Conceptual Physics Chapter 9

You weigh more at the Northpole than you do at the equator. g (NP) 9.8322 m/s₂ g(E) 9.7804 m/s₂

...

1. What exactly is a projectile?

1. A projectile is any object that is projected by some means and continues in motion by its own inertia.

Types of Forces

1. Gravitational Force (weakest of all) 2. Electromagnetic Force 3. Nucleus (weak force and strong force)

1. What did Newton discover about gravity?

1. Newton discovered that gravity is universal.

Prior to Newton, people thought there were two sets of law.

1. Stuff on earth 2. events in heaven (comic)

10. Where do you weigh more: at the bottom of Death Valley or atop one of the peaks of the Sierra Nevada? Why?

10. You're closer to Earth's center at Death Valley, below sea level, so you weigh more there than on any mountain peak.

2. What is the Newtonian synthesis?

2. The Newtonian synthesis is the union between terrestrial laws and cosmic laws.

2. Why does the vertical component of velocity for a projectile change with time, whereas the horizontal component of velocity doesn't change?

2. The vertical component moves with or against gravity, while the horizontal component moves with no horizontal force acting

3. In what sense does the Moon "fall"?

3. The Moon falls away from the straight line it would follow if there were no gravitational force acting on it.

3. A stone is thrown upward at an angle. What happens to the horizontal component of its velocity as it rises? As it falls.

3. With no air resistance the horizontal component of velocity remains constant, both in rising and falling.

33. Calculate the force of earth's gravity on a 1kg mass at earths surface. the mass of earth is 6.0 x 10²⁴kg and its radius is 6.4 x 10⁶m. Does the result surprise you?

33. F = G m₁1m₂/d ² = 6.67x 10 −¹¹ N x m² /kg² x (1kg )(6 x 10²⁴ kg )/(6.4 x 10⁶m)² = 9.8 N .

34. Calculate the force of gravity on the same 1kg mass if it were 6.4 x 10⁶m above earth's surface (that is, if it were two earth radii from earths center.)

34. F = G m₁1m₂/d ² = 6.67x 10 −¹¹ N x m² /kg² x (1kg )(6 x 10²⁴ kg )/[2(6.4 x 10⁶m)]² = 2.5N

35. Calculate the force of gravity that earth (mass 6.0 x 10²⁴kg) and the moon (mass 7.4 x 10²²kg) exert on each other. The average earth-moon distance is 3.8 x 10⁸m.

35. F = G m₁1m₂2/d ² = 6.67x 10 −¹¹ N x m² /kg² x (6 x 10²⁴ kg)(7.4 x 10²² kg)/(3.8 x 10⁶m)² = 2.1 x 10²⁰ N

36. Calculate the force of gravity that earth and the sun exert on each other (sun's mass is 2.0 x 10³⁰kg average earth-sun distance is 1.5 x 10¹¹m).

36. F = G m₁1m₂2/d ² = 6.67x 10 −¹¹ N x m² /kg² x (6 x 10²⁴ kg )(2.0 x 10³⁰kg)/(1.5 x 10¹¹m)² = 3.6 x 10²²N

38. Calculate the force of gravity a newborn baby of mass 3.0kg and the obstetrician of mass 100.0kg exerts on each other when the distance between them is 0.5m. Which exerts more gravitational force on the baby: Mars or obstetrician? By how much?

38. F = G m₁1m₂2/d ² = 6.67x 10 −¹¹ N x m² /kg² x (3.0kg )(100kg )/(0.5m)² = 8.0 x 10−⁸N The obstetrician exerts about twice as much gravitational force.

37. Calculate the force of gravity a newborn baby (mass 3.0kg) and the planet mars (mass 6.4 x 10²³kg) exerts on each other when mars is at its closest to earth (distance 5.6 x 10¹⁰m).

38. F = G m₁1m₂2/d ² = 6.67x 10 −¹¹ N x m² /kg² x (3.0kg )(6 x 10²³ kg )/(5.6 x 10¹⁰m)² = 4.1 x 10−⁸N

4. State Newton's law of universal gravitation in words. Then do the same with one equation.

4. Every body in the universe attracts every other body with a force that, for two bodies, is directly proportional to the product of their masses and inversely proportional to the square of the distance between their centers: F - G m₁m₂/d ²

4. A stone is thrown upward at an angle. What happens to the vertical component of its velocity as it rises? As it falls?

4. Neglecting air resistance, the vertical component of velocity decreases as the stone rises, and increases as it descends, the same as with any freely-falling object.

5. A projectile falls beneath the straight line path it would follow if there were no gravity. How many meters does it fall below this line if it has been traveling 1s? 2s

5. In 1 second it falls 5 m beneath the line; For 2 seconds, 20 m beneath.

5. What is the magnitude of the gravitational force between two 1kg bodies that are 1m apart?

5. The gravitational force between is 6 x 10−¹¹N.

6. Do your answers to the proceeding question depend on the angle at which the projectile is launched?

6. No, the falling distance beneath the line makes no difference whether or not the line is at an angle.

6. What is the magnitude of Earth's gravitational force on a 1kg body at earth's surface.

6. The gravitational force is about 10 N, or more accurately, 9.8 N

7. When G was first measured by Henry Cavendish, newspapers of the time hailed his experiment as "weighing earth experiment". Why

7. Actually the mass of Earth could then be calculated, but calling it "weighing of Earth" seemed more dramatic.

7. A projectile is launched upward at an angle of 70⁰ from the horizontal and strikes the ground a certain distance down range. For what other angle of launch at the same speed would this projectile land just as far away?

7. An angle of 15° would produce the same range, in accord with Figure 4.19.

8. How does the force of gravity between two bodies change when the distance between them is double?

8. The force of gravity is one-fourth as much.

8. A projectile is launched vertically at 100m/s. If air resistance can be ignored, at what speed will it return to its initial level?

8. The projectile would return at the same speed of 100 m/s, as indicated in Figure 4.22.

9. How does the thickness of paint sprayed on a surface change when the sprayer is held twice as far away?

9. Thickness is one-fourth as much.

Inverse Square Law

A law that relates the intensity of an effect to the inverse square of the distance from the cause. Gravity follows an inverse square law, as do the effects of electric, magnetic, light, sound, and radiation phenomena.

Projectile Motion

Any object that moves through the air or through space under the influence of gravity.

Weightless

Being without a support force, as in free fall.

Law of Universal Gravity

Every body in the universe attracts every other body with a force that, for two bodies, is directly proportional to the product of their masses and inversely proportional to the square of the distance between their centers. F=G x m¹m²/d²

Law of Universal Gravitation

Force of attraction Force ∼ mass₁ x mass₂/distance²

The Universal Gravitational constant is:

G=6.67 c 10−¹¹ N.m²/kg² Very small number

Equator is farthest from the center of the earth.

North and South are closer to center of the earth

Weight

The force that an object exerts on a supporting surface (or, if suspended, on a supporting rope), which is often, but not always, due to the force of gravity.

Newton said that gravity was the force which caused things to fall on earth as that force which pull on the moon and planets.

Without gravitational force, the moon would continue in a straight line.

Acceleration constant is:

g=10m/s²

X axis velocity is always constant (the same) all the way down and the y axis will always change.

y axis velocity will increase as it falls down If both the x axis and the y axis have the same mass, the y axis will be identical to the x axis.