lake point tower in chicago is the tallest apartment biulding in the united states (although not the tallest biulding in which there are apartments). supose you take the elevator from street level to the roof of the biulding. the elevator moves almost the entire distance at constant speed, so that it does 1.15 x 10^5J of work on you as it lifts the entire distance. if your mass is 60.0 kg, how tall is the building? ignore the effects of friction.
can someone please help with the steps in how to do it ?
To solve this problem, we can use the work-energy principle, which states that the work done on an object is equal to the change in its kinetic energy. In this case, the work done by the elevator is equal to the change in potential energy of your body as you move from the street level to the roof.
The formula for calculating the change in potential energy is:
ΔPE = mgh
Where:
ΔPE is the change in potential energy
m is your mass (60.0 kg)
g is the acceleration due to gravity (approximately 9.8 m/s^2)
h is the height of the building
We are given that the elevator does 1.15 x 10^5 J (joules) of work on you. This work done is equal to the change in potential energy:
1.15 x 10^5 J = mgh
Now we can substitute the given values into the equation and solve for h:
1.15 x 10^5 J = (60.0 kg)(9.8 m/s^2)h
Rearranging the equation to solve for h:
h = (1.15 x 10^5 J) / (60.0 kg)(9.8 m/s^2)
Calculating the value of h:
h = 1.95 x 10^1 m
Therefore, the height of the building is approximately 19.5 meters.
To solve this problem, we can use the concept of work-energy theorem, which states that the work done on an object is equal to the change in its kinetic energy. In this case, the work done by the elevator is equal to the change in potential energy of the person being lifted.
Here are the steps to find the height of the building:
1. Identify the known quantities:
- Work done by the elevator (W) = 1.15 x 10^5 J
- Mass of the person (m) = 60.0 kg
- Acceleration due to gravity (g) = 9.8 m/s^2 (ignoring the effects of friction)
2. Calculate the change in potential energy:
Since the elevator does work on the person to lift them, the work done is equal to the change in potential energy.
Potential Energy (PE) = m * g * h (mass * gravity * height)
3. Apply the work-energy theorem:
According to the work-energy theorem, the work done on the person is equal to the change in potential energy. So we can set them equal to each other:
W = PE
4. Substitute the known values into the equation:
We know the work done (W) and the mass (m), and we want to find the height (h).
Substitute the values into the equation and solve for h:
W = m * g * h
1.15 x 10^5 J = 60.0 kg * 9.8 m/s^2 * h
5. Solve for h:
Divide both sides of the equation by (60.0 kg * 9.8 m/s^2):
h = (1.15 x 10^5 J) / (60.0 kg * 9.8 m/s^2)
6. Calculate the height:
Plug in the values into the equation:
h = 1.95 meters
Therefore, the height of the building is 1.95 meters.
The work done ON YOU while lifting you a distance H is
W = M g H.
You have been told what W is; now solve for H.
M = 60 kg
g = 9.8 m/s^2