A box of mass 4 kg is resting on a table 1.5 m above the floor. There is also a ledge located 5 m above the floor. Find the gravitational potential energy of the box relative to the floor, and the gravitational potential energy of the box relative to the ledge.

mgh=4•9.8•1.5=...

mgH=4•9.8•6.5 =...

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To find the gravitational potential energy of an object, you can use the formula:

Gravitational Potential Energy = mass × gravity × height

where:
- mass is the mass of the object in kilograms,
- gravity is the acceleration due to gravity (approximately 9.8 m/s^2 on Earth),
- height is the vertical distance in meters.

In this case, the mass of the box is given as 4 kg. Now let's calculate the gravitational potential energy of the box relative to the floor.

Gravitational Potential Energy (relative to the floor) = 4 kg × 9.8 m/s^2 × 1.5 m

Plugging in the values, we get:

Gravitational Potential Energy (relative to the floor) = 58.8 Joules

So, the gravitational potential energy of the box relative to the floor is 58.8 J.

Now, let's find the gravitational potential energy of the box relative to the ledge, which is located 5 m above the floor.

Gravitational Potential Energy (relative to the ledge) = 4 kg × 9.8 m/s^2 × (1.5 m + 5 m)

Adding the heights, we get:

Gravitational Potential Energy (relative to the ledge) = 4 kg × 9.8 m/s^2 × 6.5 m

Plugging in the values, we get:

Gravitational Potential Energy (relative to the ledge) = 254.8 Joules

So, the gravitational potential energy of the box relative to the ledge is 254.8 J.