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
half.
the same amount.
two times.
four times.
two times
P.E. = m g h ... the potential energy is directly proportional to the height
When an object is lifted, its potential energy is given by the equation PE = mgh, where m is the mass of the object, g is the acceleration due to gravity, and h is the height.
In this case, the crane lifts the cargo box 10 m off the ground. So, the initial potential energy is given by PE1 = mgh1.
If the crane lifts the cargo box twice as high, the new height will be 2h1. So, the new potential energy will be given by PE2 = mgh2, where h2 = 2h1.
To compare the change in potential energy, let's find the ratio of the new potential energy to the initial potential energy:
PE2 / PE1 = (mgh2) / (mgh1)
= (mg(2h1)) / (mgh1)
= 2
Therefore, the potential energy will increase by two times. So, the correct answer is "two times".
To determine how the potential energy changes 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 can be calculated using the formula:
Potential Energy = mass x gravity x height
In this case, we are only concerned with how the height affects the potential energy, so we can ignore the mass and gravity factors.
Given that the crane initially lifts the cargo box 10 m off the ground, let's calculate the initial potential energy:
Initial Potential Energy = 10 m
If the crane lifts the cargo box twice as high, the new height would be 2 x 10 m = 20 m.
Now, let's calculate the new potential energy when the box is lifted to this new height:
New Potential Energy = 20 m
Comparing the initial potential energy (10 m) to the new potential energy (20 m), we can see that the potential energy has doubled (increased by two times).
Therefore, the correct answer is: two times.