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Unit 1 Class 1 PHY120 Buettner ECPI
Transcript of Unit 1 Class 1 PHY120 Buettner ECPI
Chapter 2: Newton's First Law
Chapter 3: Linear Motion
Chapter 4: Newton's 2nd Law
Newton's 1st Law of Motion--Inertia
Aristotle v. Galileo
Aristotle was a Greek philosopher who wrote a work on physics which held sway in universities during Galileo's time (around 1600).
Galileo challenged Aristotle's laws of motion.
Galileo's discovered what Newton would call the first law of motion.
The First Law of Motion: Seat belts and airbags. Protecting you from your own inertia.
Mass and Inertia
Inertia is what we call the property of matter that resists changing its state of motion.
Inertia is mass, a fundamental property of matter.
A cubic centimeter of water has a mass of 1 gram.
standard metric unit of mass
Eureka! short animations are good explanations of physics principles in a light format. Watch them for review or if you miss class.
Get Familiar with Metrics
1 liter of water has a mass of 1 kilogram.
1 paperclip has a mass of about 1 gram.
Short video explanations by the author of the textbook.
A force is a push or pull.
The Net Force acting on an object is the vector sum of all the forces acting on it.
Then two forces pull in opposite directions on a rope or chain, the tension is the amount of force pulling in each direction.
If a tug of war team pulls on a rope with a force of 1200 lb and at the other end of the rope another team pulls with 1200 lb, the tension in the rope is said to be 1200lb.
Watch this video for an explanation of adding force vectors.
An object is in equilibrium when the net force on the object is zero.
But this is also the condition for Newton's First Law.
So if an object is at rest and remaining at rest, it must be in equilibrium (net force = zero)
If an object is moving in a straight line at constant speed, it must be in equilibrium (net force = 0).
Speed is calculated.
Speed is a scalar.
Pearson Video: Definition of Velocity
Velocity is speed plus a direction.
Velocity is a vector.
Velocity and Speed Units
Units: (distance unit)/(time unit)
Examples: miles/hour, inches/minute.
1 m/s = 2.25 mi/hr = 3.6 km/hr
22 m/s = 50 mi/hr = 80 km/hr
What is the average speed of a cheetah that sprints 100 meters in 4 seconds?
Standard Problem Solving Steps
Write what you are to calculate as a variable “= ?”
Write down variables set equal to given values.
Write the equation that applies.
Substitute values into equation, including units
Calculate answer, including units.
Speed, v = ?
d = 100 m
t = 4 s
v = 25 m/s
Pearson: Changing Velocity
If either the speed of an object or its direction of motion changes (or both) the object is accelerating.
Change in Velocity
To measure the change in velocity take the final velocity and subtract the initial velocity.
In formula form this looks like this:
v - v
where v stands for final velocity and v stands for initial velocity.
v - v
______ = m = m
s s s s
read "meters per second per second" or "meters per second squared"
A bicyclist is going 10 m/s and then increases her speed to 16 m/s in 2 seconds. What is her acceleration?
(She is going in a straight line.)
a = ?
v = 10 m/s how fast she is going initially
v = 16 m/s her final velocity
t = 2 s the time it takes her to do this
v - v
a = 16 m/s - 10 m/s
a = (6 m/s) = 3 m/s
answer and units
Equations of Motion
These basic definitions can be combined to giver various equations of motion. See Section 2.4.
These are summarized at the bottom of p. 45
Eureka Animated Lessons
Eureka! Acceleration 1
Eureka! Acceleration 2
Worksheet 20 a
Force Causes Acceleration
When the net force on an object is NOT zero, the object accelerates.
The acceleration is
to the force.
This means if you double the force, you will double the acceleration.
If you apply a force to 1 kilogram of mass and it accelerates at 1 meter per second squared,
then if you apply the same force to 2 kilograms of mass and the object will accelerate only half as much.
Worksheet 20 b
Mass resists acceleration
How to Answer this Sort of Question
You will see many questions in Mastering Physics that describe a situation and then ask how a particular quantity will change if a different quantity is changed in a certain way.
The following is a simple way to answer each question of this sort.
Consider a cart pushed along a track with a certain force. If the force remains the same while the mass of the cart decreases to half, the acceleration of the cart ...
Start with the equation for the quantity whose change is to be determined, in this case acceleration.
Write the (New value)=(Old Value)(Equation)
Example 1 continued
The formula for acceleration is : a =
So write (new a) = (old a)
In the equation, if a quantity does not change, replace it with 1. If it does change, replace it with the number representing the change.
So write (new a) = (old a)
Example 1 continued
Evaluate the expression and you have your anwer.
1 divided by 0.5 = 2, so (new a) = (0ld a) x 2.
Or you might say the acceleration doubles.
Where possible use your imagination to see if the answer makes sense. Imagine pushing a cart with a load of bricks on it when half the bricks fall off the side of the cart. Would the cart's acceleration increase or decrease?
A measure of the inertia of a material object
Independent of gravity
Greater inertia => greater mass
Unit of measurement is the kilogram (kg)
Mass and Weight
Weight is the force of gravity on an object.
Mass is the quantity of matter making up an object and a measure of inertia.
Don't confuse them.
Metric Force: The Newton
One Newton is the force needed to cause a 1 kilogram object to accelerate at 1 meter/second ^2.
One kilogram weighs about 10 N because gravity accelerates objects at 10 m/s^2
It is not correct to say 1 kg = 2.2 lb, because 1 kg represents mass while pounds (lb) represent weight or the force of gravity.
The correct physics way to relate this idea is to say , "1 kg of mass weighs 2.2 lb near the surface of the earth."
Still Confused about the Difference?
Watch this video and think about the question, what makes a car hard to push? The weight or the mass of the car?
Weight vs Mass
A car is hard to lift because gravity pulls down on it with a lot of force. It's hard to overcome that force to lift the car.
But while one person could not lift a car, a person can push a car and make it slowly accelerate. The car is slow to accelerate because it has a lot of mass.
The Acceleration of Gravity
All objects in free fall accelerate at the same rate: about
10 m/seconds squared
In equations, this is represented by "
If a hammer has 10 times the mass of a feather, the force of gravity is 10 times greater on the hammer than on the feather.
But the hammer is also 10 times harder to accelerate because of the greater mass. So the acceleration doesn't change.
Most people interviewed in the next video expected a heavy medicine ball and a lighter basketball dropped at the same time from the same height would hit at the same time.
But none of them could explain why.
Some said the pull of gravity was the same. Some said they fell at the same constant speed.
What would you say if asked these questions?
The formula for calculating weight:
weight = (mass) (gravity)
Wt = m g
On earth, g = 9.80 m/s^2
On the moon, g = 1.62 m/s^2
The difference is gravity.
Example: Calculating Weight
What is the weight of an astronaut on the earth if the mass of he and his space suit is 120 kg?
Wt = m g = (120 kg)(9.80 m/s^2)
Wt on earth = 1180 N
Units: 1 kg m/s^2 = 1 N
Example: Calculating Weight
What is the weight of an astronaut on the moon if the mass of he and his space suit is 120 kg?
Wt = m g = (120 kg)(1.62 m/s^2)
Wt on moon = 195 N
Newtons, Pounds, and Kg
4.45 N = 1.00 lb
1180 N = 265 lb (weight on earth)
195 N = 43.8 lb (weight on moon)
In Europe, the kilogram is used as a unit of weight. In this case 1 kilogram weighs 2.2 lb.
Note: air friction on a falling object is the same as wind blowing on an object. The faster the wind blows, the greater the force of the wind. Likewise, the faster a person falls, the greater the air friction.
Scientific method: Principles and procedures for the systematic pursuit of knowledge involving the recognition and formulation of a problem, the collection of data through observation and experiment, and the formulation and testing of hypotheses.
An educated guess; a reasonable explanation of an observation or experimental result that is not fully accepted as factual until tested over and over again by experiment.
A statement about the world that competent observers who have made a series of observations agree on.
A general hypothesis or statement about the relationship of natural quantities that has been tested over and over again and has not been contradicted. Also known as a principle.
A synthesis of a large body of information that encompasses well-tested and verified hypotheses about certain aspects of the natural world.
Note: To dismiss a scientific theory by saying it is "just a theory,' implying it might be wrong, displays a misunderstanding of the meaning of the word
To suggest that schools teach alternative theories also displays ignorance of the fact that in science there can only be one established theory. Alternative hypotheses have been considered and dismissed as being incapable of experimental confirmation.
The property of things to resist changes in motion.
Newton’s first law of motion
(the law of inertia)
Every object continues in a state of rest or of uniform speed in a straight line unless acted on by a nonzero net force.
In the simplest sense, a push or a pull.
The vector sum of forces that act on an object.
An arrow drawn to scale used to represent a vector quantity.
A quantity that has both magnitude and direction, such as force.
A quantity that has magnitude but not direction, such as mass and volume.
The state of an object or system of objects for which there are no changes in motion. In accord with Newton’s first law, if an object is at rest, the state of rest persists. If an object is moving, its motion continues without change.
For any object or system of objects in equilibrium, the sum of the forces acting equals zero. In equation form, ∑F = 0.
Static Equilibrium: when an object is at rest and remains at rest.
Dynamic Equilibrium: when an object moves with constant speed in a straight line.
What is the net force on a cart that is pulled to the right with 100 pounds of force and to the left with 30 pounds of force?
Net force = +100 lb + (-30 lb)
= (100lb - 30 lb)
= 70 lb
What is the net force on an object that is pulled with forces of 80 newtons to the right and 80 newtons to the left?
Resultant = +70 lb
Net Force = +80 N + (-80 N)
= 80 N - 80 N = 0 N
Resultant is a vector with zero length.
Consider a book that weighs 15 N at rest on a flat table. How many newtons of support force does the table provide?
What is the net force on the book in this case?
Since the book is at rest, the support force must equal the weight of the book.
The net force is zero, as it must be for all objects at rest remaining at rest.
A bowling ball at rest is in equilibrium. Is the ball in equilibrium when it moves at constant speed in a straight-line path?
Yes. For an object to move at a constant speed in a straight line, it must have a net force of zero (Newton's First Law), and objects with a zero net force are in equilibrium. The first is called a static equilibrium; the second is called a dynamic equilibrium.
If you push on a crate with a force of 100 N and it slides at constant velocity, how great is the friction acting on the crate?
To move at a constant velocity the crate must be in equilibrium (Net Force = 0)
In order for the net force to be zero, the friction force must be 100 N (friction always acts in the opposite direction as the motion).
The sketch shows a painter’s scaffold in mechanical equilibrium. The person in the middle weighs 500 N, and the tensions in each rope are 400 N. What is the weight of the scaffold?
See diagram below.
The net force must be zero. The ropes pull up with a combined force of 800 N while the man's weight pulls down 500 N. So the board must weigh the difference between 800 N and 500 N. It must weigh 300 N.
For the pulley system shown, what is the upper limit of weight the strong man can lift?
No matter how strong the man is, he cannot lift a weight W greater than his own weight. Remember that the force a rope exerts on each end is the tension of the rope.
Two forces act on a parachutist falling in air: the force of gravity and air resistance. If the fall is steady, with no gain or loss of speed, then the parachutist is in dynamic equilibrium. How do the magnitudes of gravitational force and air resistance compare?
The gravitational force (the parachutist's weight) must be equal to the force of air resistance.
It is the same equilibrium that allows an indoor skydiving school to demonstrate techniques with a stiff wind blowing up.
How far does a horse travel if it gallops at an average speed of 25 km/h for 30 min?
If we start with v = d/t we can show that d = vt.
But be careful. Units for time must be the same.
If you try (25 km/h)(30 min)
you get nonsense: 750 km?
To work, the units of time (hours) in km/hour, must match the time interval. 30 min = 0.5 hr.
So the correct answer is
(25 km/hr)(0.5 hr) = 12.5 km
If a car moves with a constant speed, does it also move with a constant velocity?
Remember that velocity describes both the speed and direction of movement. So another way of asking this would be: Can a car move with a constant speed but with a changing direction?
What is the acceleration of a car moving along a straight road that increases its speed from 0 to 100 km/h in 10 s?
a = (change in velocity)/(time)
= (100 km/h)/ 10s
= 10 (km/h)/s
What exactly is meant by a “freely falling” object?
Things fall because of the force of gravity. When a falling object is free of all restraints—no friction, with the air or otherwise—and falls under the influence of gravity alone, the object is in a state of free fall.
When an object is thrown upward, how much speed does it lose each second (ignoring air resistance)?
The acceleration of gravity provides the answer. All objects in free fall lose 10 m/s each second. Once it turns around and falls back toward the earth, it gains 10 m/s every second it falls.
Consider these measurements: 10 m, 10 m/s, and 10 m/s^2. Which is a measure of speed, which of distance, and which of acceleration?
The units provide the key. Meters (m) measure distance. Speed is a measure of distance per time, so m/s is a speed measurement, while acceleration is change in velocity per time, so (m/s)/s or m/s^2)
Show that the average speed of a rabbit that runs a distance of 30 m in a time of 2 s is 15 m/s.
speed = (distance)/(time)
= (30 m)/(2 s)
= 30/2 m/s
= 15 m/s
What is the acceleration of a car that goes from 20 km/h to 60 km/h in 4 seconds?
a = (change in velocity)/(time)
= (60 km/h - 20 km/h) / 4 s
= (40 km/h)/4 s
= 40/4 (km/h)/s
= 20 km/(hs)
Any push or pull exerted on an object, measured in newtons (or pounds in the British system)
The resistive force that opposes the motion or attempted motion of an object either past another object with which it is in contact or through a fluid.
The quantity of matter in an object. More specifically, it is the measure of the inertia or sluggishness that an object exhibits in response to any effort made to start it, stop it, deflect it, or change in any way its state of motion.
The force upon an object due to gravity, mg. (More generally, the force that an object exerts on a means of support.)
Weight = Mass x acceleration of gravity
g = 10 m/s^2 or 10 N/kg on earth.
The fundamental SI unit of mass. One kilogram (symbol kg) is the mass of 1 liter (1 L) of water at 4°C.
The SI unit of force. One newton (symbol N) is the force that will give an object of mass 1 kg an acceleration of 1 m/s^2.
Newton’s second law
The acceleration of an object is directly proportional to the net force acting on the object, is in the direction of the net force, and is inversely proportional to the mass of the object.
a = (net force)/mass or F = m a
Motion under the influence of gravitational pull only.
The speed at which the acceleration of a falling object terminates because air resistance balances gravitational force.
Terminal speed with direction specified.
Is acceleration proportional to net force, or does acceleration equal net force?
Acceleration and net force are proportional to each other, not equal to each other.
Fill in the blanks: Shake something to and fro and you’re measuring its _______. Lift it against gravity and you’re measuring its _______.
Fill in the blanks: Shake something to and fro and you’re measuring its
. Lift it against gravity and you’re measuring its
In the string-pull illustration in Figure 4.8, a gradual pull of the lower string results in the top string breaking. Does this occur because of the ball’s weight or its mass?
In the string-pull illustration in Figure 4.8, a sharp jerk on the bottom string results in the bottom string breaking. Does this occur because of the ball’s weight or its mass?
Breaking of the top string is due mainly to the ball’s weight. The gradual pull insures that the ball moves a little bit, stretching the top string and making the net force on the top string the weight of the ball plus the tension of the bottom string.
Breaking of the bottom string is due mainly to the balls mass. A sharp jerk accelerates the string faster than the force transmitted through the string can accelerate the ball, due to its high mass. So the force on the bottom string exceeds the breaking point before the ball has been able to move and thereby exert a force on the upper string.
Is acceleration directly proportional to mass, or is it inversely proportional to mass? Give an example.
Acceleration is inversely proportional to mass.
A truck that can accelerate well with an empty bed accelerates more slowly when carrying a full and heavy load.
If we say that one quantity is directly proportional to another quantity, does this mean they are equal to each other?
Explain briefly, using mass and weight as an example.
No. Weight is proportional to mass, but not equal to mass.
If the mass of a sliding block is tripled while a constant net force is applied, by how much does the acceleration change?
The acceleration decreases to one-third.
new = old (change in force/change in mass)
new = old (1/3)
The new acceleration (on the larger mass) is one-third the old acceleration (on the smaller mass)
The ratio circumference/diameter for all circles is π.
What is the ratio force/mass for freely falling bodies?
The ratio of force to mass is g.
On earth, this is around 10 N/kg.
What is the net force that acts on a 10-N freely falling object?
The net force is 10 Newtons.
Note free fall assumes no other forces besides gravity act on the body, so the force of gravity must be the net force as well.
What two principal factors affect the force of air resistance on a falling object?
Speed and frontal area affect the force of the air resistance.
Why does a heavy parachutist fall faster than a lighter parachutist who wears a parachute of the same size?
A heavier parachutist must fall faster for air resistance to balance weight.
Remember that air resistance increases with fall speed. The eventual fall speed is the speed at which the air resistance equals the weight.
Calculate the weight in newtons of a 2000-kg elephant.
Weight = Mass x gravity
= 2000 kg x 10 N/kg
= 20,000 N
Calculate the acceleration of a 2000-kg, single-engine airplane as it begins its takeoff with an engine thrust of 500 N. (The unit N/kg is equivalent to m/s^2.)
a = (Net Force)/(Mass)
= 500 N / 2000 kg
You know 500 N is the force because Newton is a unit of force while kg is a unit of mass.
Consider a 40-kg block of cement that is pulled sideways with a net force of 200 N. Show that its acceleration is 5 m/s^2.
a = (net force) / (mass)
= 200 N / 40 kg
= 200/40 N/kg
= 5.0 m/s^2
Consider a business jet of mass 30,000 kg in takeoff when the thrust for each of its two engines is 30,000 N. Show that its acceleration is 2 m/s^2.
a = (Net Force) / (Mass)
= (30,000 x 2) / 30,000 kg
= 60,000 / 30, 000 N/kg
= 2.0 m/s^2
A rock band’s tour bus, mass M, is accelerating away from a stop sign at rate a when a piece of heavy metal, mass M/5, falls onto the top of the bus and remains there.a. Show that the bus’s acceleration is now 5/6a.b.
First note that the new mass is M + M/5 =
new mass = (6/5)M
So the change in mass of the truck is to increase by a factor of 6/5).
New = Old (Change in force)/(Change in mass)
= Old [ 1 / (6/5) ] = 5 / 6 Old
Reality check, acceleration should decrease as mass increases.
If the initial acceleration of the bus is 1.2 m/s^2, show that when the bus carries the heavy metal with it, the acceleration will be 1.0 m/s2.
New acceleration = (5/6)x old acceleration
New = (5/6)(1.2 m/s^2)
= 1.0 m/s^2