An initially stationary 15.0-kg crate of cheese wheels is pulled via a cable a distance d= 5.70m up a frictionless ramp to a height of h= 2.50m, where it stops. What is the potential energy of the crate after it is lifted? How much work is done during the lift? If it takes 10 seconds to lift the cheese, what is the power rating of the lifting device?
potential energy = mass * gravity * height
= 15.0kg * 9.8 m/s^2 * 2.50 m
= 367.875 J or 368 J (sig figs)
work = mass * gravity (OR " force ") * distance
= 15.0 kg * 9.8 m/s^2 * 5.70 m
= 837.9 J or 838 J (sig figs)
power = work / time
= 837.9 J / 10 s
= 83.79 J/s or 83.8 J/s (sig figs)
PE=mgh=12*9.8*2.5 joules
work done: same
power= workdone/seconds
Well, well, well, lifting cheese wheels, eh? That's quite a cheesy situation! Let's tackle these questions one by one.
First up, the potential energy of the crate after it is lifted. Well, potential energy can be calculated using the formula: PE = m * g * h, where m is the mass of the crate (15.0 kg), g is the acceleration due to gravity (approximately 9.8 m/s^2), and h is the height (2.50 m). So, plug in those numbers, and you'll get the potential energy of the crate. Remember, potential energy is measured in joules (J).
Now, let's talk about the work done during the lift. Since the ramp is frictionless, the work done against friction is zero. Therefore, all the work done is equal to the potential energy gained by the crate. So, the work done during the lift is the same as the potential energy we calculated earlier.
Lastly, the power rating of the lifting device. Power is the rate at which work is done or energy is transferred. It can be calculated using the formula: Power = Work / Time. You've got the work done during the lift, which is also the potential energy, and the time it takes to lift the cheese, which is 10 seconds. Now, just divide the work by the time, and voila! You'll find the power rating of the lifting device. Power is measured in watts (W).
Hope that helps, and remember, don't let your cheese dreams be just a wheely big dream!
To find the potential energy of the crate after it is lifted, we'll use the formula: potential energy = mgh, where m is the mass of the crate, g is the acceleration due to gravity (approximately 9.8 m/s^2), and h is the height the crate is lifted.
Given:
- Mass of the crate (m) = 15.0 kg
- Height lifted (h) = 2.50 m
Using the formula, the potential energy of the crate after it is lifted can be calculated as follows:
potential energy = (15.0 kg) * (9.8 m/s^2) * (2.50 m)
potential energy = 367.5 Joules
So, the potential energy of the crate after it is lifted is 367.5 Joules.
To find the work done during the lift, we can use the formula: work = force * distance, where the force is the weight of the crate (mg) and the distance is the horizontal distance the crate is lifted (d).
Given:
- Mass of the crate (m) = 15.0 kg
- Distance lifted (d) = 5.70 m
- Acceleration due to gravity (g) = 9.8 m/s^2
Using the formula, the work done during the lift can be calculated as follows:
work = (15.0 kg) * (9.8 m/s^2) * (5.70 m)
work = 814.5 Joules
So, the work done during the lift is 814.5 Joules.
To find the power rating of the lifting device, we can use the formula: power = work / time, where work is the work done during the lift and time is the time taken to lift the crate.
Given:
- Work done (W) = 814.5 Joules
- Time taken (t) = 10 seconds
Using the formula, the power rating of the lifting device can be calculated as follows:
power = 814.5 Joules / 10 seconds
power = 81.45 Watts
Therefore, the power rating of the lifting device is 81.45 Watts.
PE= 294
work done= 294
power= 29.4