Free-Body Diagrams

Free-body diagrams are useful tools for visualizing forces being exerted on a single object and writing the equations that represent a physical situation🤓 

As we’ve covered over a multitude of standards in this guide, you must understand how to correctly depict a free-body diagram in AP Physics 1. This includes the few key concepts that we’ve dealt with. If you remember two key things with free-bodies, keep in mind they only show external forces (ie. forces that cause motion) and do not draw components unless otherwise specified.

Author's suggestions for FBD

1. Make sure the arrows actually touch the object. Many kids lose points because of this strict grading rule 💯
2. Try to look at one force at a time. Some FBD in this course might be tough and complex. Look where the object is and ask yourself questions. Can we ignore resistive forces and air resistance? Is the object in a fluid and experiencing a buoyant force? Is there a normal force?
3. Draw the arrow starting where the force is applied. The normal force is not at the center of the object but rather where it touches the ground or the surface. The gravitational force doesn't act at the top or the bottom of the object but rather the center of gravity (so draw it roughly in the middle) ⬅️➡️↖️↙️↗️
4. Don't draw component on the original FBD. Draw the components and do the work on a separate FBD. Leave the original FBD for grading ✋🏻
5. When drawing components be wise about your axes. Sometimes it really helps if your axes are rotated ⭕️

Forces

Forces you are likely to encounter in this course:

1. Gravitational: points towards the earth (usually downward) 🏋️‍♀️
2. Buoyancy: points away from gravity (usually upwards) 💧
3. Normal: points in the direction away from the contact between the surfaces 🪑
4. Friction: points in the direction that opposes relative motion (friction doesn't always oppose motion: it opposes relative motion) 🥵
5. Applied: this isn't a specific force. This can just be a simple push or pull or any force that is applied to a system that wasn't there before 👨
6. Air resistance/resistive force: goes against the direction of motion (can be up or down depends if the object is falling or rising) 💨
7. Electric/Magnetic Forces: These forces really with electro-magnetic interactions and charges and currents. We will learn much more about them later ✨

Here is a step-by-step guide on how to draw a free body diagram:

1. Identify the object or system that you want to analyze. This is the object or system for which you want to draw the free body diagram.
2. Draw a simple sketch of the object or system. You should include all relevant features of the object or system, such as its shape, size, and orientation.
3. Identify all the forces acting on the object or system. These forces can include external forces, such as gravity, friction, and applied forces, as well as internal forces, such as tension in a rope or pressure in a gas.
4. Draw an arrow for each force, with the tail of the arrow at the point where the force is applied and the head of the arrow pointing in the direction of the force.
5. Label each force with its magnitude and direction. The magnitude of the force should be indicated with a number, and the direction should be indicated with an angle or a set of Cartesian coordinates.
6. Identify any constraints or supports acting on the object or system. These can include hinges, pins, and other types of supports that restrict the motion of the object or system.
7. Draw a small circle or square at the point of each constraint or support, and label it with the type of constraint or support.
8. If necessary, draw additional diagrams to show the forces acting on individual parts of the object or system. This can be helpful if the object or system is complex and has multiple parts that move independently of each other.

Example problem:

A gas is contained in a cylinder with a movable piston. The gas is initially at a pressure of 2 atm, a temperature of 300 K, and a volume of 10 L. The piston is pushed down, increasing the volume of the gas to 20 L. The final pressure of the gas is 1 atm, and the final temperature is 400 K.

1. **Create a free-body diagram:**To create a free-body diagram for this problem, we need to identify the object or system that we want to analyze. In this case, the object is the gas contained in the cylinder. Next, we need to identify all the forces acting on the gas. In this case, the forces acting on the gas include the pressure of the gas itself and the force of the piston pushing down on the gas. We can draw arrows for each force, with the tail of the arrow at the point where the force is applied and the head of the arrow pointing in the direction of the force. The magnitude of the forces should be indicated with a number, and the direction should be indicated with an angle or a set of Cartesian coordinates. 

2. Analyze the physical situation: To analyze the physical situation, we can use the free-body diagram to determine the net force acting on the gas. The net force is the sum of all the forces acting on the gas, and it determines how the gas will accelerate.

In this case, the net force acting on the gas is equal to the difference between the force of the gas pushing up on the piston and the force of the piston pushing down on the gas. We can use the ideal gas law (PV = nRT) to calculate the force of the gas, where P is the pressure of the gas, V is the volume of the gas, n is the number of moles of gas, R is the universal gas constant, and T is the temperature of the gas.

The force of the gas is equal to P * A, where A is the area of the piston. The force of the piston is equal to the mass of the piston times its acceleration. We can use the conservation of energy to solve for the acceleration of the piston.

3. Solve the problem quantitatively: To solve the problem quantitatively, we can use the information provided in the problem to calculate the missing variables.

First, we can calculate the number of moles of gas using the ideal gas law:

PV = nRT n = (PV) / (RT) n = (2 atm * 10 L) / (8.31 J/mol*K * 300 K) n = 0.24 moles

Next, we can use the conservation of energy to solve for the acceleration of the piston:

E_i + W = E_f (1/2) * m * v_i^2 + 0 = (3/2) * n * R * T_f (1/2) * m * v_i^2 = (3/2) * 0.24 moles * 8.31 J/molK * 400 K v_i^2 = (3/2) * 0.24 moles * 8.31 J/molK * 400 K / (1/2) * m a = v_i^2 / d a = [(3/2) * 0.24 moles * 8.31 J/mol*K * 400 K / (1/2) * m] / d

Where m is the mass of the piston, v_i is the initial velocity of the piston (which is assumed to be zero), d is the distance the piston moves (10 L - 20 L = -10 L), and a is the acceleration of the piston.

We can now substitute the values we calculated for n, T_f, and a into the equations for the force of the gas and the force of the piston:

F_gas = P * A = 2 atm * A F_piston = m * a = m * [(3/2) * 0.24 moles * 8.31 J/mol*K * 400 K / (1/2) * m] / d

The net force acting on the gas is equal to the difference between F_gas and F_piston. We can use the net force to determine the acceleration of the gas.