3.1 Newton’s Second Law

Force, Mass, and Acceleration

Newton’s second law of motion describes how forces exerted on an object, its mass, and its acceleration are related

Force and Acceleration

When you throw hard, you exert a much greater force on the object. The object then has a greater velocity when it leaves your hand rather than if you gently throw it

Mass and Acceleration

Objects with different masses have different speeds; if it would take the same amount of time to throw both objects the heavier one would have less acceleration

The acceleration of an object depends on its mass as well as the force exerted on it; therefore force, mass, and acceleration are related

Newton’s Second Law

Newton’s second law of motion - states that the acceleration of an object is in the same direction as the net force on the object: acceleration=net force/mass

Calculating Net Force with the Second Law

If mass and acceleration are known, Newtons second law can be used to calculate the net force by multiplying each side of the equation by the mass

Friction

Friction - force that opposes the sliding motion of two surfaces that are touching each other

What causes friction?

Microwelds - are the source of friction

Sticking Together

The larger the force pushing the two surface together, the strong the microwelds will be, because of the more bumps that come in contact with each other; to move one surface over the other a force must be applied to break the microwelds

Static Friction

Static friction - frictional force that prevents two surfaces from sliding past each other

Sliding Friction

Sliding friction - force that opposes the motion of two surfaces sliding past each other; sliding friction is caused by microwelds constantly breaking and then forming again as the object slides along the floor

Rolling Friction

Rolling Friction - frictional force between rolling objects and the surface it rolls on

Air Resistance

When an object falls down towards Earth, gravity pulls it downward

Air resistance - a friction-like force, opposes the motion of objects that move through the air

• Air resistance causes objects to fall with different accelerations and different speeds; air resistance acts in the opposite direction to the motion of an object through the air

The amount of air resistance on an object depends on the speed, size, and shape of the object; air resistance is why feathers, leaves, and pieces of paper fall more slowly than pennies, acorns, and apples

Terminal Velocity

As an object falls, the downward force of gravity causes the object to accelerate

As an object falls faster, the upward force of air resistance increases

The terminal velocity is the highest speed a falling object will reach

The terminal velocity depends on the size, shape, and mass of a falling object

3.1 Summary

Force, Mass and Acceleration

• The greater the force on an object, the greater the object’s acceleration

• The acceleration of an object depends on its mass as well as the force exerted on it

Newton’s Second Law

• Newton’s second law of motion states that the acceleration of an object is in the direction of the net force on the object, and can be calculated from this equation:

  a= fnet/m

Friction

• Friction is the force that opposes motion between two surfaces that are touching each other

• Friction depends on the types of surfaces and the force pressing the surfaces together

• Friction results from the microwelds formed between surfaces that are in contact

Air Resistance

• Air resistance is a force that acts on objects that move through the air

3.2 Gravity

What is gravity?

• When you are exerting an attractive force it by gravity

• Anything that has mass is attracted by the force of gravity

Gravity - an attractive force between any two object that depends on the masses of the objects and the distance between them; this force increases as the mass of either object increases or as the objects move closer

• Only Earth is both close enough and has a large enough mass that you can feel its gravitational attraction

Gravity—A Basic Force

Gravity is one of the four basic forces; the other four include electromagnetic force, the strong nuclear force, and the weak nuclear force. The two nuclear forces only act on particles in the nuclei of atoms

The Law of Universal Gravitation

Sir Isaac Newton published the law of universal gravitation in 1687; this law is written in the following equation:

F = Gx m1m2/d2

• G is a constant called the universal gravitational constant, and d is the distance between the two masses: m1 and m2

The law of universal gravitation enables the force of gravity o be calculated between any two objects if their masses and the distance between them are known

The Range of Gravity

The gravitational force between two masses decreases rapidly as the distance between the masses increases

No matter how far apart two objects are, the gravitational force between them never completely goes to zero

Gravity is called a long-range force because gravitational force between two objects never disappears

Finding Other Planets

Using the law of universal gravitation two astronomers independently calculated the orbit of Neptune in 1846

Earth’s Gravitational Acceleration

When all forces except gravity acting on an a falling object can be ignored the object is said to be in free fall; then all objects near earth’s surface would fall with the same acceleration

Close to Earth’s surface, the acceleration of a falling object in free fall is about 9.8 m/s2

The force of gravity on a falling object is the object’s mass times the acceleration of gravity which is expressed in this equation:

F = mg

Weight

Even if you aren’t falling the force of gravity is pulling you downward; if you are standing on the floor the net force of you is zero

Weight - the gravitational force exerted on an object

Since the weight of an object on Earth is equal to the force of Earth’s gravity on the object can be calculated with this equation:

W = mg

Weight and Mass

Weight and mass are NOT the same

• Weight is a force and mass is a measure of the amount of matter an object contains

According to the weight equation, weight and mass are related; weight increases as mass increases

Floating in Space

When you stand on a scale, you are at rest and the net force on you is zero. The scale supports you and balances your weight by exerting an upward force. The dial on the scale shows the upward force exerted by the scale, which is your weight

Projectile Motion

Thrown objects don’t always travel in straight lines; they curve downward

Anything thrown or shot through the air is called a projectile; Earth’s gravity causes projectiles to follow a curved path

Horizontal and Vertical Motions

When you throw a ball, there is a force exerted by your hand that pushes the ball forward. This force gives the ball horizontal motion.

After you let go of the ball, no force accelerates it forward so its horizontal velocity is constant if you ignore the air resistance.

When you let go of the ball, gravity can pull it downward which gives it vertical motion. Now that ball has both horizontal velocity but increasing velocity. Which results in the ball curving

Horizontal and Vertical Distance

A thrown ball and a dropped ball will hit the ground at the same time due to them traveling the same vertical distance in the same amount of time.

However the ball thrown horizontally travels a greater horizontal distance than the ball that is dropped

Centripetal Force

Centripetal acceleration - the acceleration toward the center of a curved or circular path

According to the second law of motion, when the ball has centripetal acceleration the direction of the net force on the ball also must be toward the center of the curved path

Centripetal force - the net force exerted toward the center of a curved path

Centripetal Force and Traction

When a car goes around a curve on the highway, a centripetal force acts on the car to keep it moving in the curved path the centripetal force is the frictional force between the tires and the road

Gravity Can Be a Centripetal Force

Earth’s gravity exerts a centripetal force on the Moon that keeps it moving in a nearly circular orbit

3.2 Summary

Gravity

• According to the law of universal gravitation, the gravitational force between two objects depends on the masses of the objects and the distance between them

• The acceleration due to gravity near Earth’s surface has the value 9.8 m/s2

• Near Earth’s surface, the gravitational force on an object with mass, m, is given by:

  F = mg

Weight

• The weight of an object is related to its mass according to the equation:

  W = mg

• An object in orbit seems to be weightless because it is falling around Earth

Projectile Motion and Centripetal Force

• Projectiles follow a curved path because their horizontal motion is constant, but gravity causes the vertical motion to be changing

• The net force on an object moving in a circular path is called the centripetal force

3.3 The Third Law of Motion

Newton’s Third Law

Newton’s third law of motion - describes action-reaction pairs this way: When one object exerts a force on a second object, the second one exerts a force on the first that is equal in strength and opposite in direction

Another way to explain the third law of motion is to every action force there is an equal and opposite reaction force

Action and Reaction

When a force is applied in nature, a reaction force occurs at the same time

Action and Reaction Forces Don’t Cancel

Even though forces are equal, they are not balanced since they act on different objects

Rocket Propulsion

Rocket engines exert a force on gases and cause them to escape out the back of the rocket; by Newton’s third law, the gases exert a force on the rocket and push it forward

Momentum

A moving object has momentum which is related to how much force is needed to change its motion

Momentum - of an object is the product of its mass and velocity

Momentum’s equation: p = mv

Force and Changing Momentum

Since acceleration is the difference between the initial and final velocity divided by the time, and due to the second law of motion: the net force on an object equals its mass times it acceleration.

• When you combine these two concepts you get Newton’s second law written like this: F =( mvf−mvi)/t

The equation says that the net force exerted on an object can be calculated by dividing its change in momentum by the time over which the change occurs

Law of Conservation of Momentum

The momentum of an object doesn’t change unless its mass, velocity, or both change

Momentum can be transferred from one object to another

When Objects Collide

When two object collide while going towards each other at the same speed, they have the same momentum but are going in different directions

3.3 Summary

Newton’s Third Law

• According to Newton’s third law of motion, for every action force, there is an equal and opposite reaction force

• Action and reaction forces act on different objects

Momentum

• The momentum of an object is the product of its mass and velocity: p = mv

• The net force on an object can be calculated by dividing its change in momentum by the time over which the change occurs

The Law of Conservation of Momentum

• According to the law of conservation of momentum, if objects exert forces only on each other, their total momentum is conserved

• In a collision, momentum is transferred from one object to another

Ch.3 Study Guide (Reviewing Main Ideas)

3.1 Newton’s Second Law

1. Newton’s second law of motion states that a net force causes an object to accelerate in the direction of the net force and that the acceleration is given by

   a =Fnetm

2. Friction is a force opposing the sliding motion of two surfaces in contact. Friction is caused by microwelds that form where the surfaces are in contact

3.2 Gravity

1. Gravity is an attractive force between any two objects with mass. The gravitational force depends on the masses of the objects and the distance between them

2. The gravitational acceleration, g, near Earth’s surface equals 9.8 m/s2. The force of gravity on an object with mass, m, is: F = mg

3. The weight of an object near Earth’s surface is: W = mg

4. Projectiles travel in a curved path because of their horizontal motion and vertical acceleration due to gravity

5. The centripetal force is the net force on an object in circular motion and is directed toward the center of the circular path

3.3 The Third Law of Motion

1. Newton’s third law of motion states that for every action there is an equal and opposite reaction

2. The momentum of an object can be calculated by the equation p = mv

3. When two objects collide, momentum can be conserved. Some of the momentum from one object is transferred to the other