Bell Ringer:

• Who was Isaac Newton and what did he do?

• Who was Galileo Galilei and why is famous?

• What is a force?

• What do Newton’s three laws pertain to?

4.1 Newtonian Mechanics: ForcesNewton’s 1st & 2nd Law

Physics Honors I

Objectives:

• Define Force.

• Understand the difference between balanced and unbalanced forces

• Explain the meaning of Newton’s 1st Law.

• Apply Newton’s 2nd Law to solve problems.

• Describe how the weight and mass of an object are related.

Vocabulary:

• Force• Net Force

• Inertia• Equilibrium

• Newton’s 1st Law• Newton’s 2nd Law

• Free-Body Diagram• System

Active Physics Reference:

• Chapter 2 - Section 1: p. 132- 153 (1st Newton's Law)• Chapter 3 – Section 2: p. 268 - 272

• Chapter 2 - Section 3: p. 157 - 240 (2nd Newton's Law)• Chapter 3 - Section 4: p. 294 - 297 (2nd Newton's Law)

• Chapter 2 - Section 6: p. 198 (3rd Newton's Law)

Further Learning:

Physics: Principles and Problems - the red book we have in class

Chapter 4 - Newton's LawsChapter 5 - Friction and 2-Dimensional Forces

(3) Physics Classroom:

Newton's Laws

(4) Khan Academy

Newton's Laws Balanced vs Unbalanced Forces

What are Forces?

What do we see forces being used?

Newton’s 1st Law (Biology): Animals with large body mass are generally unable to change direction quickly when in motion. Smaller animals can often elude their larger predators by making sharp turns while moving quickly.

Newton’s 2nd Law (Biology): A flea is able to exert tremendous force for its size, allowing it to jump up to 13 in. (33 cm), or 200 times the length of its body.

Newton’s 3rd Law (Earth Science): When a hurricane strikes land, the wind exerts tremendous force on topographical features and objects on the land. The reaction force of these objects on the moving air causes it to slow down, which is why hurricanes eventually dissipate as they move over land.

What is a Force?

• A force is any type of push or pull.

• Contact Forces: When we physically make contact with an object to push or pull it a certain direction.

• Non-Contact Forces: Gravitational Force, Magnetic Force, Electric Force.

• SI Unit for a force is a Newton.

1 N = 1 kg ∙m

s2

What is a Force? (Continued)

A net force causes an acceleration, which is a change in velocity.

Whenever an object in motion changes direction, speeds up, slows down, or stops, it

does so because a force is acting on it.

A FORCE CAUSES AN ACCELERATION.

A force is measured by the acceleration it produces.

There may be many forces acting on a body, but if their net force is zero, the body

cannot acceleration.

Inertial Reference Frame:

An inertial reference frame is one in which Newton’s laws hold.

A non-inertial reference frame is one in which Newton’s laws do not hold.

Inertial Reference Frame:

· For example, we can assume that the ground is an inertial frame provided we can neglect Earth’s astronomical motions (such as its rotation).

· Basically, we more or less imagine that your frame of reference isn’t moving. We are sitting in a classroom now and imagine the classroom is still. When in truth our planet is hurling around the Sun at a speed of 30 km/s (18.5 miles/s), while our Solar System is rotating around the center of the Milky Way galaxy at 486,000 mph. So we basically, we don’t have to account for the spin of the planet, the rotation of the planet around the Sun, or the rotation of the Sun around the Milky Way galaxy to do most physics problems.

Newton’s Laws of Motion:

• Newton’s 1st Law of Motion:

• An object at rest stays at rest and an object in motion stays in motion with the same speed and in the same direction unless acted upon by an unbalanced force.

Newton’s Laws of Motion:

• Newton’s 2nd Law of Motion:

• An acceleration is produced when a force acts on a mass.

• Or a force is produced whenever a mass is accelerated.

Newton’s Laws of Motion:

• Newton’s 3rd Law of Motion:

• When two bodies interact, the forces on the bodies from each other are always equal in magnitude but opposite in direction.

Comprehension Check 1:

1. Explain what a force is?

2. Explain what an inertial reference frame is?

3. What is the SI Unit for Force?

4. Is a force a vector or a scalar? Why is that important?

Newton’s 1st Law:

• Newton’s 1st Law of Motion:

• An object at rest stays at rest and an object in motion stays in motion with the same speed and in the same direction unless acted upon by an unbalanced force.

• What does this mean?

Newton’s 1st Law - An object at rest stays at rest and an object in motion stays in motion with the same speed and in the same direction unless acted upon by an unbalanced force.

THREE DISTINCT PARTS TO NEWTON’S FIRST LAW:

Part 1: If an object is at rest, it stays at rest.

Part 2: If a body is moving, it continues to move with the same velocity (same

magnitude and direction). That is, objects in motion stay in motion in a straight line

with constant speed.

Part 3: The first two parts are only true when the net force on the object is zero. An

object may have forces acting on it and still have no change in its motion. (Net force

is the sum of all forces acting on an object).

Newton’s 1st Law – Balanced Forces vs Unbalanced Forces

PHET Stimulation:

PHET - Forces and Motion - Acceleration

• Go to: Acceleration

• Try it: With and Without Friction. What happens to the box?

• Does it take longer to get to maximum speed if it weighs more?

Newton’s 1st Law – Balanced Forces vs Unbalanced Forces

PHET Stimulation:

PHET - Tug-O-War

• Go to: Net Force Tab (The tug of War)

• Try it: What happens when you put a small blue guy on one end?

• Now put a small red guy on the opposite end. Why does blue team still win?

Newton’s 1st Law – Balanced Forces vs Unbalanced Forces

From the stimulations we see that forces can be summed together to find the net force on the object.

Ԧ𝐹𝑛𝑒𝑡 = Ԧ𝐹1 + Ԧ𝐹2 + Ԧ𝐹3 + ⋯+ Ԧ𝐹𝑁

• If Ԧ𝐹𝑛𝑒𝑡 = 0 𝑁, the forces are balanced.

• If Ԧ𝐹𝑛𝑒𝑡 ≠ 0 𝑁, the forces are unbalanced.

Newton’s 1st Law - An object at rest stays at rest and an object in motion stays in motion with the same speed and in the same direction unless acted upon by an unbalanced force.

• Newton’s first law is sometimes called the law of inertia.

• Is inertia a force?

• No. Inertia is the tendency of an object to resist change.

• Forces are results of interactions between two objects; they are not properties of single

objects, so inertia cannot be a force.

Newton’s 1st Law - An object at rest stays at rest and an object in motion stays in motion with the same speed and in the same direction unless acted upon by an unbalanced force.

• Inertia – is a measure of mass – The more mass an object has the more inertia,

without respect to what the object is composed of.

• Mass is an intrinsic characteristic of a body – that is, a characteristic that

automatically comes with the existence of a body. The SI unit for mass is kg.

Equal amounts of mass imply equal amounts of inertia.

Inertia is a measure of the object’s mass only. Size, shape, volume, and speed do not

determine its inertia.

Newton’s 1st Law - An object at rest stays at rest and an object in motion stays in motion with the same speed and in the same direction unless acted upon by an unbalanced force.

• Example:

• You are standing still on a train. What happens when the train starts?

• You get jerked back because an object at rest wants to stay at rest. That is your inertia

at play.

• Now the train is coming to a stop. What happens to your body as your standing there?

• Your body wants to keep moving forward. That is your inertia again, because an

object in motion desires to stay in motion until acted on by an unbalanced force.

Comprehension Check 2:

1. Why is Newton’s first law sometimes called the law of inertia?

2. Is inertia a force?

3. What is a balanced force?

4. What is an unbalanced force?

Newton’s 2nd Law – The net force on a body is equal to the product of a body’s mass and it’s acceleration.

• So this is the biggest Newtonian Law. We can represent it in equation form as:

Ԧ𝐹𝑛𝑒𝑡 = 𝑚 Ԧ𝑎• 𝐹𝑛𝑒𝑡 = force (a vector)

• m = mass

• a = acceleration.

• RECALL: SI Unit is 1 N or 1 kg times Τm s2

Newton’s 2nd Law – The net force on a body is equal to the product of a body’s mass and it’s acceleration.

• Since force is a vector, that means we can analyze each force on its individual axis such

that we have:

𝐹𝑥 = 𝑚𝑎𝑥 ; 𝐹𝑦 = 𝑚𝑎𝑦 ; 𝐹𝑧 = 𝑚𝑎𝑧

• Thus, we are allowed to once again use these equations and treat force as a vector:

Ԧ𝐹 = 𝐹 cos 𝜃 Ƹ𝒊 + (𝐹 sin 𝜃) Ƹ𝒋

• Where 𝐹𝑥 = 𝐹 cos 𝜃 𝑎𝑛𝑑 𝐹𝑦 = 𝐹 sin 𝜃

Newton’s 2nd Law – The net force on a body is equal to the product of a body’s mass and it’s acceleration.

• This also means we can continue using the equations:Ԧ𝐹 = 𝐹 cos 𝜃 Ƹ𝒊 + (𝐹 sin 𝜃) Ƹ𝒋

• Magnitude of the Force:

𝐹 = (𝐹𝑥)2 + (𝐹𝑦)

2

• Direction (Angle):

𝜃 = tan−1 ൘𝐹𝑦

𝐹𝑥

Free-Body Diagram:

• A free-body diagram is a sketch representing the forces acting on a body. It is highly recommended to make use of free-body diagrams when solving Newton’s second law. Each force on the body is drawn as a vector arrow with its tail on the body. A coordinate system is usually included.

• Example 1: A book rest on a table.

• Example 2: Pushing a box across the floor.

Free-Body Diagram:

What is included in a free-body diagram?

• The body.• External forces.

What is NOT included in a free-body diagram?

• Other bodies.• Internal forces (think of a car).• Forces exerted by the body.

System:

• System – consist of one or more bodies that form a group of interacting, interrelated, or interdependent elements which form a complex whole. (In the box problem, our box is our system; that is, it is what the forces are being applied to).

External Force – Any force on the bodies inside the system from bodies outside the

system. (These are the forces we deal with most often).

Internal Force – are forces that are happening on the body from inside the system.

These are more so concerned with thermodynamics.

Newtons 2nd Law – Example 1:

• You are pushing an 80 kg box across the floor with an acceleration of 3.0 Τ𝑚 𝑠2? What

net force are you exerting on the box?

Ԧ𝐹 = 𝑚 Ԧ𝑎

Ԧ𝐹 = 80 𝑘𝑔 3.0 ൗ𝑚 𝑠2

Ԧ𝐹 = 240 𝑁

Newtons 2nd Law – Example 2:

• You are carrying an 80 kg box across the floor at constant velocity? What net force are

you exerting on the box?

Ԧ𝐹 = 𝑚 Ԧ𝑎

Ԧ𝐹 = 80 𝑘𝑔 0 ൗ𝑚 𝑠2

Ԧ𝐹 = 0 𝑁

Newtons 2nd Law – Example 3:

• You and your friend are pushing a 200 kg refrigerator across the floor. You push with a

force of 50 N, and your friend pushes with a force of 75 N. What is the net force on the

refrigerator?Ԧ𝐹𝑁𝑒𝑡 = Ԧ𝐹𝑌 + Ԧ𝐹𝐹

Ԧ𝐹𝑁𝑒𝑡 = 50 𝑁 + 75𝑁

Ԧ𝐹𝑁𝑒𝑡 = 125 𝑁

Newtons 2nd Law – Example 4:

• A late traveler rushes to catch a plane, pulling a suitcase with a force directed 30.0°above the horizontal. If the force exerted on the handle is 70 N, what is the horizontal component of the force on the suitcase?

𝐹𝑥 = 𝐹 cos 𝜃

𝐹𝑥 = (70 𝑁) cos(30°)

𝐹𝑥 = 60.6 𝑁

Comprehension Check 3:

• You and your friend are playing tug-o-war. You can exert a force of 80 N on the rope and your friend can exert a force of 94 N.

• What is the net force acting upon the rope?

Exit Ticket 1:

1. If a nonzero net force is acting on an object, then the object is definitely

a. at rest. c. being accelerated.b. moving with a constant velocity. d. losing mass.

2. Which of the following is the tendency of an object to maintain its state of motion?

a. acceleration c. forceb. inertia d. velocity

Exit Ticket 2:

3. A free-body diagram represents all of the following except

a. the object. c. forces exerted by the object.b. forces as vectors. d. forces exerted on the object

4. A newton is equivalent to which of the following quantities?

a. kg c. kg·m/s2

b. kg·m/s d. kg·(m/s)2