F O R C E S A N D c h a p t e r 1 2 M O T I O N
What is a FORCE? A FORCE is a push or pull that acts on an object. A force can cause a resting object to move OR Accelerate a moving object by: changing the object s speed direction
How do we MEASURE force? Forces can be measured on a spring scale WEIGHT is a FORCE UNITS OF FORCE: Newton (N) A Newton is a force that causes a 1 kg mass to accelerate at a rate of 1 meter per second each second Which is written as: 1 N = 1 kg m/s 2
Representing Forces Forces can be represented with an arrow The length of the arrow shows strength or magnitude Direction of the arrow shows the direction of the force Figure 2 on page 357 shows an example of weight Normal Force Applied Force Friction Force
Combining Forces Net Force = the overall force acting on an object after all forces are combined
Same Direction: Combining Forces
Opposite Directions:
Net Force
Balanced Forces Balanced Forces = the net force is zero, there is no change in the object s motion Question: what are some examples where the net force would equal zero?
ANSWER Net force would be zero when: You play tug-of-war and neither team moves You arm wrestle and neither person wins A car using cruise control constant speed!
Unbalanced Forces Unbalanced Forces = the net force acting on an object does not equal zero
Question: What happens to the object when the net force acting on an object is NOT ZERO, or unbalanced? (like the example below)
Answer When an unbalanced force acts on an object, the object accelerates
3 examples of a net force causing an object to accelerate Pushing against the side of a book & getting it to move A team winning a game of tug-of-war & pulling the other team towards them A person in freefall
Watch video clip: The Effects of Forces on Speed On video notes page, draw an example of when the forces are balanced & when they are unbalanced. Then describe the result of these forces.
Watch video clip: The Effects of Forces on Speed On video notes page, draw an example of when the forces are balanced & when they are unbalanced. Then describe the result of these forces.
Try these problems 1. Two tugboats are moving a barge. Tugboat A exerts a force of 3000 newtons on the barge. Tugboat B exerts a force of 5000 newtons in the same direction. What is the combined force on the barge? Draw arrows showing the individual and combined forces of the tugboats in this problem to help you answer the question
Same direction so add 3000 N + 5000 N = 8,000 N + --- = ------
2. Now suppose that Tugboat A exerts a force of 2000 newtons on the barge and Tugboat B exerts a force of 4000 newtons in the opposite direction. What is the combined force on the barge? Draw arrows showing the individual and combined forces of the tugboats in this problem.
Opposite directions, so subtract 4000 N 2000 N = 2000 N -- =
3. Could there ever be a case when Tugboat A and Tugboat B are both exerting a force on the barge but the barge doesn't move? Draw arrows showing the individual and combined forces in such a situation.
= 0 Equal in size & opposite in direction
FRICTION
FRICTION Friction: a force that opposes the motion of objects that touch as they move past each other Without friction, it would be a very different world!!! Food would not stay on your fork! Cars would slide all over the road! Walking would be almost impossible! Friction acts at the surface where objects are in contact
The 4 Types of Friction Static Friction Sliding Friction Rolling Friction Fluid Friction
STATIC FRICTION friction force that acts on objects that are not moving Static friction always acts in the direction opposite to the applied force Examples: every time you take a step and push off glass of water sitting stationary on the table
SLIDING FRICTION a force that opposes the direction of motion of an object as it slides over a surface Sliding friction is a weaker force than static friction This is why less force is needed to keep an object moving than it is to start it moving
ROLLING FRICTION The friction force that acts on rolling objects Rolling friction is about 100-1000 times less than static or sliding friction This is why we use wheeled dollies to move heavy objects! In machines, ball bearings, are often used to reduce friction between two surfaces
FLUID FRICTION Force that opposes the motion of an object through a fluid Water and a mixture of gases such as air are known as fluids Example: a submarine moving through water The motion of the submarine is slowed by fluid friction Fluid friction increases as the speed of the object moving through the fluid increase So the faster the sub goes, the greater the friction!!!
AIR RESISTANCE Air resistance is a type of fluid friction Remember gases are considered fluids Fluid Friction acting on an object moving through the air is called AIR RESISTANCE
GRAVITY
GRAVITY Gravity: a force that acts between any two masses Gravity is an attractive force so it pulls objects together Gravity does not require objects to be in contact for it to act on them Gravity can act over large distances!!!
More GRAVITY! Earth's gravity acts downward toward the center of the Earth. There is usually an upward force that acts against gravity to balance out the forces and allow objects to remain still.
FALLING OBJECTS QUESTION: What forces are acting on an object as it falls?
ANSWER: Only two forces acting on a falling object are gravity and air resistance
Forces Acting on Falling Objects Gravity causes object to accelerate downward Air resistance acts in the opposite direction of the motion Which means it reduces acceleration
Recall what happens to the amount of fluid friction as an object speeds up?
Watch video clip: The Physics of Skydiving On the video notes page, describe what is meant by terminal velocity & describe the forces on the skydiver at this point.
Falling Objects If an object in freefall falls for long enough, the upward force of air resistance will become equal to the downward force of gravity. At this point, the two forces are BALANCED Acceleration is zero when forces are balanced The object will continue to fall at a constant velocity
Terminal Velocity Terminal Velocity: the constant velocity of a falling object when the force of air resistance equals the force of gravity
Projectile Motion Projectile Motion: The motion of a falling object (projectile) after it is given an initial forward velocity
Projectile Motion Question: What are the ONLY 2 FORCES that act on a projectile??? All 3 balls are experiencing projectile motion!
Projectile Motion Answer: Initial sideways force, (Air resistanceif we are considering friction) and gravity!!! Refer to figure 9 on page 362 in textbook The combination of an initial forward velocity and the downward vertical force of gravity causes the ball to follow a curved path
If I shoot a bullet horizontally and at the same time drop a bullet from the same height as the gun which will hit the ground first?
FALLING OBJECTS The two bullets WILL hit the ground at the same time!
The two balls fall with the same acceleration and strike the ground at the same time!!! Remember the Investigating Freefall Lab with the marbles? How did that lab compare with the previous statement???
12.2 Newton s First & Second Laws of Motion
It s not ALL about Newton Aristotle incorrectly proposed that force is required to keep an object moving at a constant speed Galileo studied how gravity produces constant acceleration. He concluded that objects not subjected friction or any other force would continue to move indefinitely Newton built off the work of Galileo and later published his work in a book entitled Principia Newton summarized his study of force and motion in several laws of motion
1 st Law of Motion Law of Inertia
1 st Law of Motion Law of Inertia 1 st Law: The state of motion of an object does not change as long as the net force acting on the object is zero In other words: Unless an unbalanced force acts, an object at rest remains at rest, and an object in motion remains in motion with the same speed and direction
1 st Law Law of Inertia Example: A soccer ball resting on the grass remains motionless until a force is applied to it.
And Example: A soccer ball in motion remains in motion unless a force acts on it.
Why is it called the Law of Inertia INERTIA: the tendency of an object to resist a change in its motion so an object at rest tends to remain at rest (resist moving), and an object in motion tends to remain in motion (resist stopping)
Remember soccer ball sat motionless (forces were balanced) until an unbalanced force acted on it The ball has inertia Everything with mass has inertia The more mass, the more inertia
Inertia Front-end collision Example: Front-end collision Collision makes car stop suddenly Since you have inertia you continue moving forward Page 364/365 Figure 12
Newton s Second Law of Motion
2 nd Law of Motion Relates the acceleration of an object to the force acting on it & the object s mass. 2 nd Law: The acceleration of an object is equal to the net force acting on it divided by the object s mass. A = F/M In other words, the amount of acceleration an object has depends on: How hard it is pushed (force) How heavy it is (mass)
Net Force Acceleration = -------------- Mass
Acceleration Force & Mass Relationship What is the acceleration?
ANSWER Acceleration is calculated by dividing the FORCE by the MASS Acceleration = 100 N / 50 kg A = 2 m/s 2
2 nd Law Example: You apply force to a ball when you throw it The harder you throw, the more the ball accelerates If you double the force, the acceleration of the ball doubles as well If you double the mass of the ball the acceleration is cut in half More Examples:
Important Notes Regarding Newton s 2 nd Law of Motion The acceleration of an object is always in the same direction as the net force. In using Newton s second law, it is helpful to realize that the units N/kg and m/s 2 are equivalent Newton s second law also applies when a net force acts in the direction opposite to the object s motion producing deceleration (See figure 13, page 368) This is the principle used by automobile seat belts See Math Skills page 367 (in textbook) for extra help
Weight & Mass What really is the difference?
We often talk about weight and mass as if they were the same thing Weight: is the force of gravity acting on an object. An object s weight is the product of the object s mass and acceleration due to gravity acting on it. Written mathematically as w = m x g
Weight lessens as Weight will DECREASE if gravity DECREASES!!!
Mass Versus Weight Mass is a measure of the inertia of an object, Measure with a balance Weight is a measure of the force of gravity acting on an object Measure with a spring scale Weight = Mass x Acceleration due to gravity W = mg Value of g = 9.8 m/s 2 (Earth)
Important Note Regarding Units Be sure when you use the weight formula or Newton s second-law formula that you use the CORRECT units!!! Force (F or W) in N (newtons) Acceleration (a or g) in m/s 2 (meters per second per second) Mass (m) in kg (kilograms)
Practice Problem If an astronaut has a mass of 112 kilograms, what is his weight on Earth where the acceleration due to gravity is 9.8 m/s 2? What would his weight be on the moon (g=1.62 m/s 2 )?
Answer to Practice Problem ON EARTH: Weight = Mass Acceleration due to gravity W = 112 kg x 9.8 m/s 2 W = 1097 kg m/s 2 = 1097 N ON MOON: W = 112 kg x 1.62 m/s 2 W = 181 kg m/s 2 = 181 N
Mass & Weight are Related Doubling the mass of an object also doubles the object s weight (if gravity remains the same) If Gravity changes then Example: Think about the astronaut above On the moon, the acceleration due to gravity is only about 1/6 that on Earth Thus, the astronaut weighs only about 1/6 as much on the moon as on Earth In both locations, the mass of the astronaut is the same!
12.3 Newton s 3 rd Law of Motion
Forces CAN T Exist Alone Forces always exist in pairs. According to Newton s 3 rd law of motion, whenever one object exerts a force on a second object, the second object exerts an equal and opposite force on the first object. These two forces are called action and reaction forces
Action Reaction Forces Example: The book lying on the table is exerting a downward force on the table, while the table is exerting an upward reaction force on the book.
Newton s Third Law Ex: A rocket
More Examples: Jumping off of a raft Action force = you push on the raft Reaction force = raft pushes back A swimmer in a pool Action force = swimmer s arm pushes on water Reaction force = water pushes back on swimmer
Action Reaction Forces Question: Since these action/reaction forces are equal in size and opposite in direction then why don t they cancel each other out and produce a net force of zero?
Action Reaction Forces Because the action/reaction forces do not act on the same object! Swimmer Example: The action force acts on the water The reaction force acts on the swimmer
Momentum Momentum = the product of an object s mass and its velocity An object with a large momentum is hard to stop
Momentum = mass X velocity Practice Problem: What is the momentum of a rock with a mass of 0.5kg that is moving at a velocity of 5m/s?
Momentum = 0.5kg X 5m/s = 2.5kg x m/s The units do NOT cancel!
Momentum can be transferred from one object to another during a collision
12.4 Universal Forces
Four Universal Forces 1. Electromagnetic forces- only forces that both attract and repel. (protons & electrons) 2. Strong Nuclear forces- holds neutrons & protons together 3. Weak Nuclear forces- attractive force between particles in nucleus (neutrons) 4. Gravitational forces- attractive force between any two objects
GRAVITY Gravity is the weakest universal force On a daily basis, you don t notice the force of gravity that you exert on objects this is because your mass is sooooooo small. It takes a huge mass like the Earth s to exert a large gravitational force.
GRAVITY Gravitational force depends on two things: the mass of an object and the distance between two objects. A greater mass will exert a greater gravitational force on an object. The greater the distance between two masses significantly decreases the gravitational force.
Attractive Force of Gravity
GRAVITY how can it be so weak? Even though gravity is the weakest universal force, it is the most effective over large distances. Gravity holds you on the ground It holds the moon in orbit around the Earth It holds the planets in orbit around the Sun It holds the stars in orbit around their galaxies
Centripetal Force The force of gravity from the Earth continuously pulls the moon in a nearly circular orbit around the Earth. Centripetal force: center-directed force that continuously changes the direction of an object to make it move in a circle. As an object moves in a continuous (constant) circular motion, it is accelerating. How is it accelerating if it does not change speed? Change in direction!!!
Centripetal Force It s a lot like a string tied to an eraser The force from the center of the string allows the eraser to twirl in a circle over your head As you twirl the eraser, the string exerts a centripetal force on the eraser.
Centripetal force & Orbital Motion Objects need only a centripetal force and their own inertia to maintain an orbit. Orbital motion is a balance between the centripetal force and inertia. If Centripetal force is stronger it will crash, if inertia is stronger it will fly off into space
Examples of objects in orbit: Satellites Our moon is a natural satellite of our planet
Orbital Motion http://upload.wikimedia.org/wikipedia/commons/4/4e/orbital_motion.gif
How is this possible?!?! Same Place Same Day??? HOW!!!???
How is that possible? Ever been to the seashore? What do you notice about the level of the water throughout the day? Why does it change? The gravitational pull from the Moon produces two tides in the Earth s oceans as it moves around the Earth. One bulge where the moon is closest to the Earth One bulge where the moon is farthest from the Earth
Tides Since the Earth rotates once per day, it results in two high tides and two low tides per day on Earth! http://home.hiwaay.net/~krcool/astro/moon/moontides/
Newton s cannon
Rotation versus Revolution The Earth moves in two major ways: Rotation- the spinning of the Earth on its axis This rotation causes day and night Revolution- the movement of one body in space around another When does the Earth show revolution? Revolves around the Sun How long does it take for the Earth to revolve? 365 Days