Chapter 8 Newtonian Mechanics
Newtonian Mechanics…Net Force (a vector) acts on a mass and causes acceleration (a vector).
page 8-2 Force
Is it true that force can be described as a push, or a pull?
Does the net force determine the velocity of an object?
What is force directly related to?
Inspect the four kinetic equations you received on a handout. Describe your observation as to what affects the final velocity (V) of an object.
An object is moving in projectile motion. When air resistance is ignored what is the direction of the acceleration compared to the direction of the gravitational force?
When the rubber stopper moves in uniform circular motion what is the direction of the acceleration compared to the direction of the force the string applies to the rubber stopper?
*What general observation could you make regarding the direction of the acceleration of an object and the direction of the net force on the object?
page 8-3 The Role of Mass
Examine Equation 1 of the four kinematic equations. Consider two objects in motion. If the initial velocities are the same and the length of time is the same for both motions, what might cause a different final velocity for the two objects?
Let the initial velocity be zero for both objects. Compare the accelerations of the two objects if one object has twice the value of the final velocity of the other object.
Do the preceding two paragraphs remind you of something you observed in an earlier class meeting?
page 8-4 Newton’s Second Law
When the mass and the acceleration are known we can calculate the net force
Fnet = ma This equation serves to define force.
If Fnet and m are known can you calculate the acceleration?
*The Newton represents what collection of units?
The dyne represents what collection of units?
Does the pound measure force or mass?
Describe an easy way to calculate the gravitational force on an object near the surface of the earth.
If Fnet = 0, describe V.
page 8-5 Newton’s Law of Gravity magnitude: Fgravity = GM1M2/ r2
G = 6.67 x 10-11 m3/(kg sec2) or N m2/kg 2
Decide if the following statements are TRUE or FALSE.
*1. Every mass in the universe attracts every other mass in the universe.
2. The force of gravity between two objects is proportional to the square of the distance between the two objects.
3. If the earth attracts a person with a force of 700 Newtons, then the same person attracts the earth with a force of 700 Newtons.
4. The r symbol in the formula for the force of gravity represents the distance between "point" objects or the distance between the centers of spherical objects.
5. Gravity acts without contact between the objects.
6. In some situations the force of gravity can repel one object from another object.
Calculate the gravitational force the earth applies to you without using "g."
ME = 5.98 x 1024 kg RE = 6.38 x 106 m
Calculate the gravitational attraction between a 3 kg sphere and a 4 kg sphere. Both spheres have a radius of 12 cm. The edge of one sphere is 60 cm away from the edge of the other sphere.
page 8-6 Galileo’s Observation
Does "g" depend on the mass of the object that is falling? g = G ME / r2
page 8-7 The Cavendish Experiment
*True or False Newton knew the value for G .
How might the value of G be determined?
Decide if the following statements are TRUE or FALSE.
7. The mass of the earth can be determined by measuring g , G (the universal gravitational constant) and the radius of the earth.
8. The value of g is a constant everywhere in the United States.
9. The value of g for someone who is walking on Mars is less than 9.8 m/s2.
g is also known as the gravitational field strength .
page 8-8 What questions do you have about inertial and gravitational mass?
page 8-8b Satellite Motion
Did Newton believe that gravity was a short range or long range force?
How did the astronomical knowledge of the moon’s distance from the earth and the time for one "revolution" of the moon around the earth help Newton develop the Law of Gravitation?
Which is stronger, the gravitational force of the earth on the moon or the gravitational force of the sun on the moon?
page 8-10 Other Satellites
In your own words, explain how it is possible that a satellite can continually fall towards the earth but never hit the earth.
page 8-11 Weight
Decide if the following statements are TRUE or FALSE
10. Satellites are always falling toward the earth as they orbit the earth.
11. Orbiting satellites have a rocket that continuously fires to prevent the satellite from crashing into the earth.
*What supplies the centripetal force on a satellite that is in uniform circular motion around the earth?
Calculate g for the satellite specified in exercise 4. Now calculate V for this satellite.
Refer to Figure 14: Suppose that the mass and the bathroom scales were in circular motion around the earth. What is the magnitude of the force the scales apply to the mass?
page 8-12 What is wrong with making the following statement: The weight of this object is 1.2 kg.
page 8-12 Tides
Earlier you calculated the magnitude of the gravitational force on you due to the earth. Now calculate the magnitude of the gravitational force on the earth due to your mass.
If you fall toward the earth does the earth fall up towards you?
page 8-13 The tides are more complex than the explanation given in the book. There is a great effect due to the shape of the ocean bottom and the shoreline.
*True or False There are roughly two high tides each day for any given ocean beach on the earth.
*True or False The moon’s orbit is centered on the center of the earth.
page 8-14 Planetary Units Skip
page 8-16 Computer Prediction of Satellite Orbits PHY161 class only
Suppose NASA wants to put a satellite into a "geosynchronous" orbit around Mars. What value should be used for the radius of the orbit? Mars mass is 6.4 x 1023 kg. The radius of Mars is 3.32 x 106 m. A "day" on Mars is approximately 24 hours 37 minutes.
page 8-24 Kepler’s Laws
True or False Physics has not been advanced much by data from astronomical observations.
page 8-26 What new idea did Kepler try regarding the shape of planet orbits?
Kepler’s First Law The planets move in ellipses with the sun at one focus of the ellipse.
Kepler’s Second Law The line from the sun to a planet sweeps out equal areas in equal time intervals.
Kepler’s Third Law The cube of the semimajor axis is proportional to the square of the period of the planet orbit.
Which of Kepler’s Laws is an illustration of the law of Conservation of Angular Momentum?
page 8-29 Modified Gravity and General Relativity I will give one bonus point to the first person to send me email with the correction to an error on this page.
paragraph 4 How could someone send a signal faster than the speed of light if gravity responds instantly to the separation distance of the masses?
Why would you experience the same net force if you were in the elevators shown in Figure 32?
page 8-30 Principle of Equivalence You cannot perform an experiment that distinguishes between gravitational effects and acceleration with a value equal to the local value of "g."
Figure 33 is important. Closed, stable, orbits only occur if gravity depends on the inverse square of the distance between the centers of the two objects.
page 8-31 paragraph 3 The change in the gravitational force law is that General Relativity shows that spacetime is warped by mass and/or energy. Newton’s Law of Gravity is an approximation. It is not correct in all circumstances. It is nearly correct and useful for many calculations but it is not exact.
page 8-32 Conservation of Angular Momentum … Skip … we covered this earlier
page 8-35 Conservation of Energy … Read, but we will discuss this in Chapter 10
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