A crane lifts a cargo box 10 m off the ground. If the crane lifts the cargo box twice as high, the potential energy will increase by
Answer:
Two times
Explanation:
The crane lifts the cargo twice as high so the potential energy will increase twice the amount.
two times
To determine how much the potential energy increases when the crane lifts the cargo box twice as high, we need to understand the relationship between potential energy and height.
The potential energy of an object near the surface of the Earth is given by the formula:
Potential Energy = mass x gravity x height
Where:
- mass = mass of the object in kilograms (kg)
- gravity = acceleration due to gravity, which is approximately 9.8 m/s²
- height = height above a reference point (in meters)
In this case, let's assume that the mass and gravity remain constant.
If the crane lifts the cargo box 10 m off the ground, the potential energy is given by:
Potential Energy1 = mass x gravity x height1
Now, if the crane lifts the cargo box twice as high, the new height will be 2 times the original height:
height2 = 2 x height1
Substituting this value into the potential energy formula:
Potential Energy2 = mass x gravity x height2
= mass x gravity x (2 x height1)
= 2 x (mass x gravity x height1)
Comparing the initial potential energy (Potential Energy1) to the new potential energy (Potential Energy2), we can see the change:
Change in Potential Energy = Potential Energy2 - Potential Energy1
= 2 x (mass x gravity x height1) - (mass x gravity x height1)
= mass x gravity x height1
Therefore, the potential energy increases by the same amount as the initial potential energy, which is equal to the mass times gravity times the original height.