If gravity is the only force present, what is the total mechanical energy of a box falling of a truck at a time when it's potential energy is 100J and it's kinetic energy is 150J?

u all where wrong its 1,100 j

250 , just add

Be aware that the value of potential energy depends upon the location where you define it to be zero. That location is arbitrary.

Damon's answer is correct; I just object to the wording of the question.

100 j

250 J

To determine the total mechanical energy of the falling box, we need to consider the potential energy (PE) and kinetic energy (KE). The total mechanical energy (E) is the sum of these two forms of energy.

The potential energy of an object is given by the equation PE = mgh, where m represents the mass of the object, g is the acceleration due to gravity (approximately 9.8 m/s² near the Earth's surface), and h is the height of the object above a reference point (in this case, the point where the potential energy is zero).

The kinetic energy of an object is given by the equation KE = (1/2)mv², where m represents the mass of the object, and v is its velocity.

Since the box is falling, its potential energy is decreasing while its kinetic energy is increasing. At the specific point in time when the potential energy is 100J and the kinetic energy is 150J, we can equate these two forms of energy:

PE = KE

mgh = (1/2)mv²

Here, we can notice that the mass of the box cancels out, so we can ignore it from this equation. Solving for v, we get:

gh = (1/2)v²

v² = 2gh

v = √(2gh)

Now, we can substitute back the values given in the question. Assuming g is approximately 9.8 m/s²:

v = √(2 * 9.8 m/s² * 100 J)

v = √(1960 m²/s²)

v ≈ 44.27 m/s

Once we have the velocity, we can use it to calculate the total mechanical energy:

E = PE + KE

E = 100 J + 150 J

E = 250 J

Therefore, the total mechanical energy of the falling box, at the given time, is 250 Joules.