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Motion Chapter 2 Physical Science Spring 2009
Formula Sheet Students may bring a formula sheet to the next chapter test and should use this sheet to work out the assigned problems . • one page on which only formulas are written. • No definitions or examples of worked problems may appear on this sheet. • The instructor will mention in lecture other information that should be placed on the formula sheet such as: g = 9.8 m/s2 • You should start the formula sheet now and write formulas on it as they are covered in class. • Use the formula sheet to solve homework problems in class as well as for the test. • Have you got your sheet out ready to write on?
Definition • Velocity is the distance traveled in a certain time divided by the time it takes to travel that distance Velocity = Distance/time normal units of velocity are meters/second m/s Other ways to write the formula: If you have difficulty with algebra, you will want to put all the variations of a formula on your formula sheet. Definitions on tests and the review sheet must contain both words (you may say things in your own words) as well as mathematical equations.
Definition Acceleration is the change in the velocity divided by the time it takes the velocity to change Acceleration = (final velocity-initial velocity)/time normal units of acceleration are meters/second per second (m/s2) The acceleration measures how fast velocity is changing. Other ways to write the formula
Example Problems • Problems will be an important part of class, review sheet, and tests (~50%). • All problems must show the data and the work (including formulae and units) • See the examples that follow • Do the assigned problems from your chapter review as the material is covered in class. Ask when you have difficulties or do not fully understand anything. • Bring calculators to class and lab
Problems • On all problems, everyone must show the following four steps. • Failure to show all four steps will result in points lost, even if the answer is correct. • The four steps are: • Data • Formula • Work • Answer • The units must be correctly shown at each step
How long does it take a car traveling 30 m/s to travel 5 kilometers? • Data t = ? v = 30 m/s d = 5 km =5000m • Formula • Work
A car starts at rest and 15 sec later is traveling 20 m/s. What is the acceleration? • Data vi=0 t=15s vf=20 m/s a=? • Formula and Work
Force (A quick look for your prelab) • When a force acts on a mass it causes the mass to accelerate. • F=ma • Force=mass x acceleration • Units of mass are kilograms • Units of force are “newtons” (N) • 10 newtons = 10 N
Gravity • The acceleration of gravity is g= 9.8 m/s2 The force of gravity (weight) on a 20 gram object is F=mg = .02 kg x 9.8 m/s2 = 0.196 N Be sure to remember that in the F=ma equation, the mass must be in kilograms, not grams!
Pulleys There are 100 g (0.1 kg) more on one side of the pulley than on the other so the accelerating force will be: F = mg = 0.1 kg x 9.8 m/s2 = 0.98 N Note that the mass must be in kilograms, be sure to change grams to kilograms on your lab! 2.0 kg 2.1 kg
Lab Problem: An object falls 9 m in 5 sec. Find a) average velocity, b) final velocity, c) acceleration. • Data • d = 9m • t = 5 sec • v = ? • Formula • It is important to know that this is the average velocity as the weight is speeding up as it falls.
Final velocity • The average of anything is (vi+vf)/2 = vave • If vi = 0, then vf = 2·vave • Put these two formulas on your formula sheet • Calculation of final velocity vf = 2·vave = 2 x 1.8 m/s = 3.6 m/s
Calculation of acceleration An object initially at rest falls 9 m in 5 sec. vf = 3.6 m/s • Data • vi = 0, vf = 3.6 m/s, t = 5 sec
Definitions • Scalars – physical quantities that can be completely described by one number • Examples are: time, pressure, volume, mass, amount in your bank account, etc. • Vectors – physical quantities that need both a size (magnitude) and a direction to describe them. • Examples are: velocity, acceleration, force
More on acceleration • Can one accelerate without increasing speed? • Give some examples! • Is slowing down acceleration? 2q
Difference between speed and velocity • Speed is a scalar and is completely described by one number • 50 mi/hr • It tells you nothing about the direction which you are traveling. • Velocity is a vector and always contains information about both the speed and the direction. • 50 mi/hr North.
Acceleration of Gravity • If air friction is not a factor, all objects fall with an acceleration of 9.8 m/s2 (symbol g) • Put g = 9.8 m/s2 on your formula sheet • How does horizontal motion affect the rate at which an object falls? • The downward acceleration of an object is not affected by its sidewise velocity. • an object thrown horizontally from the top of a building will strike the ground at the same time as an object dropped from the same height.
Free fall • When the only force acting on a falling object is gravity, we say the object is in free fall. • In most cases air friction is a force that keeps the object from accelerating continually. • When the force on an object is that of gravity we call the force the object’s weight F = ma W = mg • When the force of air friction becomes equal to the force of gravity, the velocity remains constant at the “terminal velocity”
Falling with air friction • In the real world, if we first step off a tall building we fall with an acceleration of 9.8 m/s2 for only a few (perhaps 5) seconds. • Air friction then becomes a factor and begins to slow our acceleration. • When we are going fast enough the air friction is equal our weight and we no longer accelerate, we continue with a constant (terminal) velocity.
Terminal Velocity • Depends on the weight and shape of the object • Sky divers change the air friction and enable themselves to fall slower or faster.
A brick is dropped from a tall building. How fast is it falling after 5 sec? • On a sheet of paper write the data for this problem • Data vi=0 m/s a = 9.8 m/s2 vf = ? t = 5 s On your paper write the formula to be used in solving this problem. vf = vi +at
Circular Motion(Necessary for your prelab) • Centripetal means center-seeking The centripetal force is toward the center of the circle. The force necessary to keep an object moving in a circle is called the centripetal force. m is mass (kg), v is velocity (m/s), R is radius of circle (m). Units of force are newtons. Add to formula sheet
What force is necessary to keep a 1000 kg car traveling 20 m/s in a circle of radius 15 m? • Data F = ? m = 1000 kg v = 20 m/s R = 15 m
A 2000 kg truck going 30 m/s is turning a corner of radius 20 meters. What sideways force must its tires exert on the payment? • Data: m=2000kg, v=30m/s, R=20m, F = ?
How strong (newtons) must a string be to allow a 200 g yo-yo to be swung in a circle of radius 1 m at 20 m/s? • Data F = ? m = 200g = 0.2 kg v = 20 m/s R = 1 m
When gravity and centripetal forces balance • How fast must I swing a glass so that water will not fall out when it is upside down? • The water will not fall out if the centripetal force is equal to or greater than the gravitational force. FC = Fg Fg = W = mg This is the velocity an object must have to complete the circle without falling.
How fast must I swing the beaker in a 0.6 m radius so water does not fall out when it is upside down • Data • V = ? • R = 0.6 m g = 9.8 m/s2 FC = Fg Fg = W = mg mv2/R = mg
How fast must the ball go around a track of 20 cm radius so it stays on the track. • Data • V=? • D = 0.4 m g = 9.8 m/s2 FC = Fg • FC = mv2/R Fg = W = mg mv2/R = mg
Newton’s Laws(First law) • If no forces act on an object, its velocity will continue unchanged • An object at rest will remain at rest • An object in motion will continue to move with a constant velocity (in a straight line) until a force acts on it • This is also known as the Law of inertia (resistance to change in motion)
Newton’s Laws(Second law) • When a force acts on an object it produces an acceleration that is inversely proportional to its mass F = ma This may also be written a=F/m or m=F/a
Units of force • The force necessary to accelerate a mass of one kilogram, one meter per second per second is called a “newton” Symbol is (n) or (N) 1 n = 1 kg m/s2
Mass and Weight • Mass is the quantity of matter (inertia) an object contains, this will always be the same as long as the object remains intact. • Weight is the force of gravity on the object. This would be much different on the Moon, Mars or in space. • W = mg (on the surface of the Earth) • Weight = mass x acceleration of gravity • In this equation, be sure the mass is in kilograms not grams
Newton’s Laws • Forces always exist in pairs that are equal and opposite For every action there is an equal and opposite reaction
Mule problem • Explain why the mule can move the cart, given that the cart pulls just as hard on the mule as the mule pulls on the cart
More on Newton’s Laws • Clearly explain why the mule can move the cart, given that the cart pulls just as hard on the mule as the mule pulls on the cart. • The answer is Newton’s second law • An unbalanced force on any given object will cause that object to accelerate (move). • There is an unbalanced force on the cart, so the cart moves. (There is no backward force ON THE CART to balance the forward pull of the mule.) • There is also an unbalanced force on the mule, the ground is pushing harder on the mule (a reaction to the push of the mule on the ground) forward than the cart is pulling backward so the mule moves forward.
Add points to your test score • Students who have the most success after college have said the technique that they learned that most contributed to that success was how to work in groups. • To give additional incentive to work in groups points will be added to the test scores of all students who work in groups and help each other be more successful.
How the system works • You must email me with the names of the people in your group before 10:00 on the day of our test. • If the average of the group is better than their average on the chapter 1 test, the increase in the group average will be added to the score of each person in the group (up to max of 10 points.) • If the group’s average decreases, there is no penalty. • Groups may have between 2 and 6 people.
Example • On test one Judy’s score was 90, Fred’s was 70 and Jim’s was 38. (Ave = 67) • Judy, Fred and Jim study together. • On the Chapter 2 test Judy’s score is 92, Fred’s 76 and Jim’s 60 (Ave = 76) • 9 points will be added to each person’s score. • Judy’s score becomes 101%, Fred’s 85% and Jim’s 69%!
Newton’s law of universal gravitation • The attraction between any two objects of masses m1 and m2 which are a distance r apart is given by: G is a constant (a number) G = 0.0000000000667 = 6.67 x 10-11 n m2/kg2 Put this number on your formula sheet. m1 m2 r
What is the attraction between a 90 kg man and a 65 kg woman who are 0.5 m apart? • Data F=? m1= 90kg m2= 65kg r = 0.5 m F= 1.56 x 10-6n
Use the law of universal gravitation to calculate the force between two objects that have masses 10 kg and 40 kg that are 3 m apart. • Data F = ? m1= 10kg m2= 40kg r = 3 m F= 2.96 x 10-9 n
Mass of the Earth • Force of gravity on one kilogram = 9.8 n • Distance from mass to center of Earth = 6,378,000 m
Why does a person in the space shuttle feel weightless? • For the same reason as a person in a falling elevator, they are falling toward the center of the Earth. • At the same time the shuttle falls toward the center of the Earth their forward velocity carries them to the side so they never hit.
The gravity equations, when do they apply? • W = mg • Weight = mass x acceleration of gravity • g = 9.8 m/s2 • Gives the weight of an object on the surface of the Earth. • Applies to any object on the Earth
The gravity equations, when do they apply? • Calculates the force between any two objects of masses m1 andm2 that are a distance r apart • Applies to any objects, any place in the universe!
Newton’s laws • An object’s velocity will remain unchanged until a force acts on the object. • When a force acts on the object, it produces an acceleration according to the equation: F=ma • Forces always exist in pairs, for every force there is an equal and opposite force on the interacting objects.
Apply Newton’s laws of motion to the case of a soccer ball that is at rest and is kicked. • Law one says that the ball at rest will remain at rest until a force acts on it. • Law two says that the acceleration of the ball is proportional to the force of the kick and inversely proportional to the mass of the ball. • Law three says that the soccer ball exerts the same force on the foot as the foot exerts on the ball.
Density • Density is the mass per unit volume. • Density = mass/volume • D=m/v
Calculate the density of a wood cylinder of diameter 6 cm, length 10 cm and mass 250 grams. Data: d = 6 cm, (r = 3 cm), L = 10 cm and m = 250 g.