hphys unit 02 bfpm packet 2012

Name: ________________________________

Balanced Force ModelA force is _____________________________________

Common Types of ForcesType of Force Direction When is it present? Symbol Equation

the { } { } force the { } exerts on the { }Newton’s 1st Law:

Newton’s 3rd Law:

Honors Physics / Unit 02 / BFPM

– 1 – from Modeling Workshop Project © 2006

Reading: A Force is an Interaction between Two Objects


from Modeling Workshop Project © 2006 ! – 2 –

When exploring the motion of a hover puck, we decided that we needed

a force to change the motion of the block. We defined a force as an interac-tion between two objects. Thus, every force involves two objects, the object

exerting the force and the object experiencing the force.

We have noticed that some forces, such as the gravitational force, act at

a distance. These forces are non-contact forces. Electric and magnetic forces

are the other non-contact forces with which we are familiar. Otherwise,

forces are exerted by way of objects interacting by touching one another.

These forces are called contact forces. Some contact forces, such as the

tension force of a rope on a crate, have the interesting ability to adjust.

To help us keep track of the forces acting on an object, we have devel-

oped a new representation: system schema. System schema are sketches

that list all objects interacting with the object we are considering. As an

example, we will take the case of a book sitting on a table. The system

schema in figure 1 shows the book and all objects interacting with the book

as labeled ovals. Solid lines are draw between two objects if they are inter-

acting. Finally, a dotted line is drawn around the object of interest (which

we will call our system). Each line that crosses the dotted line surrounding

our object of interest indicates that we should be able to identify a force

corresponding to that interaction. In figure 1, we note that the table and

Earth interact with the book.

Book

Earth

Table

Figure 1: The system schema for a book sit-

ting still on a table top. The book is inter-

acting with the table (it is touching the ta-

ble) and Earth (the gravitational force is a

non-contact force).

The word normal means “perpendicular

to.” This force is due to the compression

of the atomic bonds (which are modeled by

springs) in the table surface, and the force

is therefore perpendicular to the surface of

the table.

After identifying the objects interacting with our object of interest (our

system), we label the forces we have identified. In figure 1 we have the

gravitational force exerted by Earth on the book (Fg,E→B), and the contact

normal force exerted by the table on the book (FN,T→B).

We now employ another new representation: the free body diagram,

as shown in figure 2. The free body diagram is a very stripped down

schematic of the object and the forces exerted on the object. For our exam-

ple of the book sitting on the table, the free body diagram shows the book

as a dot, and the forces on the book are represented by arrows whose tails

are on the dot and whose heads point in the direction of the force. You will

notice that a free body diagram is very similar to a vector diagram.

FN,T�B

Fg,E�B

normal force, table on book

grav. force, Earth on book

Figure 2: The free body diagram for a book

sitting still on a table top. Note that there

are two forces on the system (which is the

book in this case), the same number of

forces as there are lines crossing the dotted

line in the system schema.

There are two quick checks that you should perform on your free body

diagram. First, are the number of forces on the object the same as the

number of solid lines crossing your dotted line boundary around your

object? Second, are all the forces you wrote down for the object of interest

of the form “the (type of force) force exerted by (object exerting the force)

on the (object of interest)?”

In order to help you draw your system schema and your free body

diagrams, there are several steps you should take to identify all of the in-

teractions between your object of interest and the outside world. First, you

should identify all non-contact interactions between your system and its

surroundings. We currently know of three non-contact force types: grav-

itational forces, electrical forces and magnetic forces. Thus, identifying

outside objects interacting via non-contact forces is as simple as asking

whether there are gravitational, electric or magnetic forces on our system,

and what objects are exerting those forces.

Second, you should tally all surrounding objects that are touching our

system. These objects might be exerting contact forces. Contact forces

include compression forces (the normal force of the table on our book,



in the previous example, or the force of a mashed spring on the objectplaced on top of that spring), tension forces (the force of a spring or stringon an object), friction forces (always parallel to the surface on contact be-tween two objects), air resistance (due to wind or an object moving quicklythrough still air), as well as pushes and pulls by living objects (which canbe thought of as compression and tension forces, too).

It is possible for two objects to interact in more than one way, simulta-neously. To illustrate this possibility, let’s consider a book sliding to a halton a table top. The system schema is shown in figure 3. There are now twolines connecting the book and the table, representing the normal force ex-erted by the table on the book and the friction force exerted by the table onthe book. It helps to draw two separate lines for these two forces, therebyclearly indicating that there are now three forces (due to two interactionsbetween the book and the table and one interaction between the book andEarth) on the book.

Book

Earth

Table

Figure 3: The system schema for a table slowing as it slides on a table top. Noticethat there are now three solid lines crossing the dotted line, indicating three distinctinteractions of our system with its surroundings.

Using the system schema in figure 3, we can now draw a free bodydiagram for the sliding book on the table. The correct free body diagramshould have one non-contact force (the gravitational force exerted by Earthon the book, Fg,E→B) and two contact forces (the normal (perpendicular)force exerted by the table on the book, FN,T→B, and the (parallel) frictionforce exerted by the table on the book, Ff ,T→B).

FN,T�B

Ff ,T�B

Fg,E�B

normal force, table on book

fric. force, table on book

grav. force, Earth on book

Figure 4: The free body diagram for a booksliding on a horizontal table top.

Worksheet 1: Forces and MotionTake care in reading every word in these questions. Make sure you know exactly when we are taking our snapshots in each part of the problem. When making a whiteboard, arrange your work so that all parts of one question can fit on one board (neatly).

1. A cardboard box with a rubber bottom contains a cinder block at rest on a rough, concrete, horizontal floor.a. Draw a system schema for this situation.

b. Since the shape of the [box + cinder block]—your “system”—is unimportant, shrink it to a point (this is where we are treating the box like a particle) and then show and clearly label each force on the system. Make it obvious from your diagram which forces you intend to be equal and which you intend to be greater than others.

c. A person shoves the box horizontally so that it begins to move. Your answers to this part should concern the time while the person is still touching the box and shoving. (i) Draw a velocity-vs-time graph for the box, clearly marking the time when the box is at rest and the time when the person is still touching the box and shoving it. This should be qualitatively accurate (no numbers, but correct shape). (ii) Also draw a system schema for that same time period. (iii) Also draw a free body diagram for the box during that same time period. Label!

d. The shove ends when the box leaves contact with the person’s hands. (i) Draw a qualitatively correct velocity-vs-time graph for the box, clearly marking the time when the box is at rest, the time when the person is still touching the box and shoving it, and the time after the box loses contact with the person’s hands. Make it obvious which lines are horizontal, which have greater slopes, smaller slopes, or negative slopes. (ii) Also draw a system schema for the box when it leaves contact with the person’s hands. (iii) Also draw an FBD.



2. The rubber is now removed from the bottom of the box so that the cardboard surface rests directly on the same floor. It is then given a horizontal shove by a person. In the space below, modify your velocity vs. time graph as well as your system schemas and FBDs from problem 1 to accurately describe this new situation. Your diagrams do not have to be quantitatively accurate, but make it obvious which forces you intend to be equal and which you intend to be greater or less than others, so that comparisons can be made among forces in this problem as well as between forces in this problem and in problem 1. Make any differences in your graphs and diagrams obvious.

a. Draw a velocity-vs-time graph for the box, clearly marking the three time periods.

b. Draw a system schema and an FBD for this situation while the box is at rest on the horizontal floor.

c. Draw a system schema and an FBD for this situation while the person is still touching the box and shoving.

d. Draw a system schema and an FBD for this situation during the time after the box loses contact with the person's hands.



3. The box is now placed on a very smooth and polished floor. In the space below, modify your velocity vs. time graph as well as your system schemas and FBDs from problem 2 to accurately describe this new situation. Your diagrams do not have to be quantitatively accurate, but make it obvious which forces you intend to be equal and which you intend to be greater or less than others, so that comparisons can be made among forces in this problem as well as between forces in this problem and problems 1 and 2. Make any difference in your diagrams obvious.







4. Suppose that we could somehow succeed in making the floor completely frictionless. Again, make new diagrams/graphs to represent this new variation in the situation. Make any differences obvious.







5. Return to the case of the cardboard box resting on the concrete floor, with friction. A person pushes it hard enough to start it into motion and then continues pushing so that it maintains a constant velocity. In the space below, modify your velocity vs. time graph as well as your system schemas and FBDs from problem 2 to accurately describe this new situation.

a. Draw a velocity-vs-time graph for the box, clearly marking the three time periods (at rest, velocity is changing, moving with a constant velocity).


c. Draw a system schema and an FBD for this situation while the box is changing velocity.

d. Draw a system schema and an FBD for this situation while the box moves with a constant velocity.

e. After pushing the box with a constant velocity for a while, you reduce your force to half the value needed to maintain a constant velocity. Make a new (continued) velocity-vs-time graph to show what happens to the box while you continue to push with this force.



Worksheet 2: FBDs6. In each of the following situations, represent the object with a labelled free body diagram. Label each force with a

meaningful symbol (ex: Fg) AND with the object exerting the force (ex: Fg(earth)).

1.! Object lies motionless. 2.! Object slides at constant speed without friction.

3.! Object slows due to kinetic friction.

!

4.! Object slides without friction.

5.! Static friction prevents sliding.

!

6.! An object is suspended from the ceiling.

!

7.! An object is suspended from the ceiling. 8.! The object is motionless.



9. The object is pulled upward at constant speed. 10. The object is motionless.

11. The object is pulled by a force parallel to the surface.

12. The object is pulled by a force at an angle to the surface.

13. The object is falling (no air resistance). 14. The object is falling at constant (terminal) velocity.

15. The ball is rising in a parabolic trajectory. 16. The ball is at the top of a parabolic trajectory.



Empirical Force Laws Experiments (Fg, Fs)

Sketch and label the experiment setup:

What could we measure? How could we measure it?

The Objective:

Use this space for notes at the whiteboarding stage of the experiment:



Reading: Forces Add Like Vectors



Consider experiments in which two unequal forces act on a body inopposite directions. The result is an acceleration in the direction of thelarger force but smaller. Figure 1 shows an example. This should remindyou of how the force of friction slightly decreased the overall force on thecarts when we pulled them with one spring of force.

5 N 2 N 3 N

equivalent to

Figure 1: Two forces acting in opposite directions subtract, with the net force point-ing in the direction of the larger of the two forces. If we define forces pointing tothe right as positive (+2 N here) and to the left as negative (-5 N), we can alwayjust add the forces.

Thus we can simply add the two forces to get the ‘net force’ expressedin Newton’s Second Law as long as we keep track of the directions of the forcesusing positive and negative numbers (with positive numbers representingforces pointing in the direction we have defined as the positive direction).For the example in figure 1 we would have a positive force (to the right) of2 N and a negative force (to the left) of 5 N. If we add those forces we getFnet = (+2 N) + (−5 N) = −3 N.

Situations where the forces point in the same or opposite directions arefairly straightforward, but what happens when there are multiple forcespointing in all directions? In such cases, we need to treat forces as vectors.In fact, without really thinking about it too much, the example in figure1 does treat the forces as vectors. You may have noticed that by usingarrows to depict forces, we have already chosen a visual representationthat is similar to the way we depict vectors.

F1

F2

F3

F1

F2 F3

is equivalent to

adding up to zero force

Figure 2: Forces adding to zero result inequilibrium (no change in velocity). Thevectors are added using the tail-to-headmethod.

An experiment can be performed in which three forces act on a body indifferent directions to produce an equilibrium state (that is, zero net force).If vectors are used to represent these forces with their lengths proportionalto the force magnitude, it is possible to add them using our familiar head-to-tail sequence. Since the vectors add up to zero, the resulting vectordiagram forms a closed polygon, as in figure 2. This corresponds to vec-tor addition resulting in a zero resultant vector (if this is not immediatelyclear, please review your summer homework on vectors).

We experimentally determine that when two or more forces act at acuteor obtuse angles, the forces have a combined effect that is equivalent to asingle force that is their vector sum. The vector sum of force vectors repre-sents the net force vector, and this situation is shown in figure 3. Note thatwe cannot merely add the magnitudes of the vectors in this more generalcase!

F1

F2

Fnet�F1�F2

equivalent to

F1

F2

Figure 3: Forces add as vectors. This takesa little more work, but it is the only way todeal with forces in more than one dimen-sion!

Worksheet 3: Interaction Problem Solving7. The player in the photo exerts a 100 N horizontal force on a 25 kg blocking sled, pushing it across the grass with a

constant speed of 2.0 m/s. a. Fill out the chart below, determining all of the forces on the blocking sled.

!

System Schema

Motion Map Qualitatively correct sketch of FBD

REMINDERS: ◈ Does your system schema have a system boundary? ◈ In your FBD, did you represent the system with a particle? ◈ Is it obvious when you intend two forces to be equal or when you intend one force to be greater than another? ◈ Did you label your forces with the object exerting the force in parentheses?

b. On the graph below, draw an FBD to a precise scale. Make sure you write down your scale!



c. How would the situation change if the player pushed with more than 100 N, while the frictional force between the grass and the sled remained the same? Illustrate your answer with another FBD and motion map.

d. Describe, in terms of the amount of force he would have to apply, what the player would have to do to make the sled move with a constant velocity of 3.0 m/s. Assume that the frictional force between the grass and the sled remains the same under all circumstances. Illustrate your answer with diagrams and/or graphs as appropriate.

e. If he pushes the sled as originally described with a velocity of 2.0 m/s, how far will it slide in 7.5 seconds? Draw at least three diagrams/graphs to illustrate this situation, then solve this problem using at least two different methods (and getting the same answers).

f. With the sled moving at a constant velocity of 2.0 m/s, the person reduces his force to 75 N. Describe what happens to the sled. Illustrate your answer with another FBD and motion map.



8. The 80 kg box rests motionless on the 20º incline.a. Fill out the chart below, determining all of the forces on the box (including their magnitudes).

!

(Qualitative) Sketch of FBD

System Schema (Qualitative) Sketch of Vector Addition Diagram

REMINDERS: ◈ Does your system schema have a system boundary? ◈ In your FBD, did you represent the system with a particle? ◈ Is it obvious when you intend two forces to be equal or when you intend one force to be greater than another? ◈ Did you label your forces with the object exerting the force in parentheses? ◈ Did you add vectors tail to head?

b. On the graph below, draw the vector addition diagram to a precise scale. Be sure to write down your scale! Be sure to use a ruler and a protractor!

c. Is the contact normal force [greater than, less than, or equal to] the gravitational force? Explain.



Activity: Broom Ball

For each of the situations, describe (using words, pictures, etc) how to accomplish each feat. Each situation refers to pushing a bowling ball on the floor with a broom.

Speed up the bowling ball from rest. Stop a moving bowling ball.

Keep a moving bowling ball moving at a constant velocity.

Move the ball from one line to the other and back as quickly as possible and without overshooting the lines.

With a moving bowling ball, make a sharp left turn. Travel at a constant speed along a curved line.

Move the ball around a circle as quickly as possible.Move the ball around a circle as quickly as possible.



Activity: Dueling ForcesFor each of the following situations:1. Draw one system schema. In your system schema, draw the interaction between the two carts in colored

pencil. (Keep everything else in regular pencil.)2. Draw and label two FBDs (one for each cart). Draw the forces the carts exert on one another in colored

pencil. (Again, keep everything else in regular pencil.) Be sure your FBDs look balanced or unbalanced as appropriate. Draw forces to approximate scale.

3. Finally, measure the colored pencil forces with the force sensors and correct your diagrams if necessary. Remember to zero your force sensors!

4. After completing the ones on this sheet, if you have time (or outside of class), you might be interested in trying additional variations and confirming your results.

I. You may ignore friction on this particular situation.

A B

Fperson F

person

velocity = 0

II. Do not ignore friction.

A B

Fperson

constant velocity



III. Do not ignore friction.

A B

Fperson

speeding up

IV. Do not ignore friction.

AB F

person

speeding up

V. This should be a collision on a track (snapshot during the collision). You may ignore friction in this situation.

AB

initially at rest

velocity



Worksheet 4: N3L in Action

6. A block slides down a ramp at a constant speed. During that slide, the ramp sits at rest on a table. Draw one system schema for the situation, then draw an FBD for the block and an FBD for the ramp.

7. In frustration, Alec gets Henry to hold up his test and punches his fist completely through all of the sheets of paper. Which is greater: the force that Alec’s fist exerted on the paper or the force that the paper exerted on Alec’s fist? Explain.

8. Your friend’s truck stalls out on a hill, so you get out to push. However, after a couple minutes you start to tire yourself out and the truck starts pushing you back down the hill. While the truck is pushing you back down the hill, which is greater: the force that you exert on the truck or the force that the truck exerts on you? Explain.

9. At the ice skating rink, Lydia (who has a mass of 50 kg) stands face to face with her brother, Marcus (who has a mass of 80 kg). They put their hands together and Lydia pushes Marcus backwards. Draw one system schema and two FBDs (one each for Lydia and Marcus) during the push. You may assume that the ice is frictionless.

!

!



BFPM Model Summary



hphys unit 02 bfpm packet 2012

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