inertia inertia: the tendency of an object to resist change in motion hammer and lead feather mass:...

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 1st LawAn object at rest, remains at rest,

Newton’s 1st LawAn object at rest, remains at rest,ORif in motion, travels in a straight line at constant velocity,

Newton’s 1st LawAn object at rest, remains at rest,ORif in motion, travels in a straight line at constant velocity,UNLESSacted on by a net force.

Newton’s 1st LawAn object at rest, remains at rest,ORif in motion, travels in a straight line at constant velocity,UNLESSacted 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 ForceWhen forces balance, there is equilibrium.

F1 = Force felt by Bo because of Diddley.

F2 = Force felt by Diddley because of Bo.

F1 = F2

F1 F2

Bo Diddley

EquilibriumWhen forces balance, there is equilibrium.

F1 = Force felt by Bo because of Diddley.

F2 = Force felt by Diddley because of Bo.

F1 = F2

F1 F2

Bo Diddley

Net Force = Acceleration of Mass

F1 = Force felt by Dude because of Diddley.

F2 = Force felt by Diddley because of Dude.

Net Force F = F1+ F2

F1 F2

DudeDiddley

Fnet

Net Force = Acceleration of MassDude pushes Diddley

Dude Diddley Fnet

F1 F2

Net Force = Acceleration of MassDude pushes Diddley, because Diddley is Piddley.

Dude Diddley Fnet

?

!

Newton’s 2nd 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 2nd 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 AnswerAn object at rest, remains at rest, ORif in motion, travels in a straight line at constant velocity,UNLESS acted on by a net force.

Frictional ForcesFrictional 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, the object sits. If F > f, then there is acceleration with a Net Force = F-f.

F

f

Fnet = m a

F

f

Fnet = Net Force = F - fF - f = m a

Acceleration

F

fF - 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 aa = F/m


acceleration?

a = 2 N / 2 kg = 1 m/s2

F = m aa = F/m


acceleration?

a = 2 N / 2 kg = 1 m/s2

• What if a 1/2 N frictional force was also in place?

F-f = m aa = (F-f)/m


acceleration?

a = 2 N / 2 kg = 1 m/s2

• What if a 1/2 N frictional force was also in place?

a = (2 - 0.5 N)/2 kg

= 0.75 m/s2

F-f = m aa = (F-f)/m

Newton’s 3rd 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

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 GravityThings that fall, accelerate at 9.8 m/sec/sec near the Earth's surface. This means velocity of a fallingbody increases by 9.8 m/sec witheach passing second.

Acceleration is the change in velocity over the

change in time. a = v/t

Mass No MatterLead 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 ageological 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:





H-ITT Question• Newton’s third law of motion says:





H-ITT Question• A 10 kg mass is acted on by a 2 N force. What is its acceleration?

A. 0.2 m/s2

B. 5 m/s2

C. 20 m/s2

D. 9.8 m/s2

E. none of these

• A 3 kg mass accelerates by 5 m/s2 due to a force acting on it. What is the magnitude of the force? A. 1.66 N B. 7 N C. 15 N D. 0.6 N E. none of these

a = F/m = 2N / 10 kg = 0.2 m/s2

F = ma = 3 kg 5 m/s2= 15 n

H-ITT Question• A constant net force of 1500 N gives a rocket an acceleration of 2.5 m/s2. What is the mass of the rocket?

A. 3000 kgB. 10000 kgC. 1.667 x 10-3 kgD. 600 kgE. none of these

m = F/a = 1500 N/ 2.5 m/s2 = 600 kg

Weight and ForceOur weight (W) is an exampleof the force (F) we feel due tothe acceleration of gravity (g).

W = mg (F = ma)

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

Newton's Law of Universal Gravitation

Fgravity = m GM/R2

This means that the force of gravity between any two bodies in the universe is equal to a constant (the Gravitational Constant, G=6.67x10-11 N-m2/kg2)times the product of the masses of the two bodies inquestion (m and M), divided by the square of the distance between their centers (R).


Fgravity = m GM/R2

Double the mass, double the force.

Double the distance, reduce the force by 1/4.

Triple both mass and distance?


Fgravity = m GM/R2

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 R2 = Reduce the force by 1/3.

What Goes Up, Must Come DownEquating Newton's second law with gravity F = m a F = m GM/R2

m a = m GM/R2

m = apple, orm = human, or m = projectile, or m = moon?

What Goes Up, Must Come DownEquating Newton's second law with gravity F = m a F = m GM/R2

m a = m GM/R2 a = GM/R2 Acceleration is GM/R2 ,irregardless of the mass m.

Gee, its “g”• g = 9.8 m/s2

• Surface GravityBUT, note that it isdependent on r. Nearthe surface r = Rearth

Want to lose weight?Hike to the top of a hill. Acceleration dueto gravity will be less,therefore your weightwill be less.

M

m

r

F = m GM/r2

GM/r2 = g

Force ~ 1/Distance2

• Twice as far away means 1/4 the force

Moon Gravity• Moon’s Surface Gravity gmoon = G Mmoon/Rmoon

2

gmoon = 1.6 m/s/s

Weight on the moon, W = mgmoon

Since gmoon/gearth = 1/6, Wmoon/Wearth = 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 = vox t

y = voy t - 1/2 g t2

The horizontal distance (x)is just due to the initial velocity in the horizontal direction (vox).

Or, how muchenergy is imparted to theobject.

Projectiles x = vox t

y = voy t - 1/2 g t2

Trajectory Modified By Gravity x = vox t

y = voy t - 1/2 g t2

1/2 g t21/2 g t2

Path in the absence of g

Velocities x = vox t

y = voy t - 1/2 g t2

At the peak, its vertical velocity is zero.

Projectile Range x = vox t A projectile is fired!

y = voy t - 1/2 g t2

With vox = 10 m/s and voy = 20 m/s, how high will it go?

How far down range?

Projectile Range x = vox t vx = vox + axt

y = voy t - 1/2 g t2 vy = voy - g t

Equations of motion: x and vx for horizontal

y and vy for vertical

ax = 0 vox = 10 m/s

ay = g voy = 20 m/s

x = 10 t vx = 10

y = 20 t - 5 t2 vy = 20 - 10 t

x

y

Projectile Rangex = 10 t vx = 10

y = 20 t - 5 t2 vy = 20 - 10 t

t vx x vy y

0 10 0 20 01 10 10 10 152 10 20 0 20 max height3 10 30 -10 154 10 40 -20 0 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 istravelling 200 km/hr at an altitude of 1000 meters?

x = vox t

y = voy t - 1/2 g t2

x

y


x = ?y = 1000 metersvox = 200 km/hr

voy = 0

x = vox t

y = voy t - 1/2 g t2


x = 200 t Need t.1000 = 1/2 g t2

t is the amount of time the package takes to go fromthe height of the plane to the ground, accelerating atg but starting from rest.

2000 = 10 t2

200 = t = 14.1 seconds


x = 200 t Need time (t).1000 = 1/2 g t2

t is the amount of time the package takes to go fromthe height of the plane to the ground, accelerating atg but starting from rest.

2000 = 10 t2

200 = t = 14.1 secondsTherefore x = 200 (14.1)

= 2820 meters

Curvature and Force

Centripetal Accelerationa = v2/r

Centripetal Force = m a= m v2/r

Since velocity is a vector, even an object with constantspeed that does not travel in a straight line, mustexperience an acceleration since acceleration is achange in velocity. Velocity is a vector whichincludes speed AND direction. Therefore, acceleration is achanging 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/r2

x = vox t y = voy t - 1/2 g t2

inertia inertia: the tendency of an object to resist change in motion hammer and lead feather mass:...

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