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1 Free-body diagrams A free-body diagram is a vital tool for applying Newton’s laws. It shows a single object isolated from its environment, with all interactions replaced by forces. Students learn the rules for drawing these diagrams. Weight is shown acting at the center of mass of the object. The normal force acts at the point of contact with a supporting surface. When the total, or net, force acting on an object is zero, the object is in equilibrium. Anything not moving (static) is in equilibrium. In this lesson students learn the rules fro drawing free-body diagrams and use them to calculate forces on objects in equilibrium.

2 Weight vs. mass Mass is an intrinsic property that measures the quantity of matter in an object. Your mass does NOT change if you go into space. Mass is a scalar quantity. Weight is an extrinsic property that depends on the gravity force. Your weight changes if you go into space. Your weight depends on your location. Weight is a vector. Ask the students: “if you go to Mars, does your weight change? Does your mass change?”

3 Weight Weight is the force of gravity acting on objects with mass.

Weight is mass multiplied by the strength of gravity. At Earth’s surface the strength of gravity is 9.8 newtons per kilogram. Point out that N/kg and m/s2 are identical units. One newton equals one kg m/s2 so N/kg =m/s2. Ask the students to explain WHY it is helpful to use N/kg in this context.

4 What is a pound? The pound is the English unit of force.

The person standing on this scale is pushing down on it with a force of 125 pounds. If the pound is the English unit of force, what is the English unit of mass? Students may be amused to learn that it is the slug. Since F = mg, and g = 32.2 ft/s/s, a mass of one slug has a weight of 32.2 pounds.

5 What is a pound? The pound is the English unit of force.

Pounds are a unit of force, not mass. One pound = N The newton is a smaller unit of force than the pound. One newton = lbs (~3.6 ounces) One newton is roughly equal to the weight of a stick of butter.

6 Free-body diagrams FN1 FN2 Fw

If you know the forces acting on an object, you can predict its motion. Free-body diagrams are invaluable tools for figuring out the magnitudes and directions of the forces that act on an object. FN1 FN2 Fw Students sometimes think that free-body diagrams are an end unto themselves. Stress the fact that learning to draw these diagrams is a valuable skill. These diagrams are calculation tools as well as a way of visually presenting key relationships.

7 Free-body diagrams FN1 FN2 Fw

A free-body diagram is a sketch of an object isolated from its surroundings. All contacts with the object are replaced by the forces exerted ON the object. Forces are drawn as arrows. FN1 FN2 Fw Key point: the free-body diagram includes all forces acting ON an object, but NOT the forces that this object exerts on its surroundings. Point out that the two surfaces are applying forces to the ball that hold it in place. In the free-body diagram the surfaces disappear but the forces they exert are shown with force vector arrows. Reassure students that will learn about the force subscripts for FN later in this lesson.

8 Drawing Free-body Diagrams

A 10 kg dumbbell resting on a table is partly supported by a spring that pulls upward with a force of 50 N. Draw the free-body diagram for the dumbbell. What is the magnitude of the net force acting on the dumbbell? What force does the table exert on the dumbbell to hold it up? This assessment is keyed to the objectives. It will be repeated at the end of the lesson, followed by the answer.

9 Free-body diagrams Real object Free-body diagram

Start a free-body diagram by drawing an outline of the object. This program will use the outline method for drawing free-body diagrams. This is the first step.

10 Weight Next, draw the forces acting ON the object, starting with weight. mg The weight vector is drawn from the center of mass of the object, and points straight down. What are forces are acting? Students should start a free-body diagram by drawing the weight vector because weight ALWAYS points straight down and ALWAYS equals mg. The values/ of other forces may depend on the weight. Center of mass is explained on the next slide.

11 Center of mass The center of mass is the “balance point” around which all of an object’s mass is equally distributed. It is at the center of symmetrical shapes. Demonstrate the concept of center of mass by balancing a pair of scissors on your finger. The place where it balances is the place where the weight vector can be drawn. Find an object’s center of mass by hanging it from three different places.

12 Weight acts at center of mass

Draw the weight force on a free-body diagram approximately at the center of mass of the object. Assure the students that these diagrams do not need to be exact. They will be used to guide thinking and calculations.

13 Applied forces F mg This spring pulls upward on the object.

Applied forces are drawn at the point where they act, and in the correct direction.

14 Normal or support forces

FN FN mg Surfaces that contact the object exert a normal or support force, FN. There is no easy equation for the magnitude of the normal force. It must be figured out based on Newton’s laws and depends on the other forces acting on the object. Students CAN immediately know the direction of the normal force.

15 Direction of the normal force

FN FN mg Surfaces always push, never pull. The table pushes up on the barbell, so the normal forces point upward. Notice that with this style of free-body diagram, forces that push on the object point toward it, while forces that pull on the object point away from it.

16 Direction of the normal force

FN FN FN mg Normal means perpendicular. Normal forces always point at right angles to the surface. Students may need to be reminded that the word perpendicular means that there is a right angle (90°), as shown. Mention that the normal force ALWAYS acts perpendicular to the surface, even if the surface is tilted. it can be helpful to demonstrate this with a pencil (representing the vector) held perpendicular to a book (the surface), even as you tilt the book.

17 Free-body diagrams F FN FN mg This is a complete free-body diagram.

It contains ALL the forces that act ON the object. Every force is identified with a label and direction. It does not have too much detail—a rough sketch is all you need. F FN FN mg Some teachers may feel very strongly about drawing free-body diagrams to scale, so that the length of the vector arrows reflects the magnitude of the vectors. At this point in the process, these magnitudes have not yet been calculated. The object at this stage of a problem-solving process is simply to identify all forces acting on the object, and correctly show their direction.

18 Identify all the forces

On a free-body diagram, include every force that acts ON the object: weight, normal forces, and applied forces from springs, ropes, and other sources. The isolated object acts exactly as it did before being “removed” from contact with the environment. F FN FN mg

19 More on the normal force

Every contact with a surface creates a normal force. Normal forces may be vertical, horizontal, or act at an angle. Notice how these normal forces are always perpendicular to the surfaces that applied them. Examples of normal forces Point out the direction of the normal force is always perpendicular to the surface and always pushes away from the surface toward the object. Be sure to assign different names to different normal forces!

20 Styles of free-body diagrams

There are two different styles you may see for drawing free-body diagrams. A block of mass m sits on a floor partially suspended by two springs. The outline method has the advantage of getting students to decide if a force is pushing or pulling on an object. The point-mass method makes sense when an object is being treated as a particle, but cannot be used when considering torques and rotation later in the program.

21 Force is a vector To solve force problems, you have to choose which directions will be positive and which will be negative. This choice is arbitrary. Choose the positive direction that makes the problem easiest to solve. Always make a diagram to remind yourself which direction is positive!

22 The net force F FN FN mg What is the net force acting on the dumbbell?

In most situations there are many forces acting at once. Objects respond to the net force. In physics “net” means total, taking account of directions. F FN FN mg What is the net force acting on the dumbbell? Ask for an expression, in terms of the forces acting on the dumbbell.

23 The net force Fnet = F + 2FN – Fw F FN FN mg

In most situations there are many forces acting at once. Objects respond to the net force. In physics “net” means total, taking account of directions. F FN FN mg What is the net force acting on the dumbbell? Fnet = F + 2FN – Fw All these forces are vertical, so the net force equals the forces up minus the forces down.

24 Equilibrium Fnet = F + 2FN – Fw= 0 F Fnet = 0 FN FN mg

Equilibrium exists when the net force is zero. In equilibrium there is no change in motion. An object at rest stays at rest. F Fnet = 0 FN FN mg The dumbbell is at rest so the net force on it must be zero: Fnet = F + 2FN – Fw= 0 This is really a partial statement of Newton’s first law, which will be introduced formally in the next lesson.

25 Find the normal force The box shown is at rest, so Fnet = 0. What is FN in these examples? Pulled up with a force of 4 N. Pressed down with a 4 N force Pressed against the ceiling with a 15 N force F = 4 N. F = 4 N mg = 10 N mg = 10 N mg = 10 N F = 15 N.

26 Find the normal force Notice: there is no formula for calculating the normal force. Its magnitude depends on the situation. Pulled up with a force of 4 N. Pressed down with a 4 N force Pressed against the ceiling with a 15 N force FN = 5 N. F = 4 N. F = 4 N mg = 10 N mg = 10 N mg = 10 N F = 15 N. FN = 6 N. FN = 14 N.

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