**Unit 2 - Forces Component - Newtons 3 Laws**

Law 1: Every object continues in its state of rest, or of uniform velocity in a straight line, as long as no net force acts on it.

Second law: The acceleration of a body is directly proportional to, and in the same direction as, the net force acting on the body, and inversely proportional to its mass. Thus, F = ma, where F is the net force acting on the object, m is the mass of the object and a is the acceleration of the object.

Third law: When one body exerts a force on a second body, the second body simultaneously exerts a force equal in magnitude and opposite in direction to that of the first body.

Forces always have some balancing force.

Demonstration: Push your neighbor.

What is mass? Is this the same as weight?

What is acceleration?

Examples of Forces

Tension

Friction

Normal Force

Identifying Forces

What are forces on her?

What is the direction of the forces on her?

Extra Question: Can you identify the third law forces?

**Announcements - September 30th 2014**

1. HW Due Thursday

2. New Free Body Diagram HW Due Thursday ALSO

3. Quiz is one week from today, during recitation!

4. Science club meeting coming soon. Please talk to me after class if your are interested

5. Course website: https://sites.google.com/a/sunykorea.ac.kr/phy131/

1. HW Due Thursday

2. New Free Body Diagram HW Due Thursday ALSO

3. Quiz is one week from today, during recitation!

4. Science club meeting coming soon. Please talk to me after class if your are interested

5. Course website: https://sites.google.com/a/sunykorea.ac.kr/phy131/

This goes back to the meaning of velocity, imagine yourself in empty space, what is velocity?

Free Body Diagram or Force Diagram

1.

3.

Buoyant Force

Gravity

Far From Surface

2.

**Forces and Torques**

1. Newton's First Law

2. Net push on an object sum of forces, forces add as vectors

3. Forces are drawn on a single object (a person, a ball, a car, etc)

-Do some examples of drawing forces

4. Newton's Second Law, Net push on an object causes it to ACCELERATE. Acceleration is m*a. m*a is NOT a force, it is the EFFECT of all the forces on an object

1. Newton's First Law

2. Net push on an object sum of forces, forces add as vectors

3. Forces are drawn on a single object (a person, a ball, a car, etc)

-Do some examples of drawing forces

4. Newton's Second Law, Net push on an object causes it to ACCELERATE. Acceleration is m*a. m*a is NOT a force, it is the EFFECT of all the forces on an object

Near Earth Surface

F = m*g

Spring Force

F = -kx

Static and Kinetic

F = μ* Normal Force

**Recitation**

1. Draw a vector pointing at 30 degrees

2. Chapter 10, Problem 17

3. Chapter 3, Problem 46

1. Draw a vector pointing at 30 degrees

2. Chapter 10, Problem 17

3. Chapter 3, Problem 46

Based on the definition, is F a vector or a scalar?

Does your mass change if you go to the moon? Does your weight change?

For person in green

For large mass on right

For 10 kg mass,

assume table is frictionless

1. Forces of equal magnitude should have equal length vectors

2. Forces should point in the direction they act

3. Force vectors should be drawn at the point where the force acts (e.g. gravity acts at center of mass, friction acts at interface between two surfaces)

4. Each force should have a different name.

5. In a different color, draw the NET force (called F_Net) on the object somewhere above or below the surface. If F_Net = 0, then just draw a dot instead of a vector and label it as F_Net = 0

6. Draw only the forces exerted ON an object. Do NOT draw third law pair force exerted BY the object

The ball and bus are moving together at the same constant velocity to the right

1. Is it possible for the ball to sit still?

2. If the bus slows down, what happens to the ball?

F = ma

**Lecture - Math Review - September 30th**

1. Add the two vectors

V1 = 3 N at π/4 radians above the x-axis

V2 = 1 N at π/6 radians below the x-axis

1. Add the two vectors

V1 = 3 N at π/4 radians above the x-axis

V2 = 1 N at π/6 radians below the x-axis

F = ma is NOT a force, but is the net result of the forces seen below!

**Calculating Forces**

0. Draw Free Body Diagram for object of interest

1. Always start with Sum of forces = ma

2. Separate forces into x-component and y-component (this, of course, requires choosing a reference frame)

3. Solve x and y parts separately

1. A 14.0 kg bucket is lowered vertically by a rope in which there is 150 N of tension at a given instant. What is the acceleration of the bucket?

2. Example 4-9 in Text Book, page 95. (2D Example)

2. (AP Physics Example) Problem 32 Chapter 4

3.

For 10 kg mass,

assume plane is frictionless

(Tilted Reference Frame Example)

What is the normal force on the box?

What is the acceleration of the box? (Should it depend on mass?)

If the actual acceleration were 1/2 this, what would the coefficient of friction be for the box?

θ

θ

π/2 - θ

π/2

π/2

a

ax

ay

What is my reference frame?

Bad Habits for Learning Physics

1. Trying to memorize all the formulas. It is true, some formulas are worth memorizing, but only very specific ones. If you try to memorize them all, you are bound to make mistakes. For the exams, I allow you to write down anything you want onto one sheet of paper. This means you don’t need to memorize formulas.

2. Trying to memorize the solutions to problems. Each problem is unique and memorizing a solution won’t get you anywhere. However, I do recommend you test yourself to see if you can figure out how to solve a problem. Simply memorizing the steps to get there often does not help.

3. Being afraid of a problem. This often occurs when you read a problem you have no idea how to answer. Let that fear slowly dissipate, and follow the steps handed out in the problem solving guide in class. You may find that you can solve the problem without any trouble when start to think about it a new way.

4. Others? Let me know what you think.

Gravity (near Earth) = mg

Gravity (general) = Gm1m2/r^2

Friction = μN, static or kinetic

Spring = -kx

Tension = ?

Normal = ?

Frictional Forces

A. Draw the force diagram (free body diagram) for the bottom box

B. Draw the force diagram (free body diagram) for the top box

**Objects Moving in Uniform Circles**

An astronaut in a space station is swinging a ball of mass m on a string of length R in a circle at a constant speed of v.

a. Draw Free Body Diagram

b. Calculate the tension in the rope

For objects moving in a perfect circle, ΣF = ma still. In this case, however, we know that the acceleration is purely centripetal, so a = v^2/r. For uniform circular motion, ΣF = mv^2/r

Gravitational Motion

The gravitational force between two spheres when they are far apart is F = Gm1m2/r^2. m1 is the mass of the first object, m2 is the mass of the second, G is a constant, and r is the distance between their centers.

A. Draw a free body diagram for the Earth as it orbits the sun.

B. Using forces, determine the distance between the Earth and the sun. The mass of the sun is 2.0 * 10^30 kg and G = 6.67*10^-11 m^3/kg s^2.

(Hint: Put velocity in terms of angular velocity!)

**Torque**

Torque is an action on a body that causes it to rotate

**τ = r X F = r F sinθ**

F = G m1 m2 / r^2

Remember, cross product only care about part of F that is perpendicular to r, or vice versa.

Also, using right hand rule, torque direction is perpendicular to both r and F.

Common Sense about Torque: How to open a door

Common Sense about spinning a ball on a rope. Back on Earth, we spin the ball in a vertical circle. If we go too slow, what will happen?

a) What minimum velocity must the ball have to stay spinning in the circle?

b) What is the tension in the rope at the top and bottom at this minimum velocity?

b) If we go to the moon, does it change?

Friction is the force resisting the relative motion of solid surfaces, fluid layers, and material elements sliding against each other. The force is calculated by F = μ*N

Static Friction vs Kinetic Friction

Friction is independent of surface area of contact!

Friction is independent of velocity!

Examples: Static or Kinetic

1. A box in the back of an accelerating truck that is not sliding.

2. A box in the back of a nonaccelerating truck

2. A table being pushed sideways but not moving

3. Two boxes stacked on one another. Between the bottom box which is moving and the table? Between the bottom box and the top box?

F = μ_k * Normal Force

F = μ_s * Normal Force

μ_s is always greater than μ_k

The coefficient of friction depends on the materials interacting - Table 5-1 in textbook

Commonly misunderstood

Which gives better traction on a car, wider or narrower tires?

If the coefficient of kinetic friction between the box and the table is μ_k=0.1, and static friction is μ_s = 0.5.

a) Will the box slide with no outside forces on it?

b) If the box is sliding, what is the acceleration of the box?

Example Problem

Kinetic friction occurs between two surfaces that are moving relative to one another. Static exists between two surfaces NOT moving relative to one another.

**Math Review - 10/7**

Unit Vectors:

Draw x_hat and j_hat on an xy coordinate system.

What is the length of the vector?

What is x_hat · x_hat?

What is x_hat · y_hat?

Unit Vectors:

Draw x_hat and j_hat on an xy coordinate system.

What is the length of the vector?

What is x_hat · x_hat?

What is x_hat · y_hat?

**Announcements**

1. Help Desk Monday and Wednesday now from 2-4 instead of 1-3

2. Unit 2 HW will be posted today

3. Unit 1 Quiz can be picked up at help desk on Thursday

4. Unit 0 makeup quiz available until Thursday

5. No class Thursday, but help desk is open

6. Check Blackboard for update on Lab Quiz

1. Help Desk Monday and Wednesday now from 2-4 instead of 1-3

2. Unit 2 HW will be posted today

3. Unit 1 Quiz can be picked up at help desk on Thursday

4. Unit 0 makeup quiz available until Thursday

5. No class Thursday, but help desk is open

6. Check Blackboard for update on Lab Quiz