Inertia Inertia: The tendency of an object to resist change in motion –Hammer and Lead –Feather Mass: Our measure of inertia To get an object to move, or to change its motion, you must overcome its inertia. Apply some force.

Newton’s 1 st Law An object at rest, remains at rest,

Newton’s 1 st Law An object at rest, remains at rest, OR if in motion, travels in a straight line at constant velocity,

Newton’s 1 st Law An object at rest, remains at rest, OR if in motion, travels in a straight line at constant velocity, UNLESS acted on by a net force.

Newton’s 1 st Law An object at rest, remains at rest, OR if in motion, travels in a straight line at constant velocity, UNLESS acted on by a net force. Inertia can be overcome only by the application of a force. Force on a mass results in a change in velocity (acceleration). Force is a “net” force.

Net Force When forces balance, there is equilibrium. F 1 = Force felt by Bo because of Diddley. F 2 = Force felt by Diddley because of Bo. F 1 = F 2 F1F1 F2F2 BoDiddley

Equilibrium When forces balance, there is equilibrium. F 1 = Force felt by Bo because of Diddley. F 2 = Force felt by Diddley because of Bo. F 1 = F 2 F1F1 F2F2 BoDiddley

Net Force = Acceleration of Mass F 1 = Force felt by Dude because of Diddley. F 2 = Force felt by Diddley because of Dude. Net Force F = F 1 + F 2 F1F1 F2F2 Dude Diddley F net

Net Force = Acceleration of Mass Dude pushes Diddley Dude Diddley F net F1F1 F2F2

Net Force = Acceleration of Mass Dude pushes Diddley, because Diddley is Piddley. Dude Diddley F net ? !

Newton’s 2 nd Law Acceleration is proportional to the Net Force. –As the force increases, the acceleration increases –Triple the force, triple the acceleration –Without a net force, there is no acceleration and the object is in equilibrium (if at rest), or the object remains in motion at a constant velocity moving in a straight line in accordance with the 1st Law. Acceleration varies inversely with the Mass. –As mass increases, the acceleration decreases –As mass increases, the greater the force needed to keep acceleration the same.

Newton’s 2 nd Law Acceleration is proportional to the Net Force. Acceleration is varies inversely with the Mass. a = F/m Force = mass  acceleration F = m a

Things That Make You Go…Hmmmm.

Straight Line Answer An object at rest, remains at rest, OR if in motion, travels in a straight line at constant velocity, UNLESS acted on by a net force.

Frictional Forces Frictional Forces act opposite motion and oppose motion. Frictional Forces are usually proportional to velocity. To get the object to move, you must overcome friction. If F f, then there is acceleration with a Net Force = F-f. F f

F net = m a F f F net = Net Force = F - f F - f = m a

Acceleration F f F - f = m a a = (F - f )/m

Acceleration A 2 kg mass is acted on by a 2 N force. What is its acceleration? F = m a a = F/m

Acceleration A 2 kg mass is acted on by a 2 N force. What is its acceleration? a = 2 N / 2 kg = 1 m/s 2 F = m a a = F/m

Acceleration A 2 kg mass is acted on by a 2 N force. What is its acceleration? a = 2 N / 2 kg = 1 m/s 2 What if a 1/2 N frictional force was also in place? F-f = m a a = (F-f)/m

Acceleration A 2 kg mass is acted on by a 2 N force. What is its acceleration? a = 2 N / 2 kg = 1 m/s 2 What if a 1/2 N frictional force was also in place? a = ( N)/2 kg = 0.75 m/s 2 F-f = m a a = (F-f)/m

Newton’s 3 rd Law For every action there is an equal and opposite reaction. –Objects can not act on one another without being acted upon. –When you strike a wall, does it hurt your hand? You might say the wall struck you. Newton would say the force you applied to the wall was the same as that which the wall applied to you. The wall is bigger and more massive, therefore has more inertia and was not harmed as much as you.

Action-Reaction

Force on Rock from Earth = Force on Earth from Ball a = F / m = g Rock acceleration a = F / m Earth’s acceleration

Acceleration of Gravity Things that fall, accelerate at 9.8 m/sec/sec near the Earth's surface. This means velocity of a falling body increases by 9.8 m/sec with each passing second. Acceleration is the change in velocity over the change in time. a =  v/  t

Mass No Matter Lead and wood balls accelerate at the same rate when dropped from Pisa’s leaning tower. A hammer and feather fall at same rate in a vacuum. Apollo 15 astronauts tested Galileo's hypothesis on the Moon. Astronaut David R. Scott, Apollo 15 commander, watches a geological hammer and a feather hit the lunar surface simultaneously in a test of Galileo's law of motion concerning falling bodies.

H-ITT Question Newton’s first law of motion says: A. Force = mass  acceleration B. You have the right to remain silent. C. An object at rest, remains at rest, if in motion, travels in a straight line at constant velocity, unless acted on by a net force. D. For every action there is an equal and opposite reaction. E. none of these

H-ITT Question Newton’s second law of motion says: A. Force = mass  acceleration B. You have the right to remain silent. C. An object at rest, remains at rest, if in motion, travels in a straight line at constant velocity, unless acted on by a net force. D. For every action there is an equal and opposite reaction. E. none of these

H-ITT Question Newton’s third law of motion says: A. Force = mass  acceleration B. You have the right to remain silent. C. An object at rest, remains at rest, if in motion, travels in a straight line at constant velocity, unless acted on by a net force. D. For every action there is an equal and opposite reaction. E. none of these

H-ITT Question A 10 kg mass is acted on by a 2 N force. What is its acceleration? A. 0.2 m/s 2 B. 5 m/s 2 C. 20 m/s 2 D. 9.8 m/s 2 E. none of these A 3 kg mass accelerates by 5 m/s 2 due to a force acting on it. What is the magnitude of the force? A N B. 7 N C. 15 N D. 0.6 N E. none of these a = F/m = 2N / 10 kg = 0.2 m/s 2 F = ma = 3 kg 5 m/s 2 = 15 n

H-ITT Question A constant net force of 1500 N gives a rocket an acceleration of 2.5 m/s 2. What is the mass of the rocket? A kg B kg C x kg D. 600 kg E. none of these m = F/a = 1500 N/ 2.5 m/s 2 = 600 kg

Weight and Force Our weight (W) is an example of the force (F) we feel due to the acceleration of gravity (g). W = mg (F = ma)

Apparent Weight W = m(g+a)W = m(g-a)WeightlessW = mg

Newton's Law of Universal Gravitation F gravity = m GM/R 2 This means that the force of gravity between any two bodies in the universe is equal to a constant (the Gravitational Constant, G=6.67x N-m 2 /kg 2 ) times the product of the masses of the two bodies in question (m and M), divided by the square of the distance between their centers (R).

Newton's Law of Universal Gravitation F gravity = m GM/R 2 Double the mass, double the force. Double the distance, reduce the force by 1/4. Triple both mass and distance?

Newton's Law of Universal Gravitation F gravity = m GM/R 2 Double the mass, double the force. Double the distance, reduce the force by 1/4. Triple both mass and distance? 3  from M, (1/9) from R 2 = Reduce the force by 1/3.

What Goes Up, Must Come Down Equating Newton's second law with gravity F = m a F = m GM/R 2 m a = m GM/R 2 m = apple, or m = human, or m = projectile, or m = moon?

What Goes Up, Must Come Down Equating Newton's second law with gravity F = m a F = m GM/R 2 m a = m GM/R 2 a = GM/R 2 Acceleration is GM/R 2, irregardless of the mass m.

Gee, its “g” g = 9.8 m/s 2 Surface Gravity BUT, note that it is dependent on r. Near the surface r = R earth Want to lose weight? Hike to the top of a hill. Acceleration due to gravity will be less, therefore your weight will be less. M m r F = m GM/r 2 GM/r 2 = g

Force ~ 1/Distance 2 Twice as far away means 1/4 the force

Moon Gravity Moon’s Surface Gravity g moon = G M moon /R moon 2 g moon = 1.6 m/s/s Weight on the moon, W = mg moon Since g moon /g earth = 1/6, W moon /W earth = 1/6 You will weigh 1/6 as much, but your mass on the moon is the same as mass on the earth! The force you feel is different on that mass.

Horizontal and Vertical Motion

Projectiles Galileo’s Trajectories x = v ox t y = v oy t - 1/2 g t 2 The horizontal distance (x) is just due to the initial velocity in the horizontal direction (v ox ). Or, how much energy is imparted to the object.

Projectiles x = v ox t y = v oy t - 1/2 g t 2

Trajectory Modified By Gravity x = v ox t y = v oy t - 1/2 g t 2 1/2 g t 2 Path in the absence of g

Velocities x = v ox t y = v oy t - 1/2 g t 2 At the peak, its vertical velocity is zero.

Projectile Range x = v ox t A projectile is fired! y = v oy t - 1/2 g t 2 With v ox = 10 m/s and v oy = 20 m/s, how high will it go? How far down range?

Projectile Range x = v ox t v x = v ox + a x t y = v oy t - 1/2 g t 2 v y = v oy - g t Equations of motion:x and v x for horizontal y and v y for vertical a x = 0 v ox = 10 m/s a y = gv oy = 20 m/s x = 10 t v x = 10 y = 20 t - 5 t 2 v y = t x y

Projectile Range x = 10 t v x = 10 y = 20 t - 5 t 2 v y = t tv x xv y y max height hits ground Traveled 40 meters down range and 20 meters high in 4 seconds. x y

Projectile Range x = 10 t v x = 10 y = 20 t - 5 t 2 v y = t tv x xv y y max height hits ground Traveled 40 meters down range and 20 meters high in 4 seconds. x y

Projectile Range x = 10 t v x = 10 y = 20 t - 5 t 2 v y = t tv x xv y y max height hits ground Traveled 40 meters down range and 20 meters high in 4 seconds. x y

Projectile Range x = 10 t v x = 10 y = 20 t - 5 t 2 v y = t tv x xv y y max height hits ground Traveled 40 meters down range and 20 meters high in 4 seconds. x y

Projectile Range x = 10 t v x = 10 y = 20 t - 5 t 2 v y = t tv x xv y y max height hits ground Traveled 40 meters down range and 20 meters high in 4 seconds. x y

Survivor Care Package Drop How far away must the plane be, to drop the supplies to the camp if it is travelling 200 km/hr at an altitude of 1000 meters? x = v ox t y = v oy t - 1/2 g t 2 x y

Survivor Care Package Drop x = ? y = 1000 meters v ox = 200 km/hr v oy = 0 x = v ox t y = v oy t - 1/2 g t 2

Survivor Care Package Drop x = 200 t Need t = 1/2 g t 2 t is the amount of time the package takes to go from the height of the plane to the ground, accelerating at g but starting from rest = 10 t = t = 14.1 seconds

Survivor Care Package Drop x = 200 t Need time (t) = 1/2 g t 2 t is the amount of time the package takes to go from the height of the plane to the ground, accelerating at g but starting from rest = 10 t = t = 14.1 seconds Therefore x = 200 (14.1) = 2820 meters

Curvature and Force

Centripetal Acceleration a = v 2 /r Centripetal Force = m a = m v 2 /r Since velocity is a vector, even an object with constant speed that does not travel in a straight line, must experience an acceleration since acceleration is a change in velocity. Velocity is a vector which includes speed AND direction. Therefore, acceleration is a changing speed or changing direction.

Gravity Works Everywhere

Newton’s Orbit Cannon How much Velocity is Required?

Summary Newton’s Laws of Motion –Inertia –F = ma –Action/Reaction Forces, Acceleration and Equilibrium Gravity Projectiles F = m GM/r 2 x = v ox t y = v oy t - 1/2 g t 2