Force Direction & Vector Quantity – Physics
In this physics chapter we discuss force direction and vector quantity.
Are these forces opposite in direction?
Yes.
Consider the orange system. Do action and reaction forces cancel each other in the orange system?
No. They act on different objects – the apple and the orange.
Does the orange system accelerate?
Yes, towards the apple.
Consider the orange-apple system. Do action and reaction forces cancel each
other in this system
Yes, if you take them both together. One force pulls to the right and
another equal and opposite force to the left.
Do the orange and apple accelerate away from each other, or do they remain
together?
They remain together.
In the horizontal direction, how many forces are exerted on the cart?
Two, the horse pulling the cart forward and friction pulling the cart backwards.
What is the net horizontal force on the cart?
Force of pull of horse forward – Force of friction on cart backwards
How many horizontal forces are exerted on the horse.
Two: floor pushing horse forward, and cart pulling back
the horse (due to friction of the cart).
What is the net horizontal force on the horse?
Ffp – Fpc
How many horizontal forces are exerted by the horse on the other objects?
Two. One on the ground and one on the cart.
How many horizontal forces are exerted on the horse-cart system?
Two: Fp and Ff. The force pulling the system forward and the friction
holding the system back.
What is the net horizontal force on the horse-cart system?
Fp -Ff
In order to increase its speed, why must the horse push harder against the
ground than it pulls on the wagon?
Otherwise the net force would be zero and no acceleration would happen.
If you hit a wall with a force of 200 N, how much force is exerted on you?
200 N is exerted back on you.
Why can ́t you hit a feather in midair with a force of 200 N?
It cannot exert a reaction force of 200 N back on you.
How does the saying “You get what you give” relate to Newton’s
third law?
If you give a hug you get one back. If you kiss somebody, they kiss you
back. Eye for an eye, tooth for a tooth. If you hit somebody, they hit you back
with an equal and opposite force.
Your weight is the result of the gravitational force of Earth on your body.
What is the corresponding reaction force?
Your body pulling on the earth
Why can you exert a greater force on the pedals of a bicycle if you pull up
on the handlebars?
The handlebars push down with the same force as your pull. This force is
transmitted to the pedals.
Consider the two forces acting on a person who stands still, namely the
downward pull of gravity and the upward support of the floor. Are these forces
equal and opposite? Do they comprise an action-reaction pair? Why or why not?
Yes, they are the only forces acting on a non accelerating person; no they
are 2 interactions – person-earth and floor-person.
If you walk on a log that is floating in the water, the log moves backward.
Why?
You push forward on the log. The log pushes backward on you. This backward
force makes the log go backward.
Why is it easier to walk on a carpeted floor than on a smooth, polished
floor?
One can exert a greater horizontal force on a carpet than a polished floor
due to friction. So you get a greater reaction force.
If you step off a ledge, you accelerate noticeable toward Earth because of
the gravitational interaction between you and Earth. Does Earth accelerate
toward you as well? Explain.
Yes, but the accelerations produced by these equal forces are quite unequal
because of the differences in the masses
Inelastic Collisions
A collision in which the colliding objects become distorted and generate
heat during the collision is an inelastic collision.
Momentum conservation holds true even in inelastic collisions.
Whenever colliding objects become tangled or couple together, a totally
inelastic collision occurs.
Net Momentum Equation
Net momentum (before)= Net momentum (after)
Air Track
An air track nicely demonstrates conservation of momentum. Many small air
jets provide a nearly frictionless cushion of air for the gliders to slide on.
Momentum Vectors
Momentum is a vector quantity. The momentum of the wreck is equal to the
vector sum of the momenta of car A and car B before the collision.
The momentum of car A is directed due east and that of car B is directed due
north.
If their momenta are equal in magnitude, after colliding their combined
momentum will be in a northeast direction with a magnitude (root 2) times the
momentum either vehicle had before the collision.
When the firecracker bursts, the vector sum of the momenta of its fragments add
up to the firecracker’s momentum just before bursting.
Can you think of a case where a roller skate and a truck would have the same
momentum?
The roller skate and truck can have the same momentum if the speed of the
roller skate is much greater than the speed of the truck. For example, a
1000-kg truck backing out of a driveway at 0.01 m/s has the same momentum as a
1-kg skate going 10 m/s. Both have momentum = 10 kg•m/s.
Consider a 6-kg fish that swims toward and swallows a
2-kg fish that is at rest. If the larger fish swims at 1 m/s, what is its
velocity immediately after lunch?
Momentum is conserved from the instant before lunch until the instant after
(in so brief an interval, water resistance does not have time to change the
momentum).
Suppose the small fish is not at rest but is swimming toward the large fish
at 2 m/s.
If we consider the direction of the large fish as positive, then the
velocity of the small fish is -2 m/s.
When the speed of an object is doubled, its momentum
doubles.
The impulse-momentum relationship is a direct result of Newton’s
second law.
On roller blades you horizontally toss a ball away from you. The mass of the
ball is one tenth your mass. Compared with the speed you give to the ball, your
recoil speed will ideally be
one tenth as much.
A big fish swims upon and swallows a small fish at rest. After lunch, the
big fish has less
speed.
A falling firecracker bursts into two pieces. Compared with the momentum of
the firecracker when it bursts, the two pieces
combined have the same momentum.
Distinguish between mass and momentum. Which is inertia and which is inertia
in motion.
An objects inertia is basically defined by its mass. An objects momentum is
its mass multiplied by its velocity. This means that Mass is Inertia and
Momentum is inertia in motion.
Which has the greater mass, a heavy truck at rest or a rolling skateboard?
The truck as the greater mass
Which has the greater momentum?
The rolling skateboard
Distinguish between impact and impulse. Which designates a force and which
is the force multiplied by time.
Impact is basically just the force applied to an object and impulse is the
force multiplied by the amount it is applied for. This means that the force is
impact and the impulse is force multiplied by time.
When the force of impact on an object is extended in time, does the impulse
increase or decrease?
The impulse increases.
Distinguish between impulse and momentum. Which is force x time and which is
inertia in motion.
Impulse is how long a force is applied for and momentum is mass multiplied
by velocity. This means that impulse is force multiplied by time and momentum
is
inertia in motion
Does impulse equal momentum or a change in momentum?
Impulse is equal to the change in momentum.
For a constant force, suppose the duration of impact on an object is
doubled. How much is the impulse increased?
It is doubled
How much is the resulting change in momentum increased?
It is doubled
In a car crash, why is it advantageous for an occupant to extend the time
during which the collision takes place?
Because no matter how long it takes the impact will be the same because all
of the momentum needs to be taken away. Since impact is force multiplied by
time, we know that the longer you make that crash take, the less force needs to
be exerted on you and your car to take away the momentum you had before the
crash.
If the time of impact in a collision is extended by four times, how much
does the force of impact change?
It is reduced to one fourth of what it was before the time was reduced.
Why is it advantageous for a boxer to ride with the punch? Why should he
avoid moving into an oncoming punch?
Saying that a boxer rides with a punch implies that he moves away as the
punch hits him, this is one way to make the impact of the force take longer,
thus decreasing the amount of force that he feels. He should avoid moving into
an oncoming punch because this would do the opposite and would make the impact
of the punch take less time and so it would increase the amount of force that
he feels.
Visualize yourself on a skateboard. When you throw a ball, do you experience
an impulse?
Yes because when you push on the ball the ball pushes back on you. This
force has an impulse.
Do you experience an impulse when you catch a ball of the same speed?
Yes because when you catch the ball it exerts a force on you. This force has
an impulse.
Do you experience an impulse when you catch it and throw it out again?
Yes you experience the impulse that was described in b
when you catch it and the one described in a when you throw it.
Which impulse is greatest?
Catching it and throwing it out again because you experience the impulse of
catching it and the
impulse of throwing it.
Why is more impulse delivered during a collision when bouncing occurs than
during one when it doesn’t?
Because there is the impulse that comes from stopping the balls downward
momentum when it hits the ground and the impulse of giving the ball
upward momentum as it goes back up.
In terms of momentum conservation, why does a cannon recoil when fired?
Because the initial system had no momentum. If
the cannonball has momentum after it is fired, then the momentum of the cannon
must be equal to and opposite from that
momentum otherwise momentum would not be conserved – and we know that momentum
has to be conserved.
What does it mean to say that momentum is conserved?
It means that the momentum before and after the collision is the same.
Distinguish between an elastic and an inelastic collision.
In an elastic collision the objects basically bounce off of each other
(they are not permanently deformed and do not generate heat). In an inelastic
collision the objects do not bounce off of each other, but instead become
attached or tangled in some way.
Imagine that you are hovering next to the space shuttle in an Earth orbit.
Your buddy of equal mass, who is moving at 4 km/h with respect to the shuttle,
bumps into you. If he holds onto you, how fast do you both move with respect to
the ship?
2 km/h faster than the ship. This is because the momentum of the system
needs to be conserved. Momentum is equal to mass multiplied by velocity. The
velocity for just one mass was 4. In order to have the same momentum once the
mass is doubled the velocity will be cut in half.
Is momentum conserved for colliding objects that are moving at angles to
each other?
Yes, this is explained in section 7.6. In order to see this you need to use
vectors and vector addition. However, no matter what the angles are, the total
(or net) momentum before the collision must equal the total (or net) momentum
after.
What is the momentum of an 8-kg bowling ball rolling at 2 m/s?
Momentum is equal to force multiplied by velocity, so 8 kg x2
m/s = 16 kg·m/s
If the bowling ball rolls into a pillow and stops in 0.5 s, calculate the
average force it exerts on the pillow.
16/.5=32
We know that it initial momentum was 16 and that if it stops then it loses all
of that momentum, therefore the change in momentum is 16. Impulse is equal to
the change in momentum. Impulse is also equal to force multiplied by time.
Therefore if I divide my change in momentum by the time it takes to stop I will
get the force it took to stop the ball. (change in momentum = impulse = force x
time using this information I know that change in momentum / time = force)
What average force does the pillow exert on the ball?
We know from Newton’s Third law that the action force equals the reaction
force so the force of the pillow on the ball is the same as the force of the
ball on the pillow which is 32.
What is the momentum of a 50-kg carton that slides at 4 m/s across an icy
surface?
Momentum is mass multiplied by velocity, so 50 x 4 = 200
The sliding carton skids onto a rough surface and stops in 3 s. Calculate
the force of friction it encounters.
200/3=66.6N
The change is momentum is equal to the impulse. The impulse is the force
multiplied by the time. Therefore the force is equal to the change in momentum
divided by the time.
What impulse occurs when an average force of 10 N is exerted on a cart for
2.5 seconds?
10N x 2.5s= 25 N x s
Impulse is force multiplied by time.
What difference in recoil would you expect in firing a solid ball versus
firing a hollow ball from the same cannon? Explain.
There is more kick from the solid ball because of a greater change in
momentum for the solid ball.
A group of playful astronauts, each with a bag full of balls, form a circle
as they free-fall in space. Describe what happens when they begin tossing balls
simultaneously to one another.
The astronauts would recoil and the circle would widen.
A proton from an accelerator strikes an atom. An electron is observed flying
forward in the same direction the proton was moving and at a speed much greater
than the speed of the proton. What conclusion can you draw about the relative
mass of a proton and an electron?
The electron has much less mass than the proton.
A 1000-kg car moving at 20 m/s slams into a building and comes to a halt.
Which of the following questions can be answered using the given information,
and which one can- not be answered? Explain.
Multiply units of N, kgm/s2, by s and get N?s 5 kg?m/s.
What impulse acts on the car?
∆(mv) 5 (1000 kg)(20 m/s)=20,000 N/s
What is the force of impact on the car?
F =∆(mv)/ t; but we don’t know t! Without knowledge of the impact time, we
can’t solve for the force of impact
A car with a mass of 1000 kg moves at 20 m/s. What braking force is needed
to bring the car to a halt in 10 s?
F= ∆(mv)/ t 5 (1000 kg 3 20 m/s) / (10 s) 5 2000 kg?m/s2=2000 N
Force
In the simplest sense, a force is a push or a pull.
A mutual action is an interaction between one thing and another.
When you push on the wall, the wall pushes on you.
The interaction that drives the nail is the same as the one that halts the
hammer.
Newton’s 3rd Law
Whenever one object exerts a force on a second object, the second object
exerts an equal and opposite force on the first object.
Describes the relationship between two forces in an interaction.
One force is called the action force.
The other force is called the reaction force.
Neither force exists without the other.
They are equal in strength and opposite in direction.
They occur at the same time (simultaneously).
Newton’s third law is often stated: “To every action there is always an
equal opposing reaction.”
It doesn’t matter which force we call action and which we call reaction.
Examples
When the girl jumps to shore, the boat moves backward.
A person trying to walk on ice, where friction is minimal, may not be able to
exert an action force against the ice.
Without the action force there cannot be a reaction force, and thus there is no
resulting forward motion.
The dog wags the tail and the tail wags the dog.
Identifying Action and Reaction
To identify a pair of action-reaction forces, first identify the interacting
objects A and B, and if the action is A on B, the reaction is B on A.
When action is A exerts force on B, the reaction is simply B exerts force on A.
Action and Reaction on Different Masses
The cannonball undergoes more acceleration than the cannon because its mass
is much smaller.
F represents both the action and reaction forces; m (large), the mass of the
cannon; and m (small), the mass of the cannonball.
The balloon recoils from the escaping air and climbs upward.
The rocket recoils from the “molecular cannonballs” it fires and
climbs upward.
Lift
Using Newton’s third law, we can understand how a helicopter gets its
lifting force.
The whirling blades force air particles downward (action).
The air forces the blades upward (reaction).
This upward reaction force is called lift.
When lift equals the weight of the craft, the helicopter hovers in midair. When
lift is greater, the helicopter climbs upward.
Birds and airplanes also fly because of action and reaction forces.
When a bird is soaring, the shape of its wings deflects air downward. The air
in turn pushes the bird upward.
The slightly tilted wings of an airplane also deflect oncoming air downward and
produce lift.
We know that Earth pulls on the moon. Does the moon also pull on Earth? If
so, which pull is stronger?
They pull on each other with equal, but opposite forces. The reason the Moon
is not pulled into Earth is because it’s orbiting at a velocity that gives it
centrifugal force that offsets the pull of gravity. We think the Moon is
revolving around the Earth, but if we were on the Moon, the Earth would appear
to revolve around the Moon. So Earth, too, has a centrifugal force keeping it
from closing in on the Moon.
A tug of war occurs between boys and girls on a polished floor that’s
somewhat slippery. If the boys are wearing socks and the girls are wearing
rubber-soled shoes, who will surely win, and why?
The girls will win. The force of friction is greater between the girls’ feet
and the floor than between the boys’ feet and the floor. When both the girls
and the boys exert action forces on the floor, the floor exerts a greater
reaction force on the girls’ feet. The girls stay at rest and the boys slide
toward the girls.
A force interaction requires at least a(n)
pair of forces.
Whenever one object exerts a force on a second object, the second object
exerts a force on the first that is
opposite in direction and equal in magnitude at the same time
The force that directly propels a motor scooter along a highway is that
provided by the
road.
When you jump vertically upward, strictly speaking, you cause Earth to
move downward.
A system undergoes acceleration only when acted on by a(n)
net force.
If a net force acts on a horse while it is pulling a wagon, the horse
accelerates.
At a pizza shop, the cook throws the pizza dough in the air. The amount of
force the cook exerts on the dough depends on the
mass of the dough.
In the interaction between a hammer and the nail it hits, is a force exerted
on the nail?
Yes.
ON the hammer?
Yes.
How many forces occur in this interaction?
Two forces, action and reaction.
When a hammer exerts a force on a nail, how does the amount of force compare
with that of the nail on the hammer?
They are equal and opposite according to Newton’s Third Law.
When you walk along a floor, what pushes you along?
The floor pushes back on your feet.
When swimming, you push the water backward- call this action. What is the
reaction force?
The water pushing you forward.
If the action is a bowstring acting on an arrow, identify the reaction
force.
The arrow pushes back on the bowstring.
When you jump up, the world really does recoil downward. Why can ́t this
motion of the world be noticed?
The world has such a large mass that is acceleration downwards is
negligible.
When a rifle is fired, how does the size of the force of the rifle on the
bullet compare with the force of the bullet on the rifle?
The forces are the same, equal and opposite.
How does the acceleration of the rifle compare with that of the bullet?
Defend your answer.
The rifle will recoil backwards with less acceleration because it has a
larger mass. F = M x a
How can a rocket be propelled above the atmosphere where there is no air to
“push against”?
The rocket doesn ́t push against the air, the rocket pushes against the hot
gases coming out of its thrusters. The hot gases push back propelling the
rocket forward.
In the interaction between an apple and an orange, how many forces are
exerted on the apple?
One. The orange pulling on the apple.
On the orange?
One, the apple pulling the orange.
Are these forces equal in strength?
Yes.
Suppose you’re weighing yourself while standing next to the bathroom sink.
Using the idea of action and reaction, explain why the scale reading will be
less when you push down on top of the sink. Why will the scale reading be more
if you pull up on the bottom of the sink?
Action is you pushing down on sink – reaction is sink pushing up on you.
This takes some of the burden off of the scale. If the action is you pushing up
on the sink, the reaction is the sink pushing down on you. This adds burden to
the scale.v
When a high jumper leaves the ground, what is the source of the upward force
that accelerates her? What force acts after her feet are no longer in contact
with the ground?
The ground pushed upward on the jumper, which is the force that provides an
upward accelerate. In the air, only the force of gravity acts on the jumper.
Upward acceleration ceases and the acceleration is downward – g
hat is the reaction force to an action force of 1000 N exerted by the Earth
on an orbiting communications satellite?
1000 N exerted on the earth by the communications satellite.
If action equals reaction, why isn’t Earth pulled into orbit around
satellites?
It is, but negligibly, due to Earth’s huge mass
If a bicycle and a massive truck have a head-on collision, upon which
vehicle is the impact force greater? Which vehicle undergoes the greater change
in its motion? Defend your answers.
Impact force is the same. Because of the bicycle’s smaller mass, the change
in motion is greater for the bicycle
A speeding bus makes contact with a bug that spatters onto the windshield.
Because of the sudde3n force, the unfortunate bug undergoes a sudden
deceleration. Is the corresponding force that the bug exerts against the
windshield greater, less or the same? Is the resulting deceleration of the bus
greater than, less than or the same as that of the bug?
Magnitude is the same. The bug decelerates more because it has less mass
Some people used to think that a rocket could not travel to the moon because
it would have no air to push against once it left Earth’s atmosphere. We now
know that idea was mistaken. What force propels a rocket when it is in a
vacuum?
The force is that which the exhaust exerts. It is the reaction to the force
that the rocket exerts on the exhaust gases
Since the force that acts on a cannonball when a cannon is fired is equal
and opposite to the force that acts on the cannon, does this imply a zero net
force and therefore the impossibility of an accelerating cannonball?
No. There is a force applied to the cannonball that causes movement as long
as it is greater than all of the other forces acting on the cannonball. That
force is equal to the one on the cannon, which will cause the cannon to move if
it is greater than the other forces acting on it
Suppose you exert 200 N on your refrigerator and push it across the kitchen
floor at constant velocity. What friction force acts between the refrigerator
and the floor? Is the friction force equal and opposite to your 200-N push?
Does the friction force make up the reaction force to your push?
200 N; yes; no, the reaction to your push on the refrigerator is the
refrigerator’s push back on you
Your teacher challenges you and your best friend to each pull on a pair of
scales attached to the ends of a horizontal rope,in tug- of-war fashion, so
that the readings on the scales will differ. Can this be done? Explain.
You cannot do it for 2 reasons. 1 you can pull with as much force as your
friend can pull back with. 2 scales on different parts of the same rope have to
have the same reading because the rope is experiencing tension as a whole
everywhere, and it will be the same wherever you measure it.
A pair of 50-N weights is attached to a spring scale as shown. Does the
spring scale read 0, 50, or 100 N?
50 N, the same as if the pulls were horizontal
The strong man can withstand the tension force exerted by the two horses
pulling in opposite directions. How would the tension compare if only one horse
pulled and the left rope was tied to a tree? How would the tension compare if
the two horses pulled in the same direction, with the left rope tied to the
tree?
The same; doubled (if they both pull in the same direction)
A balloon floats motionless in the air. A balloonist climbs up the
supporting cable. In which direction does the balloon move as the balloonist
climbs? Explain.
Downward because he pulls as he climbs
When you get up from a sitting position, do your feet push against the floor
with a force equal to, more than, or less than your weight? Explain.
More than because you accelerate upward as you push
When a weightlifter jerks a barbell over his head, is the force exerted on
the barbell more than, less than, or equal to the barbell’s weight? Explain
More than, because the barbell accelerates upward
Newton’s third law
Whenever one object exerts a force on a second object, the second object
exerts an equal and opposite force on the first
vector quantity
a quantity that has both magnitude and direction, ex: force, velocity, and acceleration
scalar quantity
a quantity that has magnitude but not direction, ex: mass, volume, and speed
vector
an arrow drawn to scale used to represent a vector quantity
resultant
the net result of a combination of two or more vectors
a
=f/m
f
=ma
newton’s first law
an object at rest tends to remain at rest; when an object in motion tends to
remain in motion at constant speed along a straight-line path
newton’s second law
when a net force acts on an object , and the object will accelerate. the
acceleration is directly proportional to the net force and inversely
proportional to the mass
acceleration
newton’s second law is nicknamed
inertia
newton’s first law in nicknamed
interaction
newton’s third law is nicknamed
1000N
Iguana and Monitor are having a tug of war, each of them pulls in opposite
directions with a force of 1000N, the tension in the rope is?
ball falls in a curved path, landing directly under you
you are standing in a closed bus that moves at a constant velocity and drop
a ball from you outstretched hand. You pull your hand back so the ball can land
on the floor of the bus. What described the motion of the ball from the
perspective of a person standing on the side of the road?
propeller blades push air up, while air pushes the blades down to keep
static equilibrium
what keeps a helicopter hovering in place vertically?
vector
your mousetrap project’s displacement is what type of quantity
are not
The pull of the earth’s gravity down on a pumpkin and the upward support
force of the floor up on this pumpkin are equal in magnitude and in opposite
directions, keeping the pumpkin at rest. These two forces are ___ an action
reaction pair
right is hand on rock, and left is floor on rock
what are forces pushing a a round rock that is sliding across you perfectly
horizontal floor at constant velocity with friction to the right of the rock?
same for both
a car traveling at 100km/hr stikes a bug, splattering it on the windshield,
the force of impact is?
normal weight
what is an example of a vector quantity
f, 2/3f, 1/3f
force F pulls three blocks of equal mass across a friction free table, what
are the rope tensions on each block?
Force
A push or a pull
Interaction
In a broader sense a force us not a thing in itself but makes up a ____
between one thing and another
Equal, opposite
Newtons third law states whenever one object exerts another force on a
second object the second object exerts a force that is ___ in magnitude and in
the ____ direction of the force exerted by the first object
Action and reaction
We give names to the forces described in newtons third law, one is called
the ___ force, while the other is called the ___ force
True
True or false, according to newtons third law pairs of forces act on
different objects
No
Does a speeding missile posses force