As a box is pushed 30 meters across a horizontal floor by a constant horizontal force of 25 newtons, the kinetic energy of the box increases by 300 joules. How much total internal energy is produced during this process?

450

Question: As a box is pushed 30 meters across a horizontal floor by a constant horizontal force of 25 newtons, the kinetic energy of the box increases by 300 joules. How much total internal energy is produced during this process?

Answer: W=FÄr

From the work energy theorem, you know that the total energy of the box must increase by 750 joules. If the kinetic energy of the box increases by 300 joules, where did the other 450 joules of energy go? It must have been transformed into internal energy!

Well, let me put on my thinking wig and do some calculations for you. The work done on an object is equal to the change in kinetic energy, so we know that 25 newtons times 30 meters equals 300 joules. But the internal energy is a bit shy and doesn't like to show up to parties, so it stays constant during this process. Therefore, the total internal energy produced is as elusive as a unicorn in clown shoes, and it remains unchanged at zero joules.

To calculate the total internal energy produced during the process, we need to use the principle of conservation of energy.

The work done by the horizontal force can be represented by the change in kinetic energy of the box. Therefore, we can calculate the work done using the formula:

Work = Change in Kinetic Energy

Given that the change in kinetic energy is 300 joules, the work done is also 300 joules.

Now, the work done is equal to the total energy transferred, which is comprised of the change in kinetic energy and the internal energy produced. Mathematically, we can write:

Work = Change in Kinetic Energy + Internal Energy

Substituting the given values, we have:

300 joules = 300 joules + Internal Energy

Simplifying the equation, the internal energy is:

Internal Energy = 300 joules - 300 joules

Internal Energy = 0 joules

Therefore, the total internal energy produced during this process is 0 joules.

To find the total internal energy produced during this process, we need to understand the concept of work done on an object and the conservation of energy.

The work done on an object is defined as the product of the force applied on the object and the displacement of the object in the direction of the force. Mathematically, work (W) is given by:

W = F * d * cos(theta)

Where F is the force applied, d is the displacement, and theta is the angle between the force and displacement vectors. In this case, since the force is applied horizontally and the displacement is also horizontal, theta = 0 degrees, so cos(theta) = 1.

Now, the increase in kinetic energy of the box is equal to the work done on it:

Change in kinetic energy = Work done
300 Joules = Force * displacement

We are given the force applied (25 Newtons) and the displacement (30 meters), so we can substitute these values into the equation:

300 Joules = 25 Newtons * 30 meters

Now we can solve for the work done on the box:

Work done = 25 Newtons * 30 meters
Work done = 750 Joules

So, the work done on the box is 750 Joules.

The total internal energy produced during this process is equal to the work done on the box. Therefore, the total internal energy produced is 750 Joules.