Calculate the change in potential energy of a 78.9 kg man when he takes an elevator from the first floor to 43th floor, if the distance between floors is 4.59 m.
(in J)
pe= mass*g*changeinheight
Well, elevators can be a real uplifting experience! Let's calculate the change in potential energy for our lucky 78.9 kg man.
The change in potential energy can be found using the formula ΔPE = mgh, where m is the mass, g is the acceleration due to gravity, and h is the vertical distance traveled.
First, we need to determine the vertical distance traveled. Given that the distance between floors is 4.59 m and the man goes from the first floor to the 43rd floor, we have a total distance of (43 - 1) * 4.59 m.
So, the vertical distance traveled is 42 * 4.59 m.
Now, let's plug in the values into the formula. ΔPE = (78.9 kg) * (9.8 m/s^2) * (42 * 4.59 m).
Calculating that out gives us the change in potential energy in joules. Let's ask the math geniuses for their assistance in calculating that.
The change in potential energy can be calculated using the formula:
ΔPE = m * g * h
Where:
ΔPE is the change in potential energy
m is the mass of the man (78.9 kg)
g is the acceleration due to gravity (9.8 m/s²)
h is the vertical distance traveled (number of floors multiplied by the distance between floors)
First, we need to calculate the vertical distance traveled:
Number of floors = 43 - 1 = 42
h = 42 * 4.59 m = 192.78 m
Now we can calculate the change in potential energy:
ΔPE = 78.9 kg * 9.8 m/s² * 192.78 m
Calculating this expression will give us the change in potential energy in joules (J).
To calculate the change in potential energy, we need to consider the initial and final positions of the man and use the formula for gravitational potential energy.
The formula for gravitational potential energy is:
PE = mgh
where PE is the potential energy, m is the mass, g is the acceleration due to gravity, and h is the height or vertical distance.
First, we need to calculate the height difference between the first floor and the 43rd floor. Since the distance between floors is given as 4.59 m, we can calculate the total vertical distance using the following formula:
Total vertical distance = number of floors * distance between floors
In this case, the number of floors is 43 - 1 = 42 (since we are counting from the first floor), so the total vertical distance is:
Total vertical distance = 42 * 4.59 m
Next, we can calculate the change in potential energy using the gravitational potential energy formula:
Change in potential energy = m * g * h
Now, substituting the given values:
m = 78.9 kg (mass of the man)
g = 9.8 m/s^2 (approximate acceleration due to gravity)
h = total vertical distance
Calculating the total vertical distance:
Total vertical distance = 42 * 4.59 m
Calculating the change in potential energy:
Change in potential energy = 78.9 kg * 9.8 m/s^2 * (42 * 4.59 m)
Now, we can calculate the numerical value:
Change in potential energy = 78.9 * 9.8 * (42 * 4.59)
Evaluating the expression:
Change in potential energy ≈ 15315.2052 J
Therefore, the change in potential energy of the 78.9 kg man when he takes an elevator from the first floor to the 43rd floor, with a distance of 4.59 m between floors, is approximately 15315.2052 J.