For every action (a
force) there is an equal (same magnitude) and opposite reaction.
Therefore, if an object exerts a force on a second object, the second
exerts an equal an oppositely directed force on the first one.
the example above the Earth attracts the person and the person attracts
the Earth with the same force ! (same magnitude, opposite direction) If you jump, the attractive force (force of gravity) brings you back down. You accelerate downward because the attractive force is unblanced. The Earth " feels " the same force toward you but does not move. Because its mass (inertia) is so large. Ma = F = m A (same force but big mass = tiny acceleration and small mass = large acceleration) try this demonstration: 2 students play tug of war. Use 1 string with a spring scale at both end to measure the force. They pull a string and one is winning and pull the other student in his/her direction. Even so, the force1 on 2 = - Force 2 on 1. The force student 1 is experiencing = the force student 2 is experiencing . action=
- reaction. (the forces are vectors so the negative means they have opposite direction, but they have the same magnitude)
See the demonstration:
1) In the movie "Matrix" (or any other action movie) the good guy punches the bad guy who goes
flying away. Of course the good guy stays steady. What it wrong with
that? (we suppose they both have about the same inertia, that is the same mass). What if the good guy is the "rock " and the bad guy is " Dustin Offman" ? will it make more sense : Mrock arock = F = mdustinadustin (a is for acceleration that is the change of speed per second) with F dustin -rock = F rock -dustin
2) A) If you stand on a skateboard and
push on the wall, the wall pushes back on you and you move back. Why
the wall is not moving if action = reaction ? (remember Ma = F = ma ).
B) If you stand on the ground (not
on a skateboard) and you push the wall, why don't you move back ? What
is the other pair of forces involved ?
3) A) How Newton's third law can
explain the walk ? If you are standing on a small boat (not tied to the
dock), what will happen when you walk from the boat to the dock ?
Newton's third law can explain the motion of a rocket ? Can a rocket
still move in a vacuum (space) ? Is it easier for a ship to move in space than in the Earth's atmosphere ? Why? source: Paul Hewitt, conceptual Physics
C) How Newton's third law can explain your
rebound on a trampoline ? What happen to your shoulder if you shoot
using a riffle ? To spare your shoulder, is it better to use a heavy
riffle or a light one? REmember: ma = F = ma
How could you avoid being hurt by a riffle ? If riffle was free to slide along bar attached to it (no friction) and if the riffle shoots non stop, what happens ? (see image). Do both the riffle and the bullet experience the same force ? the same acceleration ? source: Paul Hewitt, conceptual Physics
D) You are traveling in a bus at highway
speed on a nice summer day and an unlucky bug splatters on the front
window. With Newton's third law in mind , Compare to the force that
acts of the bug , how much force acts of the bus ? Which undergoes the
greater acceleration ? Which therefore suffer the greater damage ? (Ma = F = ma)
The electric force between 2 charges is attractive if the charges are
unlike (+ and -) and repulsive if the are alike ( + and + or - and - ). the electric force between 2 charges is proportional to the product of the 2 charges but inversely proportional to the distance between the charges squared. So if the distance decreases, the force increases. Now answer that.
5) AN astronaut in space (no friction acting on his feet) pushes the space ship. WHat happens to him ? to the space ship ?
should never forget Newton's laws. In space there is no friction. So,
according to Newton's first law (law of inertia) , if something moves, it will keep
moving for ever, in the same direction and the same speed. If you want
to push something, it will push back on you and it is hard to stop has
no gravity brings you back to solid surface and no friction stops you.
If you want to grabs something and pulls , it will pull back to you and
it will be very chaotic.
9) watch this movie about newton's laws (watch only the segment about go to newton s law of motion ) Answer these questions: A)A force is defined as a ___________ or a ______________ that acts on an object. B) define Newton's first law of motion. This law is called the law of _____________. C) Define The second law. According to the second law, a net force causes an object to ____n__________. D) A measure of the inertia of an object is its ________ (net force? mass ? acceleration ? ) Newton;s second law is defined by Fnet = m a . So the ratio Net force / Mass is the ____________ (net force? mass ? acceleration ? ) A __________ causes an object's velocity to change. (net force? mass ? acceleration ? ) E) Define Newton;s third law. This law is also called the law of ___________ ________________. F) take this quiz on line. (go to the last video segments). part 2: Impulse and Momentum
1) Here is a new physical quantity noted p and called momentum. An object of mass m and moving at the velocity V has a momentum p.
The momentum p = m V is a measure of how hard it is to stop an object of mass m The momentum p is a vector because the velocity V is a vector p and V have the same direction The units for p is kg m /s (mass x velocity)
A light (mass m) but fast (Velocity V) ping pong ball can have the same momentum than a heavy (mass M) but slow (velocity v) golf ball. Believe it or not, they can knock you out the same way if Mv = m V
Check the image below. Do the balls have the same momentum even if they don't have the same mass ? why ? The
bowling ball is _______ times larger than the tennis ball but the
tennis ball is ___________ times faster than the bowling ball. Can they knock you over the same way ?
source: the physics of every day phenomena, McGrawHill
The momentum of an object can change if the velocity change : Suppose the velocity increase/decrease from V1 to V2 . The change in velocity is noted :∆V= V2 - V1 (change in velocity) the momentum of the object will consequently change from p1 to p2 such as ∆p= p2 - p1 (change in momentum) Since p = mV ∆p = m ∆V
index card so far : momentum p = mV change in momentum ∆p = p2 - p1 or ∆p = m∆V
2) Applying a force F, during a time t on an object of mass m will cause the velocity of the object V to change by ∆V . (Newton's second law). or applying a force F , during a time t on an object of mass m will cause the momentum p to change by ∆p. such as: F t = m∆V or F t = ∆p These are the same equations. (Newton's second law) The product F t is called the impulse.
3) This equation tells you that if the change in momentum of
an object is large (great change in velocity) , then the
impulse Ft must be large. To have a large impulse you can either
increase the __________ (like the baseball player throwing a ball) or
increase the __________ or both.
4) Consider 2 balls
of the same mass m = 1kg. One can bounce and the other can't. Some
one throws the 2 balls at a block standing on a table. Which one will exert the greatest impulse (more knocking over power, more efficient in knocking over the block) and therefore will undergo the greatest change in momentum ? let's see if you are right :
Suppose both balls have an initial velocity V1 (before hitting the block) = 5m/s @ right or + 5m/s The bouncing ball bounces (of course) and its final velocity is V2 = 5m/s@ left or - 5m/s So the change in velocity for the bouncing ball is ∆V = V2 - V1 = _________ m/s So the change in momentum is∆p = m ∆V = _______ kg m/s (use m = 1 kg) So the impulse Ft that the ball exert on the block (same as the force the block exerts on the ball) is also __________.
The ball that does not bounce stops when reaching the block. So V2 = 0. So ∆V = V2 - V1 = _________ m/s So the change in momentum is∆p = m ∆V = _______ kg m/s (use m = 1 kg) So the impulse Ft that the ball exert on the block (same as the force the block exerts on the ball) is also __________.
Which ball will exert the greatest impulse/force on the block ?
You can try to throw a bouncing ball vs unbouncing ball at a friend hand and see which one hurts more.
5) let's demonstrate that Physics concept with a bouncing dart and unbouncing dart aimed at a suspended block. WHich one will knock over the block better? TO DO IN CLASS " the dart demonstration. watch difference when the dart bounces off the block (greater force applied, the block is knocked off) and when the dart collides and sticks to the block. (less force but greater damage. more energy is transfered to the block)
6) another demonstration to do: the rolling chair. A student sits on a rolling chair and is thrown at another student. What demands more force/impulse ? To just stop the chair ? or to bounce it back to the pitcher ?
Also here is an example given by Paul Hewitt in his book conceptual Physics. During the gold rush, people were using water wheel as a machine . The falling water was spinning the wheel (like the mills in Holland). But the wheel was not spinning fast enough. A person got the idea to curve the paddle to get the water bounce off. Explain why it was a breakthrough/ (see image). He made more money than the gold miners. (the guy was Lester A. Pelton)
source: Paul Hewitt, conceptual Physics.
7) Now can you explain How a karate expert can break a stack of brick? His hand should stay with the brick when he hits it (stick to it) or the hand should bounce off the brick ? (more change in momentum = more impulse = great force is time is small).
Note that the reason why the damage (broken bones) is not important is that although the force is large enough to break the brick, the time is very small. So the brick does not have the time to go into his hand causing brews and broken bones. You will learn that energy (what causes damage) depends on force x distance (applying a force over a distance) so if the time is small, the distance over which the force is applied is small so damage (transfer of energy) is small. If the hand does not bounce, the hand will undergo more damage.
9) REVIEW Consider the equation F t = m ∆V (change in momentum occurs is an impulse is exerted ) Say you jump from the table to the ground. Your change in momentum is m ∆V (you stop at some point) this is because the impulse exerted by the ground on your legs is Ft such as F t = m ∆V (you hit the ground, the ground hits you back with the same force/impulse). You can either bend your legs when reaching the ground or you can keep them stiff and straight. (same change in motion at the end).
What do you choose (keep the legs stiff or bend them) ? To lessen the pain ? This is because for the same impulse (Ft) due to the same change in momentum, increasing the _________ will decrease the ___________.
10) likewise, a boxer will roll over with a punch, so for the same change in momentum (he is knocked over) if the time increases, the ____________ decreases
source: Paul Hewitt, conceptual Physics
index card momentum p = mV units in kg m/s change in momentum ∆p = p2 - p1 or ∆p = m∆V ∆V is the change in velocity ∆V = V2 - V1 Ft is the impulse Ft = m∆V F in N, t in seconds, m in kg, V in m/s
11) A force of 20N acts on a 2.0 kg mass for 10s, compute A) the impulse B) the change in velocity of the mass C) the change in momentum
12) A car that weight 7840N is accelerated from rest to a velocity of
25.0m/s eastward by a force of 1,000N. A) what was the car's change in
momentum ? B) how long the force act to change the car's momentum?
13) What force is needed to bring a 1.10 103 kg car moving at 22.0 m/s to a halt in 20.0 s?
13) A net force of 2.00 103 N acts on a rocket of mass 1.00 103 kg. How long does it take this force to increase the rocket's velocity from 0.0m/s to 2.00 102 m/s?
14) A car weighting 15 680N and moving at 20.0 m/s is acted upon by a 6.40 102 N force until it is brought to a halt.
A) What is the car mass ?
B) What is its initial momentum ?
C) what is the change in momentum ?
D) How long does the braking force act on the car to bring it to a halt?
15) THe velocity of a 6.00 102 mass is changed from 10.0m/s to 44.0 m/s in 68.0s by an applied, constant force.
A) what change in momentum does the force produce ?
B) what is the magnitude of the force ?
16) What is the final velocity of a rocket of mass 2.0 104 kg, starting from rest, if a net force of 1.5 105 N acts upon it for 15.0s ?
A 1400kg car moving with a velocity of 15m/s collides with a utility
pole and is brought to rest in 0.3 s. Find the magnitude of the force exerted on the car during the collision. hint:
the car pushes on the pole so the pole pushes back on the car with the
same force (opposite direction) , this force cause the momentum to change by ∆p = m ∆V such as F t = ∆p or F t = m ∆V 18)
A 0.5kg football is thrown with a velocity of 15m/s to the right. A
stationary receiver catches the ball and brings it to rest in 0.02s. What is the force exerted on the receiver ? (the force causes the change in momentum of the ball) What is the change in momentum of the ball ?
An 82 kg man drops from rest on a diving board 3.0m above the surface
of water and comes to rest 0.55 s after reaching the water. What force does the water exert on him ? What is the change in momentum of the man ?
20) A car moving at 40m/s stops suddenly. The 60kg passenger keep moving at 40m/s (inertia) until he hits either a air bag or the dashboard. A) Find the change in momentum of the passenger. (the force the airbag exerts or the force the board exerts causes the passenger to stop. THe change in momentum is the same = same change in motion)
B) Find the impulse ( F t ) hint: F t = m ∆V C) For the same impulse, same change in momentum, the airbag takes 0.75s to stop the passenger. It takes 0.026s for the board to stop the passenger. Compare the force F felt in each case. (in Fr solve for F)
D) So why do you use an airbag?
21) An ostrich with a mass of 146kg is running to the right with a velocity of 17m/s. Find the momentum of the ostrich
A 0.42kg soccer ball is moving down field at a velocity of 12m/s. A
player kicks the ball so it has a final velocity of 18m/s down field A) WHat is the change in the ball's momentum ? B) Find the constant force exerted by the player's foot on the ball if they are in contact for 0.02s
23) 2 cars are moving at the same velocity 50m/s. They both have the same mass 1 ton (1ton = 1000kg). Do they have the same momentum ? initial momentum = ____________. One car is stopped by a hay stack and 1 car is stopped by a wall. (final velocity = 0 ) Their final momentum is therefore = _________. Do they have the same change in momentum ? ( ∆p = m∆V) . The change in momentum is _________ (final - initial) Since impulse F t = ∆p , do they undergo the same impulse ?
But does it take the same time to stop the car with a wall than to stop it with hays ? (see picture below ?) So do they feel the same force ? same damage ? Compute
the force the force in each case if t = 5s for the car stopped by the
hays and t = 0.1s for the car stopped by the wall .
What is the ratio between these forces ?
Do you rather stop this way :
or this way ?
source: Pau Hewitt, conceputal Physics
" Force is war " WRONG. If you push someone weaker than you, you will experience the same force. Which one of you will experience the larger change in motion depends on the mass. But the force is the same.
1) read This law is a consequence of Newton's third law. Let's say 2 objects
interact with each other: 2 cars colliding, a car (object A) crashing
in to a wall (object B), a tennis ball (object A) bouncing off a racket
(object B) , a trampoline (object A) bouncing you (object B), a riffle
(object A) firing a bullet (object B), a rocket (object A) pushing out
the gas (object B), you best friend pushing you on an ice rink .... From Newton's third law;
Force(object A on object B) = - Force(object B on object A)
negative sign indicates that the action and the reaction have same
magnitude but opposite direction. REmember a force is a vector/ SO : FA on B = - FB on A
SO : FA on B t = - FB on A t (same time t for the interaction)
SO : ∆pA = - ∆pB
THAT: MEANS: The momentum gained by one body in an interaction is equal to the momentum lost by the other body.
SAME force, same change in momentum but the kick back for the bully is smaller because his mass is larger. but momentum gained = momentum lost
This is the law of conservation of momentum.
It only holds when a system of 2 bodies interacting is isolated. No external force are acting on them.
regardless of their mass/strength the 2 players feel the same force. The time of the impact is the same for them, so they feel the same impulse (F t) . So they undergo the same change in momentum. (∆p= F t ) They don't undergo the same change in velocity (motion). The change in velocity depends on their initial velocity and their mass (inertia).
------------------------------------------------------------------------------------------------- 2) read The law of conservation of momentum can be stated as:
THE FINAL MOMENTUM OF THE SYSTEM IS EQUAL TO THE INITIAL MOMENTUM OF THE SYSTEM.
or MOMENTUM before collision = MOMENTUM after the collision
REmember: momentum is a vector, it has a direction and a magnitude.
(PA + PB ) before = (PA' + PB') after
or mA VA + mB VB = mA VA'+ mB VB'
3) FILL BLANKS and answer questions In
the following problems, you will learn how to, mathematically,
predict the velocity of objects after they collide together. They can bounce off each other, or stick to each other, or keep the same direction but change their velocity. You need to use the conservation of momentum. Total momentum before = total momentum after. The velocity get redistributed. The redistribution depends on the inertia of the colliding objects / initial setting. Let's see examples first, then we will solve the problems. example 1; 2 football players. they stick together after they collide.
2 players run into each other. The total momentum is p1 + p2 = m1v1 + m2v2 = _______ kg m/s After the collision, they stick to each other. Their total mass after collision is therefore _____ kg. Their velocity after collision is V. Can you predict the direction of V (will they move @ right ? or @ left ? (look who has the larger weight and velocity). After the collision they conserve the same momentum (just computed) if we neglect outside forces like friction between shoes and ground. So the total momentum after is till ________. So after collision momentum = _________ = M V . M is the total mass of the pair and V is the velocity of the pair. Can you compute V ? (solve for it. ) check you answer here. In this example, the momentum is conserved (velocity is redistributed) but the kinetic energy of the players is not conserved. A lot of the initial energy goes into heat, broken bones, brews, and some into the motion of the pair. the collision is said to be non elastic. source; The physics of every day phenomena , McGraw-Hill.
video to watch : ballistic pendulum This set up is used to compute the speed of a bullet (projectile) momentum of bullet (before ) = momentum of bullet+block (after) . The velocity of the block +bullet can be found by computing the height reached by the block. (kinetic energy of block+bullet = potential energy) to discuss with instructor.
4) lab: watch the movie (U-tube) but do the experiments as you watch it. (see below) answer questions too: ------------------------------------------------------------------------------------------------------------------------------------ - a line of spheres (steel) on a track. the spheres are touching each other. A) if one sphere is moved and collide in the others, what will happen? (see image above) B) 2 sphere are colliding C) what about 3 ? 4? 5? So momentum before collision = _________________ after the __________________ - explain the motion upward of a rocket. Suppose the mass of the gas out is m and the velocity is v the mass of the rocket is M and the velocity is V. Use math to express the conservation of momentum. velocity is a vector.
2 metal spheres, of the same mass, collide with each other. The collision is said elastic because they don't stick to each other like the football players. (in that case, most of the energy of motion is conserved) . In each case, describe what happens to the initial momentum of the labs. (is it exchanged ? transfered ? ) is it conserved ? explain how you can tell. source: Paul Hewitt, conceptual Physics
This is a recoil situation. The 2 persons are pushing each other on ice. (so no outside force). The grandma has twice the mass (inertia) than the little girl. Are they going to feel the same force ? according to what law ? Are they going to move as fast ? which one is going to move faster ? The total momentum before is _________. So the total momentum after is still __________. If grandma = 100kg and the girl is 50kg, predict the ratio between their velocity. (hint: 0 = Mv1 + mv2 or 100v1 + 50 v2 = 0 so v2/v1 = ________ ) check this image to help you understand.
the velocities (change in motion) depends of course on the ________ they exert on each other.
source; The physics of every day phenomena , McGraw-Hill.
7) !!! here is your first problem on momentum. I will help you on that one/ So pay attention, don't skip line, then do the same thing for following problems.
2 freight cars A and B (see above) of equal masses (mÁ=mB = 3.0 105 kg) are on a
track. The car A is moving slowly at VA= 2.2 m/s. Car B is at rest.(VB= 0 ) The 2
cars collide and are coupled together. Use the conservation of momentum
to predict the resulting velocity of the 2 cars (locked together) after the interaction.
Here is the big idea (conservation of momentum, no friction involved): total momentum before collision = total momentum after collision REMEMBER momentum = mass x velocity = m V SO (momentum of object A + momentum of object B )before collision = (momentum of object A + momentum of object B )before collision OR AND THIS IS WHAT YOU NEED TO REMEMBER: mA VA + mB VB = mA VA' + mB VB'
here you have mA = mB = 300, 000 kg ; VA = 2.2 m/s ; VB = 0 ;
VA' = VB' because they move together after collision you get: 300,000 (2.2) + 0 = (300,000) V' + (300,000) V '
or 300, 000 (2.2) = 600, 000 V' (combine like terms) then you solve for V' This is fun and easy !!!
8) A steel glider of mass 0.50 kg (mA) moves along an air track with a
velocity of 0.75m/s (VA) . It collides with a second steel glider of mass 1.0
kg (mB) moving in the same direction at a speed of 0.38 m/s (VB). After the
collision, the first glider continues with a velocity of 0.35 m/s (VA') what
is the velocity of the second glider after the collision. Follow the
same strategy as before. hint: mA VA + mB VB = mA VA' + mB VB'
Moving at 20.0 m/s (VA) a car of mass 7.00 102 kg (mA) collides with a stationary (VB=0) truck of mass 1.4 103
kg (mB) . If the two vehicles interlock as a result of the collision,
what is the velocity of the car-truck system (V')? (VA' = VB')
10) ) A 2275 kg (mA) car going 28m/s (VA = 28m/s) rear-ends an 875kg (mB) compact car going 16m/s
(VB) on ice in the same direction. The 2 cars stick together (VA'= VB'= V'). How fast does
the wreckage move immediatly after the collision?
11) A Bullet of mass 50.0g (mA, conversion to kg !) strikes a wooden block of mass 5.0 kg (mB = 5kg, VB =
0 m/s) and becomes embedded in the block.
THe block and bullet then
flies off at 10m/s (VA' = VB' = 10m/s). What is the original velocity of the
12) non sticking problem. A plastic ball of mass 0.200 kg (mA) moves with a velocity of 0.30
m/s (VA) . THis plastic ball collides with a second plastic ball
of mass 0.100 kg (mB) that is moving along the same line at a
velocity of 0.10m/s (VB) . After the collision, the velocity of the
0.100 kg ball is 0.26m/s (VB'). What is the velocity of the second ball
(solve for VA').
13) Granny (object A) is skate boarding in a ring at a speed of VA=
3m/s when suddenly she is confronted to Alfred (object B) , at rest (VB
= 0), directly in her path. Rather then knocking him over, she picks
him up and continue in motion without braking. (they now have the same
velocity VA'= VB'= V like for problem 17). The mass of granny is
80kg (mA) , the mass of Alfred is 40 kg (mB).
A) using the law of conservation of momentum find the speed of GRanny and Alfred together after the collision. Solve for V.
B) After the collision, does GRanny's speed decreases ? increases ? (no friction)
C) After the collision, does Alfred's speed decreases ? increases ? (no friction)
15) conservation of momentum with vectors in 2D. advanced. optional.
momentum is also conserved in 2D. By studying the after math of the car accident, police can predict the inital velocities of the 2 cars. When a fire cracker explodes into 2 pieces (see image), the total momentum is conserved. (explosion is due to internal forces). To solve this kind of problem, the motion along the x-axis is considered to be independent from the motion along the y-axis. The momentum is conserved along each directions. See if it is true in the image above. another movie to watch (advanced)
Conservation of momentum in space is applied to nuclear Physics. SEE THIS APPLET A photon hits an electron at rests and transferes some of its energy to it. The electron gains energy and
the photon loses energy. Because it loses energy, its wavelength
increases (streches). (lower energy=lower frequency= high wavelength) the formula below is derived by the conservation of energy and momentum.
We find also the opposite effect. A fast particle can hit a photon , increasing its frequency. Around
black holes very energized gas around the black hole can hit a photon
from the radio wave background and boost it to a gamma ray photon. This is the inverse compton effect.
16) How conservation apply when a bom exploses and when predicting where the pieces will end up ?
can use conservation of momentum to find the speed of a bullet. A
bullet is fired and get stuck in a block, moving with it after collision. The block is suspended by strings.
So m V1 = (m+M) V2/ V1 is the speed of the bullet, the unknown, m is the mass of the bullet, known. M is the mass of the block. V2 is the speed of the system bullet + bullet after the collision. (stick collision). V2 can be known by measuring the height reached by the block after collision. (using conservation of kinetic energy . kinetic energy = potential energy or 0.5 mV2 = mg h ). See video :
motion of the 2 objects is dur to inside forces so the momentum is
conserved. The riffle and the bullets feel the same force. The change in motion is not the same because the inertia is not the same.
source: The Physics of everyday phenomena - McGraw-Hill
17) 2 skaters are standing still on ice. Skater A has a mass of
60.0kg and skater B has a mass of 30.0kg. We neglect frictions so there
is no external force, all the forces are internal and we can use the
law of conservation of momentum.
A) Because the are standing still VA =
VB= 0, initial momentum of the system = _________.
B) Skater A pushes skater B.
as a result, skater A moves back (left) at a velocity of VA'= -
0.2m/s. The negative sign indicates that the skater moves backward,
toward the left. Can you find the velocity VB'of skater B ? hint: 0 = mAVA' + mBVB' , because the interaction no one is moving.
18) What is the recoil velocity of a 1.20 103 kg (mA) launcher if it projects a 20.0kg (mB) mass at a velocity of VB'= 6.00 102 m/s
19) Upon launching, a 4.0 kg (mA) model rocket expels 50.0g (mB, conversion)
of oxidized fuel from its exhaust at an average velocity if 6.00 102m/s
(negative because the gas moves down) . What is the vertical velocity
of the model rocket after the launch ? (disregard gravity). !!! convert
g to kg.
19) 2 campers dock a canoe. One camper steps onto the dock. THis camper
has a mass of 80.0 kg (mA) and moves forward at 4.0m/s VA'
positive) . With what speed and direction will the canoe and the other
camper move if their combined mass is 110 kg (mB) ? Make the table as
before. You are solving for VB'.
A thread holds 2 carts together on a frictionless surface. A compressed
spring act on both carts. After the thread is burned , the 1.5kg mass
(mA) cart moves back with a velocity of 27cm/s to the left. What is the
velocity of the 4.5kg cart ?
hint: total momentum before =
total momentum after. The total momentum before = 0 and a car moving to
the left has a negative velocity
21) An astronaut at rest in space
fires a thruster pistol 35 g of hot gas at 875m/s. The combined mass of
the astronaut and the pistol is 84kg. How fast and in what direction is the astronaut moving after firing the pistol ?
Draw the situation
22) two campers dock a canoe. One
camper has a mass of 80kg and moves forward at 4m/s as she leaves the
boat to step onto the dock. With what speed and direction do the canoe and the other camper move if their combined mass is 115kg ?
After the baseball bounces back from the ground it moves toward the ping pong ball. They both have about the same speed. Let's put the frame of reference on the baseball. from that frame, the ping pong is coming at a speed 2V . The ping pong collides and bouvces back from the baseball still at the speed 2V. (we neglect the loss of energy). But
from our point of view , in the frame of reference of the lab, the
speed of the ping pong ball is V (moving baseball) + 2V = 3V so the ping pong moves with 3 times the speed. The speed is multiplied by 3 , that means the kinetic energy is multiplied by 9. The kinetic energy is tranfered to potential energy so after the ping pong bounces back it reaches 9 times its inital height !!
24) conservation of mometum is also true for isolated system like binary stars or planet + star. The planet is attracted by the star and the star is attracted by the planet/ the force is the same but not the motion that derived from the force. A star has huge mass therefore a small speed/ A planet has a small mass therefore a large speed. Before they interact momentum = 0 after momentum = mstarVstar - MplanetVplanet so : Mstar Vstar = Mplanet Vplanet This is also true for binary system of stars. Given the mass of the Earth (on internet), the mass of the Sun (internet) find the speed of the Sun. hint: speed earth = distance / time = 2 pi R / time with R = 1 AU = 150 million km , time = 1 year = 3 107 seconds find the speed in km/s convert to miles/s and mph