copute the power output of a machine that lifts a 500 kg crate through a height of 20.0 m in a time of 60.0 s .
book answer is 1.63 kw
can you help me plug the numbers into the correct formula to use. then i should have no problem doing the other problems i have to do. thanks
Sure, I can help you with that!
To compute the power output, you can use the formula:
Power = Work / Time
Where:
- Power is the rate at which work is done or energy is transferred (in watts, W)
- Work is the amount of energy transferred (in joules, J)
- Time is the duration or the time it takes to do the work (in seconds, s)
First, we need to find the work done. The work done can be calculated using the formula:
Work = Force × Distance
Where:
- Force is the force applied to lift the crate (in newtons, N)
- Distance is the vertical distance the crate is lifted (in meters, m)
Given:
- The mass of the crate, m = 500 kg
- The vertical distance it is lifted, h = 20.0 m
- The time it takes to do the work, t = 60.0 s
First, we need to calculate the force applied using the equation:
Force = mass × gravitational acceleration
Gravitational acceleration is approximately 9.8 m/s^2.
Force = 500 kg × 9.8 m/s^2
Next, we can calculate the work done using the formula:
Work = Force × Distance
Work = (Force) × (Distance)
Work = (500 kg × 9.8 m/s^2) × 20.0 m
Finally, we can calculate the power output using:
Power = Work / Time
Power = (Work) / (Time)
Power = [(500 kg × 9.8 m/s^2) × 20.0 m] / 60.0 s
Simplifying this expression will give us the answer in watts (W). To convert watts to kilowatts (kW), divide the result by 1000.
Let me know if you would like me to calculate the result for you!
Certainly! To calculate the power output of a machine, we can use the formula:
Power = (Work done) / (Time)
In this case, the work done is equal to the force applied multiplied by the distance traveled. The force can be determined using Newton's second law:
Force = mass * acceleration
Since the crate is being lifted vertically, the acceleration can be considered as the acceleration due to gravity, which is approximately 9.8 m/s^2.
Let's break down the steps to solve the problem:
Step 1: Calculate the force applied.
Force = mass * acceleration
Force = 500 kg * 9.8 m/s^2
Step 2: Calculate the work done.
Work done = Force * distance
Work done = (500 kg * 9.8 m/s^2) * 20.0 m
Step 3: Calculate the power.
Power = Work done / Time
Power = [(500 kg * 9.8 m/s^2) * 20.0 m] / 60.0 s
Now, let's plug in the numbers:
Force = 500 kg * 9.8 m/s^2 = 4900 N (Newton)
Work done = (4900 N) * 20.0 m = 98000 J (Joules)
Power = (98000 J) / 60.0 s
Power = 1633.33 W (Watts)
To convert Watts to kilowatts (kW), divide the power by 1000:
Power = 1633.33 W / 1000 = 1.63 kW
So, the power output is 1.63 kW, as given in the book answer.
Remember to always check your units and make sure they are consistent throughout your calculations.
computer the power out in Watts of a machine that lift's a 50kg crate through a height of 20cm in one minute
Power is work/time
work= mg*height
I don't understand your difficulty with this.