Forces and Newton’s Laws

Remnants of supernova 1987A, a cosmic display of forces

• For millennia, thinkers around the world sought to incorporate the idea of forces into a complete physical description of motion:

Historical Perspectives

• Circa 350 BCE: Aristotle proposes that the “natural” state of an object is stationary

• 1553: Galileo Galilei says that an objects retain their velocity unless acted upon by a force

• 1679: Isaac Newton incorporates Galileo’s ideas into his Laws of Motion

Falling Apples or Pure Genius?

• Isaac Newton was probably one of the 3 smartest individuals in human history (at least mathematically)

• When he encountered a problem he couldn’t solve with current mathematical techniques, he’d invent new branches of math

Unification, Part 1

• Newton’s work was very significant, as it represented one of the first attempts to unify natural phenomena

• Falling apples, rocks, and even the motion of planets could all be explained with one simple idea

• In a sense, this demystified nature

Interesting Tid-Bits

• Unfortunately, his social skills weren’t on par with his intellect…

• He was a deeply religious individual• After publishing Principia and Opticks, he spent a large portion of life working on Alchemy

• His autopsy revealed large amounts of mercury in his body, which might explain his eccentricity

Newton’s 1st Law

• An object moving at constant velocity will stay that way unless acted upon by an outside force

• Objects at rest will remain at rest unless acted upon by a force

• In other words, objects are lazy…

Examples?

• Hoop/ring• Penny Drop• Egg/Beaker• F4 Videos

• Why did Aristotle get it backwards?

• It’s likely that he didn’t think to include how friction and air resistance affect motion

• We’ve seen the clarity of Newton’s 1st Law in the absence of air resistance

How Lazy Are Objects?

• An objects resistance to a change in motion is called inertia

• We can also describe an object’s inertia as its laziness

• Mass is actually a measure of an object’s inertia

Rank the inertia of the following in increasing order: a car, bug,

you, and NCSSM• 1. NCSSM, car, you, bug• 2. car, NCSSM, you, bug• 3. bug, car, you, NCSSM• 4. you, NCSSM, bug, car• 5. bug, you, car, NCSSM

Imagine sitting in a car at rest. If you throw a tennis ball in the air, it will land back in your hand. What will happen if you throw it up, then

accelerate? • 1. It will land in front of you

• 2. It will land back in your hand

• 3. It will hit you in the face

Which car accident would cause a person to get thrown through

their windshield? • 1. A car moving at high speeds hits something in front of it

• 2. A car at rest is rear ended by a fast moving car

• 3. A car moving at high speeds is hit by a car behind going a few miles/hour faster

• 4. A car loses control and spins out

If the sun were to disappear, what would happen to Earth?

• 1. It would continue moving in its normal orbit

• 2. It would move off in a straight line

• 3. It would spiral in towards the sun’s previous location

• 4. It would stop

Reference Frames Are Key

• Your reference frame is essentially your point of view

• A reference frame is inertial if it does not accelerates

Which reference frame is not inertial

• 1. A car moving at constant velocity• 2. A rock, sitting at the edge of a cliff

• 3. A car rounding a curve at constant speed

• 4. A rock rolling down a hill at constant velocity

Why is this so Important?

• Imagine a baby, born on a bus with the windows blacked out

• The baby spends its first few years on the bus, learning about the world with no knowledge of life outside the bus

• How would their ideas of motion contrast with ours?

Types of Forces• Gravity• Tension• Friction• The “Normal” Force• Electrical and Magnetic Forces• Nuclear Forces

“Net” Forces

• What happens if more than one force acts upon an object?

• Forces are vector quantities, so they add like any other vectors

• The Net force is simply the vector sum of all forces acting upon an object

• An object with a net force of 0 is said to be in equilibrium

Which object is in equilibrium?

• 1. A car accelerates from rest• 2. A sky diver falls at constant velocity

• 3. An object is pulled upon by +200N and -300N forces

• 4. An air puck slides across the air table with the air supply turned off

Newton’s 2nd Law

• The Net Force Acting upon an object is proportional to the resulting acceleration

• Net Force = mass x acceleration• Fnet = ma

Mathematical Notation

• Fnet = F• a = F/m• (Bold indicates a vector quantity)• This law holds for each direction (x,y,z)

Units?

• kg m/s2

• We call these units Newton’s, in honor of the man himself

A 10N forces pulls a 4kg box to the left, while a 8N force pulls it to the

right. What is the box’s acceleration?

Free-Body Diagrams

• With all the forces around us, computing net force can get complicated

• We use the concept of free-body diagrams to deal with this complexity

• A Free Body Diagram, or Force Diagram, is simply a picture of object that displays all the forces acting upon it

Rules of Force Diagrams

• Forces vectors are drawn from the application point of a force

• Most of our diagrams will involve point masses (draw your vectors pointing away from the COM)

• The length of a force vector indicates the magnitude of the force

Rules, Part 2

• Include forces acting on an object• Do not include forces produced by an object

• Ex: Two skaters initially at rest push off of one another. In the diagram for skater 1, you would only include the force from skater 2

The Jumbo Jet Revisited

• Fully loaded, a 747 jumbo jet has a mass of 300,000kg. Assuming it needs 1900m of runway to reach a takeoff speed of 100m/s, how much force does each of 4 engines provide?

• Each engines provides 197kN of force (thrust), for a total of 788kN

• Now, let’s think about the impact of air resistance

• Imagine that at takeoff (v = 100m/s), the plane encounters 450,000N of air resistance

• How long will it take the plane to reach its cruising speed of 250m/s?

• 133 seconds

A Falling Body (without Air Resistance)

A Hanging Mass

• A rock hangs freely, held up by two ropes

Which is the correct force diagram for a mass hanging from

the ceiling by a rope?

Which is the correct diagram for a block pushed along a rough surface at

constant velocity?

Same situation as before, but now the object accelerates to the right

Weighing In

• What causes weight?• How can weight change while mass remains constant?

• It turns out that weight is simply a measure of the gravitational force acting upon an object

• Weight = mg

Force Diagram Implications

• From now on, indicate an object’s weight with mg on your force diagram

Falling Bodies Revisited

• A hammer and a feather both accelerate at little g

• Does that mean they experience the same gravitational force?

• Definitely not; Earth has to pull harder on the hammer to create the same acceleration

Lift

• The force that keeps a plane in the air is called lift. Imagine a plane, flying perfectly level at constant velocity. What is the magnitude of the lift necessary to keep a 300,000kg Boeing 747 in the air?

• Lift = 3,000,000 N (up)

Back to the F4…

• Useful information• Force of wall on the plane = 13.3 MN• Force of thrust on the plane = .30 MN• Plane mass = 27,000 kg

• Find the plane’s acceleration while in contact with the wall (express your answer in “g”s)

Yoda’s Force?

• Yoda has an uncanny ability to make things happen, despite his size

• I seem to recall a scene in Star Wars where he accelerates a very massive object (m = 30,000kg) straight up at a rate of 5.0 m/s/s

In a Galaxy Far, Far Away…

• Now, Star Wars does not occur on Earth, which means g is not necessarily 10 m/s/s

• Let’s say Yoda is on a planet where g = 15 m/s/s (although is sure looks like g = 10m/s/s when you watch Star Wars…)

• What force is necessary for Yoda to accelerate this massive object (30,000 kg) upward at 5.0m/s/s?

• Just for comparison, how does this force compare to Yoda’s body weight (m = 15 kg)?

The Rising Box…

• Imagine a person with mass 65kg, standing on a box

• If the box accelerates upwards at a rate of 3 m/s/s, what is the normal force of the box acting upon the person?

• What would it feel like if you were standing on the box?

• What would a scale read?

Apparent Weight

• Think of a situation in which you feel heavier or lighter than normal

• Why do you feel this way?• In such a situation, your apparent weight is more or less than your actual weight

• Why?

Feeling Weight

• The sensation of weight comes from normal forces acting upon us

• Don’t believe me? Try standing in an elevator in free fall

• At the bottom of a roller coaster loop, the rider’s (mass 80kg) seat pushes him up with a force of 900N. What is the magnitude of the rider’s acceleration?

• a = 1.45 m/s/s (points up)

Newton’s 3rd Law

• This is likely the most familiar law• For every action, there exists an equal and opposite reaction

• In other words, nature always fights back

• Forces always come in pairs

Examples

• Rockets• Two Ice Skaters Push One Another• Rifle Recoil

• 1) In a horse drawn carriage, the horse pulls the cart forward. According to Newton’s 3rd Law, the car pulls back with an equal force. If that’s the case, how does the horse or cart move?

• 2) A mack truck and bicycle collide. Which experiences the greater force?

• 3) What happens if you use a fire extinguisher in space?

• 4) What force actually moves a car forward?

Forces in Space

• An astronaut (m = 120kg with gear) working on the ISS needs to push a massive object (m = 1500kg) forward

• If he pushes on it with 500N of force, what happens

• How can he safely push it forward?

3 Block Problem• Imagine three blocks of different masses on a table

• Find the force of block one on block two• Find the force of block two on block one• Find the force of block two on block three

• Examine the Atwood’s machine below, with m1 = 10kg and m2 = 30kg. If m2 rests upon a block, what is the normal force acting upon it?

• Normal Force = 196N (up)

• Let’s return to the block/pulley situation. If block one lies on a frictionless surface, what is its acceleration? (m1 = 5kg, m2 = 10kg)

• a = 6.5m/s/s (to the right)

• On the diagram below, two blocks are connected by a rope. Block 1 has a mass of 5kg, while block 2 has a mass of 10kg. If block 1 is at rest, sitting on a rough surface, what is the magnitude of the frictional force acting upon block one?

• Friction = 98N, pointing to the left

• A person’s weight is 600N, when standing on a normal bathroom scale. What would the scale read if this person were in the Bryan elevator, arriving at the 4th floor (a = 0.8m/s/s)?

• Normal Force/Apparent Weight = 552N(up)

Tension: The Force That Binds Us

• Tension is a very important force• The magnitude of the tension force in the same rope is always equal

• Why?• Newton’s 3rd…

Pulley Problems

Variations

• We can ask a variety of questions about the previous situation

• If the blocks are stationary or move at constant velocity, what is the frictional force?

• By how much do they accelerate? • How much tension exists in the rope?

Tension in 2D

• Think about the situation below

• Draw force diagrams for the block• Write net force equations• Find the tension in rope 1• Find the tension in rope 2

• T1 = 173N

• T2 = 87N

2D Tension, Part 2

• Now imagine a different block, suspended from the ceiling by two ropes

• Find the mass of the hanging object

• m = 3.5kg

• Imagine a different box, suspended by two different ropes

• Find the magnitude of the tension in the second rope, and the angle the rope makes w/ the horizontal

• Theta = 21.5 degrees• T2 = 14.7N