FREE-BODY DIAGRAMS A free-body diagram uses arrows to represent all forces acting on the object or objects in the system. The tail of an arrow representing a force is placed at the point where the force acts on the object and the arrow points in the direction of the force. Try to make the relative lengths of the arrows representative of the magnitudes of the forces (this is not always possible. Label each force arrow with a symbol that indicates: (a) the object in the environment that causes the force, (b) the object in the system on which the force acts, and (c) the magnitude of the force, if known. Alternatively, make a separate list of the forces using abbreviated symbols (T, w, N, etc.) and indicate in some other way (for example, a list) the object causing the force and the object on which the force acts. Remember that some other object must cause each force shown in your free-body diagram. Do not include in your diagram forces that an object in the system exerts on another object in the system or on objects outside the system. We only want forces that act on an object in the system caused by an object outside the system. Your free-body diagram should also have a set of coordinate axes. Usually, one axes is oriented in the direction of motion, and the other axis is oriented perpendicular to the direction of motion.

How do we decide what forces act on an object in the system? You first need a sketch of the whole situation described in the problem (see the example shown in Fig. l.lOa). For now, we assume that the sketch is provided in the problem statement. To construct a free-body diagram for some object in the system, look for two types of forces: (1) short-range forces caused by objects in the environment that touch one in the system, and (2) long-range (action-at-a- distance) forces between an object in the environment (like the earth) and one in the system. First, consider short-range forces. Look along the boundary of the system for an object in the environment that touches an object in the system. These touching environmental objects might exert a short-range force on the object in the system: a normal force pointing perpendicular to the surface of contact, a friction force parallel to the surface of contact and opposite the direction that the object in the system moves or tries to move relative to the object it touches, a rope or cable tension force parallel to the direction of the cable, an air or water drag force opposite the direction of motion, and so forth. For the system shown in Fig. l.lOa, the floor touches the base of the piano and exerts an upward normal force N, and the cable above the piano pulls up on it with a tension force T. These

are the only two places where environmental objects touch the system. The second type of force to include in a free-body diagram is a long-range (action-at-a Distance) forces caused by an object in the environment that does not touch objects in the system. For now, the only long-range force we use is the weight force w. Note that the downward weight force acting on the piano is not considered a contact force because the piano does not touch most of the earth's mass. As far as weight is concerned, the average position of the earth's mass pulling down on the piano is at the earth's center, far from where the piano resides. A completed free-body diagram for the piano, including a coordinate system, is shown in fig. 1.7b. A checklist for types of forces that might act on an object in a system is provided in Table I.l. Use the table to help construct free-body diagrams. The construction of a free-body diagram is illustrated on the next page for a skier being pulled up a ski slope by a rope.

Table I. 1 Forces to include in Free-Body Diagrams. Normal Force Static Friction Force Kinetic Friction Force Tension Force _ Air or Water Drag Forces _ Other Long-Range Forces _ Weight _ Gravitational _ Other

A brief note about Newton's Third Law of Motion: This is a very important law and needs to be studied in some depth, which we'll do later. But to do even the simplest free body diagram analysis requires at least an awareness that it exists and what it is. It says that whenever any object applies a force to a second object, the second object always applies the exact same force on the first object. This seems impossible to most people at first glance, but that is because the world of friction in which we live gives us a deep down instinct conceptional definition of force that causes us to confuse velocity and acceleration with force. For instance, consider the following question.

Alps II - 3 ------------------------------------------------------------------------

Free Body Diagrams - 1

Construct free body diagrams for the boldface objects described below.

a) A person hanging from a rope.

b) A book sitting on a table.

c) A person sitting on a stool.

Construct free body diagrams for the boldface objects described below.

a) A person climbing down a rope.

b) A skydiver before opening her parachute.

c) A skydiver after opening her parachute.

Construct free body diagrams for each of the objects pictured below.

a)

b)

Qualitative Reasoning About Forces - 1
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A block is hung by a string from the ceiling of an elevator. For each of the situations below state which force is larger, the force of the string on the block or the force of gravity on the block.

a) The elevator is at rest.

b) The elevator is moving upward at an increasing speed.

c) The elevator is moving upward at a decreasing speed.

d) The elevator is moving upward at constant speed.

e) The elevator is moving downward at decreasing speed.

f) The elevator is moving downward at constant speed.

A man stands on a bathroom scale inside an elevator. When the elevator is at rest, the scale reads 750 N (170 lb). Compare the scales reading to 750 N when:

a) The elevator is moving upward at an increasing speed.

b) The elevator is moving upward at a decreasing speed.

c) The elevator is moving upward at constant speed.

d) The elevator is moving downward at decreasing speed.

e) The elevator is moving downward at constant speed. Free Body Ranking Task #2

The figures below depict eight identical 60 kg people riding eight identical elevators. Each elevator is moving in the direction of the arrow on its right. The reference frame for each of these pictures assumes that up is the positive direction, so a negative acceleration implies a downward acceleration. Give the highest rank to the person whose scales registers the most weight, and the least rank to the person whose scales registers the least weight. (Use acceleration due to gravity g = 10 m/s2.)

Highest 1_____ 2_____ 3_____ 4_____ 5______ 6 ______ 7 ______ 8_______ Lowest

All the scales read the same weight_______.

Please carefully explain your reasoning:

How sure are you of your reasoning?

Basically Guessed Sure Very Sure

1 2 3 4 5 6 7 8 9 10 Newton's Second Law - 1
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A 1000 kg elevator initially moving down at 7.0 m/s slows to a stop in 2.5 s.

A 40 kg child is hanging from a rope by her hands. She exerts a burst of strength and 3 s later is traveling at 3 m/s up the rope.

A 100 kg man is riding an elevator which initially is moving up at 10 m/s. The elevator slows to 5 m/s in a distance of 6.0 m.

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Newton's Second Law - 17
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A 70 kg student is lifted from rest to a height of 10 m in 1.2 s by a rope that passes around a pulley.

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A 40 kg student lifts herself up at a constant speed of 10 m/s. The bosun's chair has a mass of 20 kg.

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A 70 kg student lowers himself down 100 m in 15 s at an approximately constant speed. The bosun's chair has a mass of 20 kg.

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