Total Work Calculator, Formula, Calculation

Total 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 total work, W_t(J).

Total Work Calculation Formula:

Total Work is a fundamental concept in the field of physics, specifically in the study of mechanics.

It quantifies the energy transferred to an object when a force causes it to move. This concept is essential in understanding how much energy is involved in accelerating an object from one velocity to another.

Total work is crucial in various practical applications including mechanical engineering, physics, automotive design, and many other fields that involve movement and force interactions.

The formula for calculating total work is based on the change in kinetic energy of an object, where acceleration is assumed to be constant.

Total work, W_t(J) in joules is calculated by one half of the mass, m_(kg) in kilograms and difference of square of final velocity, V_f(m/s)­ in metres per second and initial velocity, V_i(m/s) in metres per second.

Total work, W_t(J) = ½ * m_(kg) * (V²_f(m/s)­ – V²_i(m/s))

W_t(J) = total 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.

Total Work Calculation:

1. Calculate the total work done on a car:

Given:

• • Initial velocity, Vi (m/s) = 10 m/s
  • Final velocity, Vf (m/s) = 20 m/s
  • Mass, m (kg) = 1500 kg

Total work, W_t(J) = ½ * m_(kg) * (V²_f(m/s)­ – V²_i(m/s))

W_t(J) = ½ * 1500 * ( 20² – 10²)

W_t(J) = ½ * 1500 * 300

W_t(J) = 225000J.

2. Suppose a sports car increases its speed from 30 m/s to 50 m/s, and its total work is 960000J. Calculate the mass of the sports car.

Given:

• • Total work, W_t(J) = 960000kg
  • Initial velocity, Vi (m/s) = 30 m/s
  • Final velocity, Vf (m/s) = 50 m/s

Total work, W_t(J) = ½ * m_(kg) * (V²_f(m/s)­ – V²_i(m/s))

m_(kg) = 2 * W_t(J) / (V²_f(m/s)­ – V²_i(m/s))

m_(kg) = 2 * 960000 / (50² – 30² )

m_(kg) = 2 * 960000 / 1600

m_(kg) = 1200kg.

Applications and Considerations:

• Mechanical Engineering: Knowing the total work is vital for designing machines that are efficient in terms of energy use.
• Automotive Industry: Calculating the total work helps in assessing vehicle performance and energy requirements.
• Sports Science: Understanding the work involved in athletic movements can improve training regimes and enhance athletic performance.

How to calculate the total Work: