Work Calculator

What is Work in Physics?

Generally, work (W) is often defined as the product of the force (F) over a distance of displacement. In other words, work is an energy transfer to or from an object by the application of force along with a displacement (d). Joule (J) is the SI unit for work. The joule (J) is described as the work is done by the force (F) of a newton acting over a distance (d) of one meter (m). SI units of work (W) is kgm2s-2. An online work calculator provides all calculations with SI work units. According to the work definition the equation for work is: $$W = F * d$$

Where:

• \( d \) = distance covered by an object
• \( F \) = force applied to an object
• \( W \) = work done

Work Formula:

The work done by a force is given by:

\( W = F \cdot d \)

Or equivalently:

\( W = \text{force (F)} \times \text{distance (d)} \)

The force can also be calculated as:

\( F = \frac{W}{d} \)

And the displacement can be calculated as:

\( d = \frac{W}{F} \)

Work from Velocity (\(v\)) Change:

Suppose an object changes its speed from the initial velocity \(v_0\) to the final velocity \(v_1\) over a time \(t\). We can calculate the force \(F\) using the acceleration \(a\):

\( F = m \cdot a = m \cdot \frac{v_1 - v_0}{t} \)

The distance \(d\) covered can be approximated as:

\( d = t \cdot \frac{v_0 + v_1}{2} \)

Now, combining these into the work formula:

\( W = F \cdot d = \left[m \cdot \frac{v_1 - v_0}{t}\right] \cdot \left[t \cdot \frac{v_0 + v_1}{2}\right] = \frac{m}{2} \cdot (v_1^2 - v_0^2) \)

Therefore, work can also be calculated directly from the change in velocity using the kinetic energy approach. You can also use an Online Velocity Calculator to determine the velocity and speed of a moving object.

Types of Work (W):

There are three types of work.

• +ve work done
• Zero (0) work done
• -ve work done

Positive (+) work done:

Work done is positive, when the force (F) and the displacement (d) are in the same directions. Or when the value of theta θ is between 0 to 90 degrees. For instance, pushing or pulling of the door.

Zero (0) work done:

Work done on any object is zero when force (F) and displacement (D) are normal to each other. Apart from this, when the value of theta θ is equal to 90 degrees. For example, when a person moves while holding a jug full of water.

Negative (-) work done:

Work done is negative, when the force and the displacement are in opposite directions. On the other side, work is negative, when the value of theta θ is between 90 to 180 degrees. For example, work is done on a football moving up due to gravity.

How to Calculate Work Done?

If you want to know how to find work by hand then follow these steps:

• Firstly, find force using its formula, which is F = ma.
• Measure the angle.
• Then convert values into SI units and plug in all the values in the formula for work and solve it.

Otherwise, you can determine work and related terms by plug in the known values in the work calculator.

Example:

Find the work done by a force acting at an angle.

• Force: \( F = 15 \, \text{N} \)
• Angle: \( \theta = 45^\circ \)
• Displacement: \( d = 22 \, \text{m} \)

Solution: Using the work formula:

\( W = F \cdot d \cdot \cos\theta \)

Calculate the component of force in the direction of displacement:

\( F_{\text{effective}} = 15 \cdot \cos 45^\circ \approx 10.60 \, \text{N} \)

Work done:

\( W = F_{\text{effective}} \cdot d = 10.60 \cdot 22 \approx 233 \, \text{J} \)

An Online Displacement Calculator can also be used to compute displacement using average velocity, acceleration, initial/final velocities, and time.

Definition of Power (\(P\)):

Power is the rate at which work is done or energy is transferred. Its SI unit is the watt (W), equal to joule per second.

\( P = \frac{W}{t} \)

Where:

• \( P \) = power
• \( W \) = work done
• \( t \) = time

How to Use Work Calculator?

This free online calculator determines the work, power, force, and displacement with the following steps:

Input:

• First of all, choose work or power from the drop-down list.
• If you select the work then choose an option to calculate from force & displacement or change in velocity.
• Now, click on an option that you want to find and enter the corresponding values with different units.
• Click on the calculate button.

Output:

• The work calculator provides the answer with a unit according to the option that you selected before.
• Then displays formula and step-by-step solution.

FAQs:

Define the relationship between torque and rotation?

Torque changes the angular velocity, and the amount of angular momentum which, depends on its angular velocity. So, the torque can transform angular momentum this is how both are related.

What is the relationship between work and energy?

Energy changes the position of an object and this amount of energy changed by the force to move a particular object is called work done. Hence the direct relationship between energy and work.

Conclusion:

An online work calculator that allows you to compute the work and power when two of the variables are known. Find these values by hand is such a difficult and time-consuming task so, you can use this handy calculator that helps to find exact values with SI units quickly without any cost.

Reference:

From the source of Wikipedia: Work and energy, Constraint forces, Work done by a variable force, Torque and rotation. From the source of Britannica: Work and potential energy, Work by gravity, Work by gravity in space, Work by a spring. From the source of Physics Info: conservative vs. nonconservative forces, work-energy theorem, Sign conventions, Derivation for a particle moving along a straight line.