Total Work Calculator

Understanding Total Work Calculator

The work-energy theorem states that the net work done on an object equals its change in kinetic energy.

How to use this calculator

1. Enter the object mass, usually in kilograms, and make sure both velocities use the same units.
2. Type the initial velocity and the final velocity.
3. Calculate the net work, which is the change in kinetic energy.
4. Check the sign, positive means the object gained kinetic energy, negative means it lost kinetic energy.

The formula explained

This calculator uses the work-energy theorem, which says net work equals the change in kinetic energy, written as \(W_{net} = \Delta KE = \frac{1}{2}m(v_f^2 - v_i^2)\). It computes how much work was done on the object from its change in speed.

• \(W_{net}\) = net work done on the object
• \(\Delta KE\) = change in kinetic energy
• m = mass of the object
• \(v_i\) = initial velocity
• \(v_f\) = final velocity

Step by step method

1. Square the initial and final velocities.
2. Subtract \(v_i^2\) from \(v_f^2\).
3. Multiply the result by \(\frac{1}{2}m\).

Worked example

Problem. A 4 kg cart speeds up from 3 m/s to 7 m/s. Find the total work done on the cart.

1. Use \(W_{net} = \frac{1}{2}m(v_f^2 - v_i^2)\).
2. Substitute the values, \(W_{net} = \frac{1}{2}(4)(7^2 - 3^2)\). Then \(7^2 = 49\) and \(3^2 = 9\), so \(W_{net} = 2(49 - 9)\).
3. Compute \(W_{net} = 2(40) = 80\).

Tips and common mistakes

• Use the same unit system for both velocities, because mixed units will give a wrong answer.
• If the result is negative, the object slowed down, so the net work removed kinetic energy.

Frequently asked questions