# Newton’s Laws of Motion

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Newton’s Laws of Motion
Sir Isaac Newton described the relationship between motion and force in 3 laws

Newton’s First Law- aka:the law of inertia
An object at rest remains at rest and an object in motion maintains its velocity unless it experiences an unbalanced force. An object at rest tends to stay at rest An object in motion tends to stay in motion at the same velocity This is known as inertia Inertia: tendency to resist change until an outside force acts upon the object Example: When in a car and the car stops, your body continues forward. Seat belts are used to counter this effect.

Inertia is related to an object’s mass
Mass is actually a measure of inertia An object with a small mass has less inertia An object with a greater mass has more inertia Which object would be easier to change the motion of?

Inertia Why you slide into your friend on the Music Express Ride
Why you can’t stop instantaneously when driving a car We use seat belts and air bags to help our bodies slow down when inertia keeps them going

Safety! Seat belts and car seats provide protection.
Because of inertia, you slide toward the side of a car when the driver makes a sharp turn. When the car you are riding in comes to a stop, your seat belt and the friction between you and the seat stop your forward motion.

On earth objects in motion appear to slow down on their own, however an outside force is acting on them. This outside force is usually friction. In space, where there is no friction and object in motion will continue to stay in motion and just keep going unless something acts upon it.

Newton’s Second Law Newton’s first law depends upon the net force being zero or balanced Newton’s second law depends upon the net force being unbalanced Newton’s Second Law: The unbalanced force acting on an object equals the object’s mass times the acceleration Force = mass x acceleration F = ma

F = ma

F = ma The force needed will increase when the mass increases F = ma
F and m are directly proportional Which requires more force? A) B)

F = ma The force needed will increase when the acceleration increases F = ma F and a are directly proportional Which requires more force? A) B)

F = ma If force is constant, then the higher the mass the lower the acceleration F = ma m and a are inversely proportional

Force is measured in Newtons
1 Newton = 1 kg x 1 m/s2 The pound (lb) is sometimes used as a unit of force. 1 N = lbs or 1 lb = N Example: a baseball accelerates downward at 9.8 m/s2. If the gravitational force is the only force acting on the baseball and is 1.4 N, what is the baseball’s mass?

Newton’s Second Law Zookeepers lift a stretcher that holds a sedated lion. The total mass of the lion and stretcher is 175 kg, and the lion’s upward acceleration is m/s2. What is the unbalanced force necessary to produce this acceleration of the lion and the stretcher? 1. List the given and unknown values. Given: mass, m = 175 kg acceleration, a = m/s2 Unknown: force, F = ? N

Newton’s Second Law, cont.
2. Write the equation for Newton’s second law. force = mass  acceleration F = ma 3. Insert the known values into the equation, and solve. F = 175 kg  m/s2 F = 115 kg  m/s2 = 115 N

Gravity Law of gravitational force: objects in the universe attract each other through gravitational forces. The force of gravity is increased if one or both of the object’s masses increase The gravitational pull between two heavy objects is greater then the gravitational pull between two light objects The farther apart (the greater the distance) between two objects, the less the gravitational pull.

Universal Gravitation Equation
GRAVITY Sir Isaac Newton (1642–1727) generalized his observations on gravity in a law now known as the law of universal gravitation. Universal Gravitation Equation F = G m1 m2 d m1 and m2 are the masses of the two objects d is the distance between the two objects G is a constant G = x 10-11 N m2/kg2

Huh…What do you need to know?
Force of gravity is directly proportional to the masses of the objects Masses go up, force of gravity goes up Force of gravity is inversely proportional to the distance between the objects Distance goes up, force of gravity goes down

An apple hanging from a tree;
No matter how big or small an object is, it will exert a gravitational force. We just don’t notice it for small objects. You have a gravitational attraction for all objects around you, but since the earth is so large, the pull of gravity towards the earth is greater and the only force you feel An apple hanging from a tree; There is a gravitational attraction between the apple and the tree There is a gravitational attraction between the apple and the earth When the apple stem breaks, the apple falls to the ground because the force of gravity is greater between the apple and the earth than the apple and the tree.

Free-Fall Acceleration
As an object falls to the earth, the distance between the object and the earth decreases, thus increasing the gravitational pull. As two objects move farther apart, the force of gravity between them decreases. When gravity is the only force acting on an object, the object is said to be in free fall. Free-fall acceleration due to gravity is abbreviated by “g” and is approx equal to 9.8 m/s2 at the earth’s surface.

In the absence of air resistance (fluid friction), all object near the earth’s surface accelerate at the same rate. ALL objects exhibit the SAME free-fall acceleration (g). But how can this be if the objects do not have the same mass….how can a heavy object not accelerate faster? Well….A heavier object has greater gravitational pull, but a heavier object is more difficult to accelerate. The extra mass compensates for the additional gravitational force, thus allowing free-fall acceleration (g) to remain the same.

Weight Weight is dependant upon gravity, mass is not.
Weight: the force on an object due to gravity Weight = mass x free-fall acceleration w = mg Since weight is a force, we measure weight in newtons (N) a newton = kg x m/s2 A small apple weighs approx 1N A 1.0 kg book has a weight of 9.8 N F = m x a F = Weight = 1 kg x 9.8 m/s2 = 9.8 kg x 9.8 m/s2 = 9.8 N Less gravity in space gives apparent weightlessness, because weight changes but mass does not. An object can not be weightless! It can be close because of increased distance between object, so a very low gravitational pull would result.

Mass to Weight Weight is gravity acting on the object’s mass. On Earth 9.8 m/s2 W = ma weight = mass x acceleration due to gravity 9.8 N = 1 kg x 9.8 m = 9.8 kg x m  s2 s2 (that’s a newton) Therefore 1 kg = 9.8 N

Weight loss plan? How much does a 50. kg student weigh on Earth?
50. kg| 9.8 N = 490 N | kg How much does she weigh on the moon, with 1/6 gravity? /6 =1.6 50. kg| 1.6 N = 80 N

Air resistance When air resistance balances the force of gravity (weight), the object’s velocity will be constant. This is because the two forces are equal but opposite. Terminal velocity: the maximum velocity that can be reached when the force of gravity and the force of air resistance are equal. When a skydiver opens his parachute, the air resistance increases greater, thus slowing them down

A skydiver is not in free fall. This is a misnomer.
Free-fall only occurs when the only force acting upon an object is gravity. So free-fall can only occur when there is no air resistance, in other words…it can only occur in when there is no air…..in a vacuum. Because there is no air in space, free-fall can occur in space. Astronauts float in space because they are in free-fall, not because they are “weightless”!

Orbiting An object is said to be orbiting when it is travelling in a circular path around another object Gravity pulls a space shuttle towards earth causing free-fall The shuttle is also moving forward at a constant speed When these two actions combine, orbiting occurs

Orbiting

Orbiting

Orbiting Orbiting objects are in free fall.
The moon stays in orbit around Earth because Earth’s gravitational force provides a pull on the moon. Two motions combine to cause orbiting.

Projectile Motion Projectile motion: when two forces combine to form a resultant motion Orbiting is an example of projectile motion. When a curved path forms when an object is thrown, launched, or projected

Projectile motion combines vertical force and horizontal force
Projectile motion combines vertical force and horizontal force. These forces are independent of each other and do not affect each other, but when they combine, they form an arc or curved path. Horizontal force: comes from the projecting object. You are responsible for the horizontal force when throwing a ball. Vertical force: comes from gravity Because object always accelerate downward, your aim should be above the target when firing an arrow

How does something go into orbit?
Newton's Cannon A “thought” experiment Not too slow…drops back to earth Not too fast…escapes earth Just right…horizontal force balances with vertical gravity to maintain orbit The thought experiment becomes real with satellites and space stations and planets and moons and…

ACCELERATION, GRAVITY, AND VELOCITY FORMULAS Use algebra to rearrange for the desired quantity.
a = vf - vi v = velocity (final velocity-initial velocity) t t = time a= acceleration (due to gravity 9.8 m/s2 ) Use this if the problem involves acceleration…change in velocity. You may be asked to calculate velocity. If the object is dropped its initial velocity=0 and you will calculate for final velocity. _______________________________________________ d = at2 a = acceleration (due to gravity 9.8 m/s2 ) 2 t = time d = distance Use this if you are asked to calculate how far a dropped object travels in a certain amount of time. _________________________________________________ v = d d= distance v= velocity t= time t Use this for average velocity, not acceleration. It does not account for changes in velocity (acceleration)

Newton’s Third Law For every action force, there is an equal and opposite reaction force When you kick a soccer ball, you are exerting force on the ball, but the ball is also exerting an equal but opposite force on your foot. Action force: the force exerted ON the ball BY your foot Reaction force: the force exerted ON your foot BY the ball

When you sit on a chair, you are exerting an action force by pushing on the chair and the chair is exerting a reaction force on you, by pushing upward to keep you supported. Force always exists in pairs. These forces are always equal but opposite. However, they do not cancel each other out because they are acting on different objects The force from your foot is equal to the force from the ball when you kick it, but the force from the ball on your foot is not as effective because it is coming from an object with small mass and acting on an object with greater mass

Momentum The product of the mass and velocity of an object
Momentum = mass x velocity p = mv When a car and a truck are traveling at the same velocity, and both brake at the same time with the same brake force, the truck takes longer to stop than the car because of its increased mass

A bowling ball has greater momentum than a kickball even though they are approximately the same size and could be travelling at the same velocity. The bowling ball has a greater mass! The speed also affects momentum: a fast moving train has more momentum than a slow moving train even though they are the same mass If an object is not moving its momentum is zero Like velocity, momentum has direction. It is in the same direction as the velocity

When you catch a baseball, if you extend the time as your are changing the ball’s momentum, then you can reduce the sting on your hand by reducing the force exerted on your hand by the ball. Momentum is conserved in collisions. It can be transferred from one object to another, but the same amount of momentum is constant. When two cars hit head on, if they get stuck together, they will move together in the direction of the car with the greater momentum. When two cars hit head on, if they bounce off of each other, the momentum is still conserved. When playing billiards: the cue ball hits another ball and transfers its momentum to the ball. The other ball is moved forward by the action force from the cue ball. The cue ball stops due to the reaction force from the other ball

Momentum Calculate the momentum of a 6.00 kg bowling ball moving at 10.0 m/s down the alley toward the pins. 1. List the given and unknown values. Given: mass, m = 6.00 kg velocity, v = 10.0 m/s down the alley Unknown: momentum, p = ? kg • m/s (and direction)

2. Write the equation for momentum.
momentum = mass x velocity p = mv 3. Insert the known values into the equation, and solve. p = mv = 6.00 kg  10.0 m/s p = 60.0 kg • m/s down the alley

Conservation of Momentum

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