Introduction to Work and Examples| Physics Club
In physics, work is defined as the amount of energy transferred when an external force moves an object over a certain distance. The units of work are kg·m/s², or the joule. The general definition of work is
where F is the force applied on the object and ds is the displacement. But, when the motion is in one direction, which is what we will mostly focus on, the equation is reduced to
where F is the force applied on the object, s is the displacement, and α is the angle between the force and displacement.
The following are a few example problems.
Example 1
The problem: You pull a crate with a force of 98N at an angle of 25° above the horizontal for a distance of 62 meters. What is the total work done by you on the crate?
In this problem, the angle between the force and the displacement is 25°, precisely the angle given in the problem. This won’t always be the case, just as a warning.
We first define our variables then plug them appropriately into the equation for work:
Therefore, you perform 5507 joules of work on the crate by pulling it 62 meters.
Example 2
The problem: A boy is pulling his sister in a wagon. He exerts a force of 55.5N at an angle of 30°. How much work does the boy do pulling his sister if he pulls her 30.5 meters?
This example and example 1 above are very similar. The only difference is the scenario, but we are given the same variables.
Again, let’s define our variables and plug them into the equation for work:
The boy performs 1466 joules of work pulling his sister 30.5 meters.
Example 3
The problem: A box weighing 23.0 kilograms slides down an inclined plane at a constant velocity. The incline is 37.0° above the horizontal, and the box slides 1.50 meters. What is the work done by the normal force, gravity, and friction? What is the total work done on the box?
In this problem, we are really asked four questions. We need to find
- the work done by the normal force;
- the work done by gravity;
- the work done by friction;
- and the total work done on the box.
To answer the first three questions, we need the values of the three forces. To find these values, we must utilize Newton’s laws of motion. Here is a representation of the scenario and a free-body diagram:
Utilizing Newton’s first law of motion in the y-direction, we get the normal force to be:
The force of gravity is given by:
Finally, the force of friction is given by:
Work done by the normal force (note that the angle between the displacement and the normal force is 𝛼 = 90°):
The work done by the normal force is 0J since the normal force acts in a direction perpendicular to the displacement.
Before the we calculate the work done by the gravitational force, we need to figure out the angle between it and the displacement, which is θ = 37°. We can find the angle we need, 𝛼, by going back to the free-body diagram:
When calculating the normal force, we saw that N = Fgy, therefore Fgy = 180N. Likewise, Fg = 225N. Now, we can use trigonometry to solve for the angle 𝛼:
Now that we have our angle 𝛼, the angle relative to the displacement, we can calculate the work done by the gravitational force:
Now we need to calculate the work done by the frictional force. Since the frictional force acts in the opposite direction of displacement, the angle between them is 180°.
The work done by the frictional force is:
Lastly, we need to calculate the total work done on the object, which we can do by simply adding the work done by the normal force, gravitational force, and frictional force:
Therefore, the total work done on the object is 0J. This makes sense when you realize that no actual object or person is applying any force on it.
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