This sheet is meant to supplement your learning

http://ola4.aacc.edu/PHS100SelfCheck/ Competency 1

This sheet is meant to supplement your learning. Please also refer to in-class activities and explanations as well as your textbook.

Force Diagrams

What is a force diagram?

A force diagram (often called a ‘free-body diagram’) is a drawing that shows what forces are acting on an object at a particular time. It also shows the strength of each force and the direction it is acting in.

Why should I draw a force diagram?

Force diagrams are a necessary first step in analyzing a wide range of problems involving motion, buoyancy, astronomy and others.

How do I draw a force diagram?

Follow these 3 steps:

Identify the object of interest (this is important because there is almost always more than one object present in a demonstration, example, or test question)
Identify the time of interest (this is essential, because the forces acting on an object can change quite rapidly, so you want to know which time or times are the most important to analyze)
Draw an arrow for each force acting on the object at the chosen time. Do not include forces acting on another object or forces that were acting on the chosen object, but are no longer acting.

What are the types of forces?

Here is a list of some common forces:

gravity, F_G- Use Newton’s Law of Universal Gravitation to determine the length of the force
applied force, F_applied- Is there a person touching the object at that time?
support force, F_support - Is another object pushing against the chosen object? This force acts perpendicular to the surface.
friction force, F_friction- This force is created when an object is in contact with a surface and is moving along that surface (or is resisting a force that would otherwise cause it to move along that surface). For a moving object, the force of friction acts opposite the motion. The magnitude of this force depends on the nature of the surfaces and how tightly they are pressed together.
air resistance, F_AR- Is the object moving through air? Remember that air resistance depends on two things- speed and cross-sectional area. Air resistance always acts opposite to the motion.
buoyant force, F_Buoyant- Archimedes principle states that the buoyant force is equal to the weight of fluid displaced.

What are some things that are not forces and should not be on a force diagram?

These are not forces:

inertia
momentum
velocity
acceleration
speed

Can you give me an example of how to draw a force diagram?

Sure, let’s go through a few examples.

Example A: You give a box a brief push to the right and then watch as it slides across the floor and stops. Draw a force diagram for the box while you are pushing it.

Step 1: This is easy- since the problem clearly asks about the box, we will draw a force diagram for the box.

Step 2: Again, the problem statement clearly states that you should analyze the box while it is being pushed, so we will make sure our force diagram corresponds to that time period.

Step 3: What forces are acting on the box?

The box has mass, so there is a force of gravity pulling down on the box. The box is on the floor- therefore, the floor is pushing up on the box (support force). For the time while you are pushing the box, there is an applied force acting on the box to the right. Also, there is friction between the box and the floor. This force is acting opposite to the box’s motion (to the left). Air resistance is likely to be insignificant in this problem because the box is not moving very fast. Now, let’s see what those forces look like on a diagram.

Example B: You give a box a brief push to the right and then watch as it slides across the floor and stops. Determine the acceleration for the box while it is slowing down (after you stopped pushing it).

This problem does not ask that you draw a force diagram. Nonetheless, drawing a force diagram is the best first step you can take!

Step 1: This is easy- since the problem clearly asks about the box, we will draw a force diagram for the box.

Step 2: Again, the problem statement clearly states that you should analyze the box while it is sliding, but after you stopped pushing it.

Step 3: What forces are acting on the box?

The box has mass, so there is a force of gravity pulling down on the box. The box is on the floor- therefore, the floor is pushing up on the box (support force). Since the problem asks for the time period after we stopped pushing it, we will NOT include an applied force. We know that the box slows down during this time. The box is not moving fast, so air resistance is likely to be insignificant in this problem. Friction between the box and the floor is the probably the force that is causing the box to slow down. The friction force is acting to the left (since friction opposes the motion). Now, let’s see what those forces look like on a diagram.

Let’s not lose sight of what the problem asked us to find, which is the acceleration during this time. We know from Newton’s 2^nd Law that acceleration is equal to net force divided by mass:

Note that acceleration and the net force are both vectors. The acceleration will therefore be in the same direction as the net force. We can figure out the direction of the net force from our force diagram and this will tell us the direction of the box’s acceleration.

Looking at the force diagram above, the force of gravity and support force are the same size. This means the vertical net force is zero and thus the vertical acceleration is zero.

However, there is only one force acting in the horizontal direction and it is to the left. This means the horizontal net force is to the left and thus the horizontal acceleration is to the left.

Let’s summarize: The box is moving to the right, but accelerating to the left. What does this mean?? This means that the box is slowing down. We could say also say it is decelerating.