1.
Find an area with some space in all directions and stand on one foot. Describe the normal force that you are experiencing. Be precise.
Section 5.10 Extended Free-body Diagrams
Exercises Warm-up Activities
2.
Slowly tilt your upper body forward (not so far that you fall over). Describe how the normal force you experience changes. Why do you think this happens?
When you are considering the motion of rigid bodies, you will still be concerned with the forces acting on an object, as these forces still impact the translational motion of the object. You now also need to know where each force acts on the object, as this extra information is needed to understand how the forces impact the rotational motion of the object.
Note 5.10.1. Where does the gravitational force act?
The gravitational force is a non-contact force, so there is no point of contact for the force to act. Instead, the gravitational force is treated as acting at the Center of Mass of the object. You will learn how to calculate center of mass in a future section; until then, treat the geometric center of an object as its center of mass, which is true for any symmetrical object.
Representation 5.10.2. Extended Free-body Diagram.
An Extended Free-body Diagram is a more detailed pictorial way to represent forces, in which the object is represented as a shape and each force is shown acting at its point of contact. As in a free-body diagram, each force should be labeled using the following symbol
\begin{equation*}
\vec{F}_{BC}^A
\end{equation*}
where \(\vec{F}\) indicates that the symbol represents a force, the superscript \(A\) represents the type of force (for example, \(G\) for gravity), \(B\) represents the system on which the force is acted, and \(C\) represents the system that is exerting the force.
Exercises Activities
1.
Sketch an extended free-body diagram for yourself in the two warm-up activities. Describe how the diagrams are different.
2. The Catapult.
A catapult consists of a long, straight arm mounted on a pivot point, as shown in the figure below, with a round rock on the left and a square block on the right. Neglecting the mass of the arm, predict which of the following must be true for the catapult to launch the rock? Explain your reasoning.
- \(\displaystyle m_2 > m_1\)
- \(\displaystyle m_2 = m_1\)
- \(\displaystyle m_2 < m_1\)
- None of these
3.
What do you expect the physical behavior of the catapult should be? Answer in terms of the quantities for angular motion you have learned about.
Answer.
If you want the catapult to launch the rock, then the catapult needs to have a clockwise angular acceleration!
4.
Sketch an extended free-body diagram for the catapult (continue to neglect the mass of the arm). How did you decide where to draw each force?
