From last time Newton s laws. Review of forces. Question. Force and acceleration. Monkey and hunter. Equal and opposite forces

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Edwin Hall
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From last time Newton s laws 1st law: Law of inertia Every object continues in its state of rest, or uniform motion in a straight line, unless acted upon by a force.

1 From last time Newton s laws 1st law: Law of inertia Every object continues in its state of rest, or uniform motion in a straight line, unless acted upon by a force. 2nd law: F=ma, or a=f/m The acceleration of a body is proportional to sum of all forces acting on body inversely the mass of the body 3rd law: Action and reaction For every action there is an equal an opposite reaction. Review of forces Force results in a change in motion (change in momentum p=mv) during application Equivalently, an acceleration. Example of constant force is gravity Acceleration results from the sum total of all forces (net force) applied (a = F net /m) Zero acceleration -> no net force is being applied. Friday, Feb. 2 Phy107 Spr07 Lect6 1 Friday, Feb. 2 Phy107 Spr07 Lect6 2 Force and acceleration I throw a 5 kg ball up in the air with a force of 10 N. Halfway to the ceiling, the acceleration of the ball is A. 2 m/s 2 B. 0.5 m/s 2 C. 10 m/s 2 D. 2.5 m/s 2 E. 20 m/s 2 I throw the 2 N apple horizontally. After I throw it, what is the acceleration of the apple? A. 10 m/s 2 downward B. 2 m/s 2 horizontally C. 10 m/s 2 horizontally C. Need to know throwing force This is because, after I throw the apple, gravity is the only force. The only acceleration is that due to gravity. Friday, Feb. 2 Phy107 Spr07 Lect6 3 Friday, Feb. 2 Phy107 Spr07 Lect6 4 Monkey and hunter Dart gun fired just as the monkey drops. After shot, only force on dart is from gravity. Deviation from straightline motion is acceleration downward. Two motions are superimposed Equal and opposite forces I apply a force to a ball for a short time Δt to get it to move. During that time, the ball exerts an equal and opposite force on me! The forces cause the ball and I to move in opposite directions Monkey & dart have exactly same acceleration downward, dart hits monkey. Friday, Feb. 2 Phy107 Spr07 Lect6 5 e.g. water forces Friday, Feb. 2 Phy107 Spr07 Lect6 6 1

Force of gravity acts downward on the block. Block is not accelerating. ->Net (total) force is zero. Another force is present, equal and opposite, balancing gravity.

The interaction between the table and the block is a microscopic one. Friday, Feb. 2 Phy107 Spr07 Lect6 7 Friday, Feb.

This is the reaction force. Like an object on a scale Spring compresses until force on object equals force from gravity. So weight is the force of gravity on an object.

2 Force of gravity acts downward on the block. Block is not accelerating. ->Net (total) force is zero. Another force is present, equal and opposite, balancing gravity. It is exerted by the table, on the block. Balancing forces Force of gravity on block Force of table on block How can the table exert a force? The interaction between the table and the block is a microscopic one. Friday, Feb. 2 Phy107 Spr07 Lect6 7 Friday, Feb. 2 Phy107 Spr07 Lect6 8 Force exerted by table on block The table can compress, bend, and flex by distorting the atomic positions. The atomic bond is like a spring - exerts a force when compressed. This is the reaction force. Like an object on a scale Spring compresses until force on object equals force from gravity. So weight is the force of gravity on an object. Weightless means no gravitational force Then what is mass? Friday, Feb. 2 Phy107 Spr07 Lect6 9 Friday, Feb. 2 Phy107 Spr07 Lect6 10 Mass Mass is the amount of inertia of an object. Quantifies amount of matter in an object. Symbol for mass usually m Unit of mass is the kilogram (kg). F = ma " F = (kg)#(m/s 2 ) = kg $ m /s 2 % Newton 1 Newton = force required to accelerate a 1 kg mass at 1 m/s 2. What do you think? On Earth you weight 600 N. But suppose you are out in space, far from any planets A. Your weight is zero but your mass is the same. B. Both your weight and mass are zero. C. Your weight is the same and your mass is zero. D. Your weight is zero, and your mass has decreased. Mass is an intrinsic characteristic of a body. The force of gravity on the body (weight) will depend on the other bodies around it. Friday, Feb. 2 Phy107 Spr07 Lect6 11 Friday, Feb. 2 Phy107 Spr07 Lect6 12 2

Is pounds really weight? In the English system (feet, pounds, seconds), pounds are a measure of force. Correct to say my weight is 170 pounds.

What should the thrust be? A. 60 N B. 600 N C. 60 kg D. 10 m/s 2 Friday, Feb. 2 Phy107 Spr07 Lect6 13 Friday, Feb.

of mass? Gravitational force must depend on mass: F gravity = mg so that acceleration is independent of mass: a = F gravity m = mg m = g Friday, Feb.

2 Phy107 Spr07 Lect6 16 A fortunate coincidence Newton s laws and gravity A force exactly proportional to mass, so that everything cancels nicely. But a bit unusual.

3 Is pounds really weight? In the English system (feet, pounds, seconds), pounds are a measure of force. Correct to say my weight is 170 pounds. Force of gravity on me is 170 pounds Then what is my mass? m = F g = 170lbs = 5.3 slugs!! 2 32 ft /s A person with a mass of 60 kg wants to hover using a jet pack. What should the thrust be? A. 60 N B. 600 N C. 60 kg D. 10 m/s 2 Friday, Feb. 2 Phy107 Spr07 Lect6 13 Friday, Feb. 2 Phy107 Spr07 Lect6 14 Other jet packs Equal accelerations If more massive bodies accelerate more slowly with the same force why do all bodies fall the same, independent of mass? Gravitational force must depend on mass: F gravity = mg so that acceleration is independent of mass: a = F gravity m = mg m = g Friday, Feb. 2 Phy107 Spr07 Lect6 15 Friday, Feb. 2 Phy107 Spr07 Lect6 16 A fortunate coincidence Newton s laws and gravity A force exactly proportional to mass, so that everything cancels nicely. But a bit unusual. Einstein threw out the gravitational force entirely, attributing the observed acceleration to a distortion of space-time. Friday, Feb. 2 Phy107 Spr07 Lect6 17 Gravitational force on Earth by apple Gravitational force on apple by earth These forces are equal and opposite, m Earth a Earth = m apple a apple " a Earth a apple = m apple m Earth But m earth =6x10 24 kg m apple =1 kg Friday, Feb. 2 Phy107 Spr07 Lect6 18 3

Velocity of the moon If an apple falls toward the Earth, why doesn t the moon fall toward the Earth? What is the direction of the velocity of the moon? A C B A. It is is too massive B.

4 Velocity of the moon If an apple falls toward the Earth, why doesn t the moon fall toward the Earth? What is the direction of the velocity of the moon? A C B A. It is is too massive B. It is too far away C. It is moving too fast D. It does fall toward the earth. Friday, Feb. 2 Phy107 Spr07 Lect6 19 Friday, Feb. 2 Phy107 Spr07 Lect6 20 Acceleration of the moon What is the direction of the acceleration of the moon? D. Zero accel C A B Acceleration = change in velocity change in time Velocity at time t 1 Velocity at time t 2 Speed is same, but direction has changed Velocity has changed Friday, Feb. 2 Phy107 Spr07 Lect6 21 Friday, Feb. 2 Phy107 Spr07 Lect6 22 How has the velocity changed? Velocity at time t 1 Velocity at time t 2 V(t 2 ) V(t 1 ) Change in velocity Centripetal acceleration = v 2 /r, directed toward center of orbit. r = radius of orbit (In this equation, v is the speed of the object, which is the same at all times) Friday, Feb. 2 Phy107 Spr07 Lect6 23 Earth s pull on the moon The moon continually accelerates toward the earth, But because of its orbital velocity, it continually misses the Earth. The orbital speed of the moon is constant, but the direction continually changes. Therefore the velocity changes with time. True for any body in circular motion Friday, Feb. 2 Phy107 Spr07 Lect6 24 4

Newton s falling moon Throwing the ball fast enough results in orbital motion From Newton s Principia, 1615 Acceleration of moon The moon is accelerating at directly toward the earth!

5 Newton s falling moon Throwing the ball fast enough results in orbital motion From Newton s Principia, 1615 Acceleration of moon The moon is accelerating at directly toward the earth! This acceleration is due to the Earth s gravity. Is this acceleration different than g, the gravitational acceleration of an object at the Earth s surface? Can calculate the acceleration directly from moon s orbital speed, and the Earth-moon distance. v 2 r m /s 2 Friday, Feb. 2 Phy107 Spr07 Lect6 25 Friday, Feb. 2 Phy107 Spr07 Lect6 26 Moon acceleration, cont Distance to moon = 60 earth radii ~ 3.84x10 8 m Speed of moon? Circumference of circular orbit = 2"r orbital distance = 2"r Speed = =1023 m /s orbital time = 27.3 days Centripetal acceleration = m/s 2 This is the acceleration of the moon due to the gravitational force of the Earth. Distance dependence of Gravity The gravitational force depends on distance. Moon acceleration is 9.81!m/s !m/s 2 " 3600 times smaller than the acceleration of gravity on the Earth s surface. The moon is 60 times farther away, and 3600=60 2 So then the gravitational force drops as the distance squared Newton: I thereby compared the force requisite to keep the Moon in her orb with the force of gravity at the surface of the Earth, and found them answer pretty nearly. Friday, Feb. 2 Phy107 Spr07 Lect6 27 Friday, Feb. 2 Phy107 Spr07 Lect6 28 5

From Last Time. position: coordinates of a body velocity: rate of change of position. change in position change in time

From Last Time. position: coordinates of a body velocity: rate of change of position. change in position change in time From Last Time position: coordinates of a body velocity: rate of change of position average : instantaneous: average velocity over a very small time interval acceleration: rate of change of velocity average: