# Work Done Calculation by Force Displacement Graph

To calculate the work done using a force-displacement graph, you need to find the area under the graph. The work done is equal to the area under the curve of the force-displacement graph.

## Definition And Formula Of Force Displacement Graph

Workdone in Force Displacement Graph is a fundamental concept in physics that describes the energy transferred when a force acts on an object and causes it to move a certain distance. To calculate the work done by a constant force, you can use the following formula:

Where:

– W is the work done (measured in joules, J).

– F is the magnitude of the force (measured in newtons, N).

– d  is the displacement of the object in the direction of the force (measured in meters, m).

– theta is the angle between the force vector and the direction of displacement (measured in radians).

Here are the key details and steps for calculating the work done by a constant force:

1. Identify the Force: Determine the magnitude and direction of the constant force acting on the object. This force can be applied in various ways, such as pushing, pulling, or lifting.
2. Determine the Displacement: Find the distance and direction over which the object is displaced by the force. The displacement should be measured in the direction of the force.

Also Check – Work Done by a Variable Force Formula

1. Calculate the Angle \theta: If the force and displacement are not in the same direction, you need to calculate the angle \theta\) between them. This angle is measured in radians and can be found using trigonometry.
2. Plug Values into the Formula: Use the formula W = F *dcos(θ) and substitute the values you have gathered for F\), d\), and θ
3. Calculate the Work: Perform the calculations to find the work done by the constant force. Ensure that you use consistent units for force (N), displacement (m), and angle \theta.
4. Consider Sign and Interpretation: The sign of the work done can provide information about the nature of the work. Positive work is done when the force and displacement are in the same direction (e.g., lifting an object), while negative work is done when they are in opposite directions (e.g., lowering an object against gravity).
5. Units and Final Answer: Make sure your final answer has the appropriate units (joules, J) and includes the sign to indicate whether the work is done on the object (positive) or by the object (negative).

Also Check – Work Done in Raising a Box Formula

In summary, the work done by a constant force depends on the magnitude of the force, the distance over which the force is applied, and the angle between the force and the direction of displacement. Calculating work is essential in understanding the energy transfer associated with various physical processes and is a fundamental concept in mechanics and physics.

## Some Examples Of Force Displacement Graph

Certainly! Here are some examples of calculating the work done by a constant force in different scenarios:

1. Lifting a Weight:

– Scenario: You lift a 10 kg weight vertically upward by applying a constant force of 50 N over a height of 2 meters.

– Work Done W = Force F × Displacement d × cos(θ)

– θ = 0 degrees (since the force is applied vertically upward)

– Work Done W = 50 N × 2 m × cos(0°) = 100 J (joules)

Also Check – Unit, Dimension & Vector Formula

## Work Done Calculation by Force Displacement Graph

To calculate the work done using a force-displacement graph, you need to find the area under the graph. The work done is equal to the area under the curve of the force-displacement graph. The formula for calculating work in this context is:

Work (W)= Area under the Force-Displacement Graph

Here’s how you can do it:

1. Plot the force-displacement graph: Make sure you have a clear graph of force (F) on the y-axis and displacement (d) on the x-axis. The graph should represent the relationship between these two variables.
2. Divide the graph into shapes: Depending on the complexity of the graph, you may need to divide it into different shapes, such as rectangles, triangles, or trapezoids. These shapes should approximate the curve of the graph.
3. Calculate the area of each shape: For each shape, calculate its area. The area of a rectangle is given by Area} =Length*Width,
4. Sum up the areas: Add up the areas of all the shapes to find the total area under the graph. This total area represents the work done by the force in displacing the object.
5. Units: Make sure your units are consistent. If your force is in Newtons (N) and displacement is in meters (m), the work done will be in joules (J).

Here’s an example:

Let’s say you have a force-displacement graph where the force increases linearly with displacement, forming a triangle. The graph shows a force of 10 N at a displacement of 5 meters. To find the work done:

1. Calculate the area of the triangle:

Area =1/2Base)(Height) = (½(10*5)\text{N} = 25 joule

So, in this example, the work done by the force is 25 Joules.

## Work Done Calculation by Force Displacement Graph FAQs

### What does the area under the force-displacement graph represent?

The area under the force-displacement graph represents the work done by the force in displacing an object. It quantifies the energy transferred to or from the object due to the force.

### How do I interpret a negative area under the graph?

A negative area under the graph indicates that work is done against the force or that the object is doing work on the force (e.g., when the force opposes the displacement). It represents a decrease in energy.

### Can I use any shape to approximate the graph for calculating work?

Yes, you can use various shapes like rectangles, triangles, or trapezoids to approximate the graph. The choice of shape depends on how accurately you want to estimate the work done.

### Is this method applicable to all types of force-displacement graphs?

This method is applicable to graphs where the relationship between force and displacement is continuous and can be approximated by geometric shapes. For more complex or irregular graphs, numerical integration techniques may be required for accurate calculations.