## Net Work Calculator:

Enter the values of mass, m_{(kg)}, final velocity, V_{f(m/s)} and initial velocity, V_{i(m/s)} to determine the value of net work, W_{(J)}.

__Net Work Formula:__

__Net Work Formula:__

Net work is the total amount of work done on an object when it undergoes a change in velocity, indicating the energy transferred to the object. This concept is vital in understanding how objects accelerate under various forces.

Net work is represented in physics by the change in the kinetic energy of an object, which is calculated based on the mass of the object and the square of its velocities at the beginning and end of the motion.

The formula for net work, derived from the work-energy principle, states that the work done on an object is equal to the change in its kinetic energy.

Net work, W_{(J)} joules equals one-half times the mass, m_{(kg)} kilograms times the square of the final velocity, V_{f(m/s)} metres per second minus one-half times the mass, m_{(kg)} in kilograms times the square of the initial velocity, V_{i(m/s)} in metres per second.

Net work, W_{(J)} = (1 / 2 * m_{(kg)} * V^{2}_{f(m/s)}) – (1 / 2 * m_{(kg)} * V^{2}_{i(m/s)})

W_{(J)} = net work in joules, J.

m_{(kg)} = mass in kilograms, kg.

V_{f(m/s)} = final velocity in metres per second, m/s.

V_{i(m/s)} = initial velocity in metres per second, m/s.

__Net Work Calculation:__

- A cyclist increases their speed:

Given:

- Mass, m
_{(kg)}= 70 kg - Initial velocity, V
_{i(m/s) }= 5 m/s - Final velocity, V
_{f(m/s)}= 10 m/s

Net work, W_{(J)} = (1 / 2 * m_{(kg)} * V^{2}_{f(m/s)}) – (1 / 2 * m_{(kg)} * V^{2}_{i(m/s)})

W_{(J)} = (1 / 2 * 70 * 10^{2}) – (1 / 2 * 70 * 5^{2})

W_{(J)} = 35 * (100-25)

W_{(J)} = 35 * 75

W_{(J)} =2625J.

- Suppose the net work done on a system is 870,720 joules, the mass of the object is 1200 kg, and the final velocity is 44 m/s. Calculate the initial velocity.

Given:

- Mass, m
_{(kg)}= 1200 kg - Net work, W
_{(J)}= 870720J. - Final velocity, V
_{f(m/s)}= 44 m/s

Net work, W_{(J)} = (1 / 2 * m_{(kg)} * V^{2}_{f(m/s)}) – (1 / 2 * m_{(kg)} * V^{2}_{i(m/s)})

V_{i(m/s)} = √ (V^{2}_{f(m/s)} – 2 * W_{(J) }/ m_{(kg)} )

V_{i(m/s)} = √ (44^{2} – 2 * 870720 / 1200)

V_{i(m/s)} = √ (1936 – 1451.2)

V_{i(m/s)} = 22m/s.

__Applications and Considerations:__

**Vehicle Performance**: Engineers calculate the net work done on vehicles to optimize fuel efficiency and performance.**Sports Science**: Understanding the work done on athletes can help in designing better training regimens.**Physics Education**: Net work is a fundamental concept that helps students understand energy transfer.**Engineering Applications**: Net work calculations are essential for the design and analysis of mechanical systems where energy transformation is crucial.