A Crane lifts a cargo Box 10M off the ground if the Crane lifts the cargo Box toys as high the potential energy will be increased by

The correct answer is two times.

To determine the increase in potential energy when the crane lifts the cargo box twice as high, let's first understand the concept of potential energy.

Potential energy (PE) is the energy possessed by an object due to its position relative to other objects or forces acting upon it. In the case of objects near the earth's surface, potential energy is often associated with the object's height above the ground.

The potential energy of an object at a certain height can be calculated using the formula:

PE = mgh

Where:
PE = Potential Energy
m = mass of the object
g = acceleration due to gravity (approximately 9.8 m/s²)
h = height above the reference point (in this case, the ground)

Given that the crane lifts the cargo box 10 meters off the ground initially, let's assume the mass of the cargo box is 'm' kg.

Using the formula, the initial potential energy (PE_initial) can be calculated as:
PE_initial = m * g * 10

Now, if the crane lifts the cargo box twice as high, the new height (h_new) will be 2 * 10 = 20 meters.

The new potential energy (PE_new) at this height can be calculated as:
PE_new = m * g * 20

To find the increase in potential energy, we subtract the initial potential energy from the new potential energy:
Increase in Potential Energy = PE_new - PE_initial
Increase in Potential Energy = (m * g * 20) - (m * g * 10)
Increase in Potential Energy = m * g * 10

Therefore, the increase in potential energy when the crane lifts the cargo box twice as high is equal to m * g * 10, where 'm' represents the mass of the cargo box and 'g' represents the acceleration due to gravity.

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PE = mgh

So,
∆PE = mg*∆h