiency = (Output Power / Input Power) * 100
To get the final values, please calculate the above steps using the appropriate formulas and units conversion, if needed.