Calculate the average horsepower required to raise a 200-kg drum to a height of 20 in a time of 1:0 minute. Show the solution and answer
20in *0.0254m/in = 0.5084 m.
P = F * d/T = mg * d/T
P = 200*9.8 * 0.5084/60 = 16.6 J/s = 16.6 Watts.
P = (16.6/746) * 1 hp = 0.0223 hp.
Why did the drum want to go up? Because it was tired of being on the downbeat! Now, let's calculate the average horsepower required to lift it.
First, we need to convert the given height to meters since the unit of mass is in kilograms. To convert 20 inches to meters, we use the conversion factor 1 inch = 0.0254 meters:
Height = 20 inches × 0.0254 meters/inch = 0.508 meters
Now, let's calculate the work done to raise the drum. The work formula is given by:
Work = Force × Distance
The force required to lift the drum can be calculated using Newton's second law:
Force = Mass × Acceleration due to gravity
Since the drum is lifted vertically, the acceleration due to gravity is 9.8 m/s². Let's calculate the force:
Force = 200 kg × 9.8 m/s² = 1960 Newtons
Now, the work done to raise the drum is:
Work = Force × Distance = 1960 N × 0.508 m = 996.8 Joules
Finally, let's calculate the average power required using the given time of 1 minute.
Time = 1 minute = 60 seconds
Power = Work / Time = 996.8 J / 60 s = 16.613333... Watts
To convert the power to horsepower, we use the conversion factor 1 horsepower = 745.7 Watts:
Average Horsepower = Power / 745.7 = 16.613333... W / 745.7 = 0.022273... horsepower
So, the average horsepower required to raise the 200-kg drum to a height of 20 inches in 1 minute is approximately 0.02227 horsepower. Keep on drumming!
To calculate the average horsepower required to raise a 200-kg drum to a height of 20 m in a time of 1 minute, we can follow these steps:
Step 1: Convert the height in meters to feet:
1 meter is approximately equal to 3.2808 feet.
20 meters * 3.2808 = 65.616 feet
Step 2: Calculate the work done:
The work done (W) is equal to the force (F) exerted multiplied by the distance (d) traveled.
The force exerted (F) can be calculated using the formula:
F = m * g
where m is the mass and g is the acceleration due to gravity.
Given:
Mass of the drum (m) = 200 kg
Acceleration due to gravity (g) = 9.8 m/s^2
F = m * g
F = 200 kg * 9.8 m/s^2
F = 1960 N
The distance traveled (d) is 65.616 feet.
W = F * d
W = 1960 N * 65.616 feet
W ≈ 128,353.45 ft•N
Step 3: Convert the work done to horsepower:
1 horsepower is equal to 550 ft•lb/s.
To convert ft•N to ft•lb:
1 N = 0.737562 ft•lb
128,353.45 ft•N * 0.737562 ft•lb/N ≈ 94,659.98 ft•lb
To convert ft•lb to horsepower:
1 horsepower = 550 ft•lb/s
94,659.98 ft•lb / 550 ft•lb/s ≈ 172.018 horsepower
Therefore, the average horsepower required to raise a 200-kg drum to a height of 20 meters in a time of 1 minute is approximately 172.018 horsepower.
To calculate the average horsepower required to raise the drum, we need to consider the work done and the time taken.
1. Convert the height from inches to meters:
- 1 inch = 0.0254 meters
- Height = 20 inches * 0.0254 meters/inch = 0.508 meters
2. Convert the time taken:
- 1 minute = 60 seconds
3. Calculate the work done:
- Work = force * distance
- The force required to lift an object is equal to its weight.
- Weight = mass * gravitational acceleration
- Gravitational acceleration (g) ≈ 9.8 m/s² (on Earth)
- Weight = 200 kg * 9.8 m/s² = 1960 Newtons (N)
- Work = 1960 N * 0.508 meters = 995.68 Joules (J)
4. Calculate the power:
- Power = work / time
- Time in seconds = 1 minute * 60 seconds/minute = 60 seconds
- Power = 995.68 J / 60 seconds = 16.59 Watts
5. Convert power to horsepower:
- 1 horsepower (HP) = 745.7 Watts
- Horsepower = 16.59 Watts / 745.7 HP = 0.0222 HP
Therefore, the average horsepower required to raise the 200-kg drum to a height of 20 inches in 1 minute is approximately 0.0222 horsepower (HP).