Lab 10 - Free Body Diagrams PDF

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Activity 10 Free-Body Diagrams Objective: To draw free-body diagrams allowing us to isolate an object from its environment and identify forces acting only on it. An application of Newton’s 2nd Law. Activity 10.1. Free-Body Diagram Practice Free-body diagrams allow us to separate an object from a system of interacting objects to analyze the forces on it. Use the following procedure to draw free-body diagrams: 1. Draw a dot, small circle, or small square to symbolize the object you want to analyze. The

shape of the object itself doesn’t matter, so make sure that the drawing is small and simple. We are only interested in the motion of the center of mass of the object. 2. Identify all the forces exerted on the object. Don’t forget the gravitational force and

contact forces. 3. List, not draw, all of the items in the object’s environment that exert forces on the object.

Drawing other items will only confuse the forces exerted on the object with those exerted by it. 4. Draw an arrow to represent each force. The tail of the arrow should be located on the

simple object, and the arrow should point in the direction the force is exerted. The arrows should be drawn to the correct relative lengths (if you know one force is three times as big as another, the arrow for that force should be three times as long). 5. Label the force arrows by the following convention: 𝑡𝑦𝑝𝑒 𝐹𝑏𝑦,𝑜𝑛

“Type” identifies what kind of force it is. We will name forces based on what we know about the force. “On” identifies the object subjected to the force, that is, the object represented by the circle in step 1. Any forces which are “on” any object except the one we are interested in, do not belong in the free-body diagram. 6. Verify that your forces are exerted on, not by, the object. 7. Draw a small arrow next to the object to represent acceleration. Label this arrow “𝑎”.

Check that the vector sum of the force vectors points in the direction of this acceleration. If the object is in equilibrium, write “𝑎 = 0” and make sure the vector sum is zero as well. If your forces don’t add up for the given acceleration, make sure you drew the right forces and that they are to scale.

8. Make a legend for the symbols you choose to use in your free-body diagram. For example, 𝑔

if you make a free-body diagram for a box, and you label a force “𝐹𝐸,𝑏 ”, indicate that it means “The force of gravity by the Earth, on the box” just so there are no misconceptions.

10.1.1. Example Free-Body Diagram Consider pushing a box across the floor. For this case, the box is the system and you are causing the box to increase in velocity. The system experiences the force of gravity downward, however it does not fall into the earth, so there must be a normal force pointing upward. The box slides as you push, so there is a frictional force pointing opposite the direction of motion. But this force is not as large as the force you are applying. The free-body diagram below has been drawn for the forces acting on the box, including proper labels for these forces.

10.1.2 Newton’s 2nd Law Newton’s second law of motion states that the force on an object is equal to its rate of change of momentum. Because, in this class, we do not deal with changing masses, we can simplify this law to state that the acceleration is proportional, by its inertia (mass), to the net force acting upon it: 𝐹 = 𝑚𝑎 Since forces are vectors, the equation above means: add the x components of all the forces, and set that equal to ax (the x component of the acceleration). Then do the same for all the y components (and the z components if necessary). In other words, when applying this equation in more than one dimension, we must deal with only one direction at a time, and we may end up with two (or three) equations as a result of that.

Q1: Using Newton’s 2nd law, write an equation of motion for the box in the x direction. FAm,b = ma->

Q2: Using Newton’s 2nd law, write an equation of motion for the box in the y direction. Fg – Fb = ma = 0

Activity 10.2. More Free-Body Diagram Practice 1. Follow the link on BlackBoard to access the interactive free-body diagram software

(https://www.physicsclassroom.com/Physics-Interactives/Newtons-Laws/Free-BodyDiagrams/Free-Body-Diagram-Interactive). Enlarge the interactive box and click the “start” button. 2. Click on the expand arrows icon on the upper left hand of the interactive window to full-

screen the viewing window. 3. Select each of the 12 situations and follow in the on-screen instructions and create a free-

body diagram for the described situation. 4. Record four of the situations which do not involve air resistance, including an accurate

free-body diagram 5. Using Newton’s 2nd Law, derive both the x and y equations of motion for each chosen

case.

Situation #

1

Full description of situation: A football is moving upward and rightward towards of the peak of its trajectory.

Free-body Diagram:

x-Equation of Motion: no equation because at the top of the trajectory, v = 0, no acceleration, so no force

y-Equation of Motion: F = Fgrav

Situation # 3 Full description of situation: A rightward-moving car is skidding to a stop across a level roadway with locked wheels

x-Equation of Motion: F = ma + Ffriction

Free-body Diagram:

y-Equation of Motion: Fnorm = Fgrav = 0

Situation #

4

Full description of situation: A rightward force is applied to a dresser to accelerate to the right across the bedroom floor.

Free-body Diagram:

x-Equation of Motion: Fapp – Ffriction= ma

y-Equation of Motion: Fnorm = Fgrav = 0

Situation #

5

Full description of situation: A hockey puck glides to the right across ice with constant speed.

Free-body Diagram

: x-Equation of Motion: constant speed means acceleration = 0, so no equation

y-Equation of Motion: Fnorm = Fgrav = 0

Activity 10.3. Practice problems A locomotive is pulling on a train and picking up speed. Draw separate free-body diagrams for (a) the locomotive and (b) the rest of the train. Make sure you identify the physical origin of all the forces acting on them, and make sure you indicate which (if any) of the forces acting on the two bodies have the same magnitude. Q3:

A block and tackle is a system of two or more pulleys with a rope or cable threaded between them, usually used to lift heavy loads. For the simple “gun tackle” shown below, draw separate free body diagrams for the two pulleys, under the assumption that the system is not accelerating. Assume that the masses of the rope and pulleys are negligible. Make sure you get all the forces right in magnitude as well as direction. On the picture provided (not the free-body diagram) show the magnitude of all the forces as a function of the weight W....