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Wize University Physics Textbook (Master) > Newton's Laws of Motion: Forces and Dynamics

Free Body Diagrams

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Free Body Diagrams


The study of forces will focus on the application of Newton's Laws and the creation of free-body diagrams (commonly abbreviated as FBD).

What is a Force?

  • In the most general possible terms, a force is a push or a pull. (That's it!)
  • It's important to remember that force is a vector quantity; that is, it has both magnitude and direction, and all of the operations of vectors can be applied to them. Many problems in dynamics begin by resolving forces into components.
  • The unit of force is a Newton [N]. This is a derived unit, with 1 N = 1kg ms21\ N\ =\ 1\frac{kg\ m}{s^2}.


What is a Free Body Diagram?

  • Free body diagrams are used to show all the forces acting on an object. Drawing a proper free body diagram for each object should be your first instinct when encountering a force-related question.
  • Mass (m) is usually represented as a block and the forces acting on the mass are shown as vectors with appropriate relative size and direction.
  • Remember to include a coordinate axis to define positive directions
  • It’s also a good idea to include an arrow indicating the direction of acceleration so you know which forces add up to ma.
Example:





Watch Out!
A free body diagram accounts for all forces acting ON the object only (not the forces the object may exert on other objects)

A FBD allows you to isolate the object of interest, and observe the forces acting on it.

Exam Tip
For problems involving Forces, you should ALWAYS draw a free body diagram!


Steps to Construct a FBD:

  1. Decide what you’re interested in, and draw a diagram of it
  2. Draw and label all forces acting on the body, and indicate angles where necessary
  • If you don’t know the direction of a force, assume a direction
  • Exaggerate the angles if it helps
3. Define a coordinate system
  • This can be the general xyz coordinate system you’re used to
  • Or it could be a rotated coordinate system that simplifies the problem

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Example: Free Body Diagram Samples


1. A man is dragging a box of mass m on a horizontal rough floor with a coefficient of kinetic friction ofμ\mu.








2. A box on a rough inclined plane.





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checklist
Mark Yourself Question
  1. Grab a piece of paper and try this problem yourself.
  2. When you're done, check the "I have answered this question" box below.
  3. View the solution and report whether you got it right or wrong.
Two tennis players are rallying a tennis ball.
Describe the forces (draw a FBD) on the ball when it is:
a) In flight
b) Being hit by a racket. How does the force the ball exerts on the racket compared to that of the racket on the ball (>, < or =).
A man pulls 200Kg crate with rope angles 30 o above the horizontal with force 200N. The crate sits on the frictionless surface. Calculate the normal force. Enter answer in N.
Extra Practice
Practice: Three books on a table
Three books are sitting at rest on a table.
a) Draw a sketch.
b) Draw a complete free-body diagram for each book.
Example Problem: force of tension
Two blocks of mass m1=2Kgm_1 = 2Kg and m2=3Kgm_2 = 3Kg linked by a string through a pulley, where the block of mass m1 slides on the frictionless table. We assume that the string is massless and the pulley is massless and frictionless
a) Find the magnitude of the acceleration of the two masses b) Find the tension in the string
Two tennis players are rallying a tennis ball. Draw a free body diagram for the ball when it is in flight between the two players. Neglect air resistance.
Practice: Three books on a table
Three books are sitting at rest on a table.
a) Draw a sketch.
b) Draw a complete free-body diagram for each book.
A 45 kg45\ kg man is standing in an elevator.
Draw a free body diagram of the system then determine whether the statements about the apparent weight of the man are true. Let upward be +y.
Practice: Inclined Plane Theory
Inclined Plane
Sliding down an inclined plane is another example of motion with constant acceleration.
Source of the motion is still gravity of earth but only part of it is affecting the sliding of the object
Two tennis players are rallying a tennis ball.
Describe the forces (draw a FBD) on the ball when it is:
a) In flight
A 2.0 kg ball is suspended by a 1.20 m long string. A girl grabs the string and swings it downwards in front of her at a constant speed. The string makes an angle of 35º with the vertical. Determine the speed of the ball.
If the angle that the string makes with the vertical increases, what happens to the ball speed?
A block of mass 4 kg is suspended on two strings between two walls. The angles each string makes below the horizontal is 30°. What is the tension forces in each string? Provide an answer in Newtons and 1 decimal place.
Normal force
A man pulls 200Kg crate with rope angles 30 o above the horizontal with force 200N. The crate sits on the frictionless surface. Calculate the normal force. Enter answer in N.
Example Problem: force of tension
Two blocks of mass m1=2Kgm_1 = 2Kg and m2=3Kgm_2 = 3Kglinked by a string through a pulley, where the block of mass m1 slides on the frictionless table. We assume that the string is massless and the pulley is massless and frictionless
a) Find the magnitude of the acceleration of the two masses b) Find the tension in the string
A 65 kg man is riding a Ferris wheel with radius of 15 m, that moves at 1.5 rpm. Determine the normal force that the man experiences at the top of the ferris wheel and at the bottom.
New Practice Question
An engineer plans to design a levitating piston which can support loads up to 500kg. He decides to make a cylindrical chamber with radius of 0.5m with a moving piston which weighs 20kg. The chamber is filled with 10 moles of a diatomic ideal gas which is initially kept at 200K. By adding loads on the piston, the gas underneath is heated such that the height of the piston remains unchanged. (Assume that heating process is happening extremely fast such that the height of the piston remains constant while the gas is heated)
a) When there is no load on the piston, what is the pressure of the gas inside the chamber?
b) What is the temperature of the gas when maximum load is added to the piston?