Ch. 3 Forces
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
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
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
- 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
- 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
- The weight of an object near Earth’s surface is: W = mg
- Projectiles travel in a curved path because of their horizontal motion and vertical acceleration due to gravity
- 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
- Newton’s third law of motion states that for every action there is an equal and opposite reaction
- The momentum of an object can be calculated by the equation p = mv
- When two objects collide, momentum can be conserved. Some of the momentum from one object is transferred to the other