# Work & Force-Distance Curves: Physics Lab

Instructor: Matthew Bergstresser
This lesson will go through a lab aimed at generating a force vs distance graph. We will go through the theory of what we are trying to accomplish with the lab, explain the set up of the equipment, execute the experiment, gather data, analyze the data, and make a conclusion.

## Work Lab

The term work in physics is the act of applying a force to a mass making it move. The equation for work is

• W is work in joules (J)
• F is the force applied to the mass in newtons (N)
• d is the distance the mass moves in meters (m)
• θ is the angle between the force and the displacement. The angle between the applied force, which, in this case will be 0o , and the cosine of 0o is 1.

If we generate a graph of force versus distance, the area under the curve will represent the work done by the force. In this lab, we are going to drag a mass across a surface at constant velocity with a very light string attached to a force scale. There are two forces acting along the line of the mass's displacement; the tension in the string, and friction because the tabletop is not frictionless. Tension and friction are both doing work. Since the velocity is constant, the applied force has to be countered by an equal friction force in the opposite direction. If the force varies, the distance the mass moves will have to measured independently for each change in force. To avoid this, we have to be very careful when pulling the mass so the scale represents a constant force. This ensures that the mass remains at constant velocity with no acceleration. In addition, we want to be sure the string stays parallel to the table so the angle θ is 0o. If we can do this, the friction force will be the same as the applied force.

#### Materials Needed

1. Table

2. 5 kg mass

3. Very light, extension-less string

4. Spring scale

5. Meter stick

6. Marker

#### Procedure

• Place masking tape along the entire length of the table.
• Mark 10 cm intervals on the masking tape for 1 meter.
• Begin pulling the mass, adjusting the pulling force if necessary to ensure constant velocity, and a constant force reading on the scale.
• Note the mark on the table when your are confident the mass is moving with constant velocity.
• Continue to pull to the end of the table noting the force reading at each 10 cm interval mark.

#### Data

• The distance the mass moves at constant velocity is 0.5 m.
• The force scale reads a constant 8 N.

#### Plotting Data

We will plot the scale's force value versus the distance the mass moved, and the equal but opposite friction force value versus the same distance traveled.

#### Analyzing Data

The top line of the graph represents the tension force in the string that is moving the mass. The area between it and the x-axis is the work done by the tension force, and it is shaded in red.

Determining the area of this shaded region is the area of a rectangle; length times width.

The bottom area is shaded in blue, and this is the work done by the friction force.

The area of this shaded region is also the area of a rectangle; length times width.

#### Conclusion

What do we notice about theses areas? They are equal in value, but opposite in sign! Therefore, the net area between the two curves and the x-axis is 0. Does this mean 0 work was done? Yes. Overall, there was no work done on the mass. The person did work, but friction did the same amount of negative work making the overall work done 0.

Let's look at this conclusion we came to through the lens of the net-work kinetic energy theorem. The net work done on an object is equal to the change in kinetic energy of the object. Kinetic energy is one-half of the mass of the object times the square of its velocity.

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