*A current carrying wires feel a force in a magnetic field and that force causes a torque; that's how a motor works.
I built this contraption to allow the wire to spin freely on its own. Each part of the device serves an important purpose.
Battery - supplies voltage that supplies current
Magnet - supplies magnetic field that makes charges move
Paper clip - allows rotation of the wire while also conducting current.
Motor loop (wire) - spins as a result of the flowing current
*I scrapped the paper clip (at the point where the wire sits on the paper clip loop *at the same point on each side*) to allow the current to flow through the wire, because otherwise the coating on the wire would get in the way. If you don't scrap the wire in the same place and on the same side on each end of the wire, the wire won't make a complete circle when spinning.
The wire spins because of moving charges. The magnetic field is going up towards the wire, the current is flowing across the wire, and thus the force is going to the side of the wire. That felt force creates a torque, so the loop spins.
All moving charges feel a force in a magnetic field if they are moving perpendicular to the magnetic field.
*This is why the equator is generally shielded from cosmic rays entering, and the northern countries aren't.
This motor could be used as a cake mixer. You could attach whisks to the motor loop, and then when you turn on the current, the wires will spin thus creating a cake mixer with the whisks spinning.
A charge is an unbalanced number of protons and electrons. If there is more positively charged particles than negatively charged particles or more negatively charged particles than positively charged particles, then the charge is unbalanced; it is either more negatively or positively charged.
There are two types of charges: contact and friction.
Induction is a way to charge something without touching it.
Electricity is energy being carried by charges.
Why does your hair stand on end when you take a winter cap off?
The cap steals e- from your hair though friction, making your hair become (+) and the hat (-).
Like charged repel each other, so the hair strands repel each other and stick up.
Why do clothes stick together in the drier?
Positive and negative charges are present when there is friction. When there aren't drier sheets in the drier with the clothes, the clothes will stick to each other because they are transferring electrons to each other. BUT when there are drier sheets, the clothes don't stick to each other, because the drier sheets steal e- from the clothes, making the sheets (-) and the clothes (+). Then the clothes are all positively charged, and like charges repel each other so the clothes don't stick to each other.
How does lightning work?
Clouds rub up against each other and become (-) though friction. This induces a (+) charge on the ground structures. The opposite charges will creep towards each other through the air, and if the path is completed energy will rush from the ground to the sky, and release light, heat, and sound in the form of lightning and thunder.
How do lightning rods protect structures?
Lighting rods are pointy and charges like to build up on pointy things. If the lighting strikes the rod it will channel the lighting around the house and directly to the ground. Since the charges are on the rod, the lightning will be more likely to hit the rod than the house and the house will be safe.
Polarization
An object is polar if the charges are separated (as in the ceramic bowl and balloon problems below)
A conductor lets charges move through the object.
An insulator stops charges from moving.
Why does plastic wrap stick to ceramic bowls?
As the plastic wrap is unrolled, it becomes charged through friction. When it comes over the bowl, the (+) charges in the bowl go toward the (-) plastic wrap because opposite charges are attracted to each other. The (-) charges in the bowl are repelled by the plastic wrap because they're like charges, so they move away from the wrap.
Coulomb's Law says F = kq1q2/d^2
and since the opposite attractive forces are closer in distance, the force between them is stronger than the repulsive forces, and thus the wrap sticks to the bowl. The bowl becomes polarized.
Why does a balloon stick to the wall after bring rubbed on your hair?
The balloon is charged through friction and become (-) when rubbed on your hair. When the ballon is brought close to the wall, the (+) charges in the wall are attracted to the (-) charges in the ballon, and then (-) charges in the wall repel from the like charges in the balloon, so the wall becomes polarized.
Coulomb's Law says F = kq1q2/d^2
and since the opposite attractive forces are closer in distance, the force between them is stronger than the repulsive forces, and thus the balloon sticks to the wall. The wall becomes polarized.
Electric Fields
An electric field is the area around a charge that can influence another charge.
The arrows show which way a positive charge will be pulled. In this case, the charge is going away from the other charge because they are like charges.
The arrows show which way a positive charge will be pulled. In this case, the charge is going towards the other charge because they are opposite charges.
The closer the lines are together, the stronger the electric field. Because of Coulomb's Law...
F = kq1q2/d^2
d = F
D = f
How does electric shielding work?
If you are inside a metal container, the charges will distribute evenly around that container. No matter where you are inside of the container you will feel no force from the electric field, because even if you're closer to a couple of the charges you are still further away from enough of them that you will feel no net force, thus your charges, electrons, and protons will all stay where they need to be.
Why are electronics placed in metal boxes?
Metal acts as an electric shield, so the electric field inside the metal zero (neutral), so the charges in the box won't be pushed/pulled by outside charges. The charges distribute evenly within the box as the are constantly moving. All the charges in the box will have equal and opposite forces in all directions. Because of the electric shielding, the sensitive electronic equipment inside of the metal that relies on the movement of charges, since it's running on electricity, is not going to feel a force inside that metal box. If the electronic equipment wasn't inside the metal box, it would feel a net force and then the device wouldn't work anymore, because it would be forced out of position and the charges wouldn't be where they needed to be.
Why can't your flash work continuously?
Capacitors are how flash works. Two oppositely charged plates that aren't connected continually add charges to each side and increase the electric field and energy between them. When the plates are connected briefly, the energy rushes from one plate to the next, and the energy is released as light thus the flash (cameras). It takes time to build up the charge on the plates and enough stored energy in the field, so flashes can't be used continuously.
Electric Potential
Electric potential energy is the energy the particle posses by virtue of its location. The stored energy in electric fields.
Electric potential is the electric potential energy per unit charge --> electric potential = PE/q
*measured in volts (V)
*electric potential does not equal electric potential energy
volt = joule/coulomb
Current is energy being carried by charges (energy flow)
*measured in amps (A)
*current = I
*more current = more/faster movement
Voltage is the difference in electric potential which causes current.
*Current and voltage are proportionate.
V increases = I increases
V decreases = I decreases
How to increase the resistance of an electric wire.
How to decrease the resistance of an electric wire.
According to Coulomb's Law, distance and force are inversely proportionate.
If the distance is doubled, the force is 1/4.
If the distance is halved, the force is 4x.
*Remember that we never manipulate the force, only the distance.
*If you double both charges in Coulomb's Law, the force will remain the same.
How can something have a higher voltage, but not be as dangerous as something with a lower voltage?
A high voltage, but a low energy.
--> safer
A low voltage, but high energy.
--> more dangerous
Circuits
Power = brightness measured in watts
P = IV
AC current = back and forth movement; electrons constantly dancing (plugs)
DC current = one direction moment (batteries)
Series Circuit
--> increase in resistance
--> decrease in current
*Will draw out less current than a parallel circuit would, because
Parallel Circuit
--> decrease in resistance
--> increase in current *Will draw out more current than a series circuit would, because
Why don't birds get harmed when they stand on a wire, but would get harmed if one ran into both power line wires with it's wings?
If a bird is sitting on a wire (just one) then there isn't a complete circuit. If the bird touches both wires with it's wings then there is a complete circuit. In a complete circuit, there is a difference in electric potential and that difference causes current to flow through the bird. If there isn't a complete circuit, there won't be a difference in electric potential, so the current won't flow through the bird and it will be safe.
Why does connecting a dead battery with jumper cables to a working battery with the car running make the battery work?
When the two batteries are connected, it creates a complete circuit so the energy can be transferred from the working battery to the dead battery. This will create a difference in electric potential and will cause current to flow (even though they always have the same amount of current) so the dead battery will then work.
Why are electric wires so thick?
Being thick is a way to decrease resistance. Since resistance and current are inversely proportionate due to I = V/R when resistance decreases, current increases. So if the wire is thick the resistance will decrease, increasing the current. If the device was a lightbulb, it would shine brighter because the current had increased.
Why is it dangerous to plug American appliances into European circuits?
American appliances are used to less voltage, and they also have a lower resistance which increases current. So when the American appliance is plugged into a European outlet, there is a higher voltage than the American is used to along with the high American current. Current is increased and high current plus high current is dangerous, because it could start a fire.
Why do lightbulbs typically burn out when they are immediately turned on, but not when they have been on for a while?
When the lightbulb is just turned on it's cold, and cold is a factor that decreases resistance. When resistance is decreased, current increases and a high current breaks the old filament in the lightbulb. When the lightbulb has been on for a while it is hot which increases the resistance and decreases the current, and a lower current won't break the filament like the higher current will.
How does a fuse/circuit breaker protect your house?
A fuse stops the current flow when it (the fuse) gets to be a certain degree of heat, when too much current is drawn from the wall. When the current gets too high, the fuse will burn breaking the fuse, cutting off current flow to all devices, so the wires don't cause a fire. A fuse is only added to parallel or parallel/series combined circuits, because they each branch of the circuit is individually power sourced (what your house has). Too much current = hot = possible fire = dangerous
My partner was Holt Mettee, and we worked very well together. The process was long, tedious, and frustrating but in the end we figured out how to correctly apply our physics concepts to the car. All our hard work paid off in the end, because we won our class race! Our car went.... velocity = distance time = 5 2.91 =1.718 m/s This time put us in 1st place for our class as well as out of all the classes!
This is our car!!
First, we built our body out of a mousetrap car hot glued onto a rectangular piece of wood. We wanted a stable body so the overall car would be stable, and not wobbly which would cause the car to drift to one direction more than another.
Next we glued on our wheels. We put rubber bands around them to create a small amount of friction between them and the ground, thus giving the wheels something to grab onto. Newton's 3rd law --> car pushes ground back, ground pushes car forward. This is the force that is doing work on the car, and causing it to accelerate.
The tricky part was making sure that they were straight, and parallel to each other. We added styrofoam on either side of the wheels to keep the wheel steady while rolling. This insured that the wheel wouldn't wobble while rolling, thus that it wouldn't move in one direction more than another.
We added some electrical tape in between the wheels and the axis slot to insure more that the wheels wouldn't slide towards one direction more than another.
This is the axis. The axis goes through the metal holes, having little friction, allowing it to rotate. The wheels are glued onto the axis, so when the axis rotates it allows the wheels to rotate as well, while keeping them straight and parallel.
The next part was to add a lever arm. A common misconception is that the lever arm increases the force, thus creating the car to go faster. In fact, the lever arm is increasing the distance and decreasing the force. The longer distance allows the force to act on the car for a longer period of time.
This is where the lever arm attaches to the axis. One side of the pink string is wrapped around the axis (here), and the other end is connected to the lever arm on the other side of the car.
When you pull the spring on the mousetrap back (and have it like so), potential energy is created, because this is where the power source for the car is. When I lift my finger, the spring will rotate back to the other end (where it initially was), the lever arm will follow it, the string will unravel as the lever arm rotates to the other side, and the unraveling string will cause the axle to rotate, thus causing the wheels to rotate and accelerate the car in the forward direction. 1) How Newton's Laws apply to the Mousetrap car and how it works Newton's 1st law states, "An object in motion will stay in motion and an object at rest will stay at rest, unless acted upon by an outside force." --> A car in motion will continue in motion unless a force pushes it backward (friction) *Remember that we only like friction in this experiment when there is a little bit on the wheels. Everywhere else, friction is your enemy. Newton's 2nd Law states, (a = F/m) --> Acceleration = force/mass *big force = big acceleration *too much mass = little acceleration *We want a small amount of mass with a big force. Newton's 3rd Law states, "Every action has an equal and opposite reaction." --> Car pushes ground back, ground pushes car forward. This is the force that is doing work on the car and causing it to accelerate. 2) Our wheels relied on friction due to Newton's 3rd law. We put rubber bands around them to create a small amount of friction between them and the ground, thus giving the wheels something to grab onto. rough surface = more friction smooth surface = less friction ... so we had to find the right balance between rough and smooth. *On the wheels was the only place that friction was our friend. 3) In terms of wheels, Holt and I changed our wheels at least 100 times, because we needed to find the right balance for wheel size, so that we could cause a torque on the wheels. The body shouldn't have a torque, but the wheels need a torque to turn. The force of friction on the ground is what causes a torque. Bigger wheels = longer lever arm, but too much rotational inertia Smaller wheels = not a long enough lever arm, and not enough rotational inertia. Medium size wheels = a good size lever arm and the right amount of rotational inertia.
4) The Lawof Conservation of Energystates, "the total amount ofenergyin a system remains constant (is conserved), althoughenergy within the system can be changed from one form to another or transferred from one object to another.Energy cannot be created or destroyed, but it can be transformed." --> When the mousetrap is pulled back, there is potential energy built up before the trap is released. When the trap is released, the energy become kinetic energy, because kinetic energy is the energy of movement. 5) Rotational velocity - the amount of rotation that a spinning object undergoes per unit time. The wheels have a rotational velocity. Big wheels = large rotational velocity Small wheels = small rotational velocity Medium sized wheels = a medium/good amount of rotational velocity Rotational inertia - an object's resistance to rotate. The bigger the wheels the bigger the mass and thus the bigger the rotational inertia The smaller the wheels the smaller the mass and thus the smaller the rotational inertia Tangential velocity - the linear speed of an object moving along a circular path. *You want a large tangential velocity, which means the wheels are moving at a fast pace. *Remember that different sized wheels will have different tangential velocities (example: your car's wheels and your friend's car's wheels). BUT all the wheels on the same car with have the same tangential velocity, just different rotationalvelocities and rotational inertias, because each wheel is covering the same distance in the same amount of time. 6) We can't calculate the instantaneous speed of the car (potential energy, kinetic energy, or force exerted from the spring) because the force of the spring isn't parallel to the axle spin, so work can't be calculated. Reflection 1) Our final design was COMPLETELY different than our original. We were trying all the wrong things before any of the right. Our first model was using a cardboard tea box as a body, mason jar tops as wheels, and balloons as the power source. Our final model was using wood as the body, CD's with rubber bands as the wheels, and a lever arm as the source. The promotion of the changes was to test the car, fail, and try something different that would fix that current problem. We just kept encountering issues with the car and making small change after change until we finally applied the correct physics concepts to the car. 2) The major problems with our car was the wheels. They were always either uneven, not touching the ground, not parallel with the axle, or causing the car to drift to one direction more than another. This is why we changed them so many times, but then we figured out that our body was falling apart, thus not allowing our axles to be stable and parallel to each other. So we thought the problem was the wheels (which it was) but the body was also making a big difference in the movement of the car. Once the body was stable, the car started to respond a lot better. 3) If I were to make my car go faster, I would lighten up the body and even out the axles/wheels because I think they were still a little uneven. 4) If I were to do this building process again, I would most definitely do more research. Holt and I just started gathering materials and building without any knowledge of which physics concepts to apply. We should have drawn a model to demonstrate how we wanted to use those concepts, before building the actual model. That would have speeded up the process a significant amount, because we spent a lot of time taking apart the model and rebuilding it.
work = a transfer of power work = (force)(distance) --> measured in joules (J)
*but remember that force and distance must be parallel for work to be done
For example, if a man was walking down the street holding a dog, no work would be done on the dog because the man's distance is moving forward and the dog's gravity is downward.
... But if the man was picking up the dog from the ground, there would be work on the dog, because the man is moving upward thus making the force and the distance parallel.
There is work being done, because the man's weight is 600N and the stairs have a vertical height of 4m
--> the force and distance are parallel *the slanted height of the stairs DOES NOT matter because it isn't parallel with the force Example problem: There are two people who weigh 500N. One man walked up the stairs, and the other man took the elevator. Which person did gravity do more work on?
-->
*There is an exception to the force and distance parallel rule.
Work can still be done if something is slanted, because gravity is still parallel to the y-component, so it doesn't have to be completely parallel to the actual distance (velocity in this case).
power = how quickly work is done power = work/time --> measured in watts
*If you halve the time, you double the work
Work and Kinetic Energy
kinetic energy - energy of movement
kinetic energy = .5mv^2 --> measured in joules (J)
work = ∆ kinetic energy
*if you have mass & velocity, you have the potential to do work
Say an 8g bike was moving at 10m/s and then 10 seconds later was moving at 20m/s. What was the
∆ kinetic energy = KE final - KE initial = 1,600 J - 400J
= 1,200J <--------- ∆ KE
work = ∆ KE so since there was 4x as much KE in KE new than in KE original, we know there was 4x as much work in KE new than in KE original.
*remember when you're solving for work that kg IS NOT a force, so you must convert the kg into N using w=mg because weight IS a force.
Go two decimal places to the left when converting from kg --> N
Go two decimal places to the right when converting from N --> kg
Potential Energy
potential energy = mgh --> (mass)(gravity)(height)
*movement IS NOT necessary to have potential energy
*the amount of potential energy is affected by the height (energy of position), so if something has height it has potential energy.
PE = ∆KE = work
(mgh) = (.5mv^2) = (F)(d)
The potential energy = the kinetic energy
(potential) (actual)
*The Law of Conservation of Energy says that, "the total amount of energy in a system remains constant, or is conserved. Energy can't be created nor destroyed, but it can change form." Just like in this problem PE = KE so the energy went from potential energy to kinetic energy.
PE = mgh
*if you double the height, you double the PE
*if you double the mass, you double the PE
*if you double the height & mass, you quadruple the PE
*gravity always remains constant .98 or 10
Machines
These are three different machines.
left = ramp
middle = pulley
right = lever
The purpose of machines is to decrease the amount of force needed, thus making the job easier.
The work put in = the work that comes out work in = work out (F)(d) = (F)(d) In terms of work and energy, how do airbags keep you safe?
Airbags keep you safe, because you go from moving to not moving no matter how you're stopped, because ∆KE is the same with or without the airbag because (KE = .5mv^2) and
∆KE = KE final - KE initial. Since the ∆KE is the same, the work is also constant because
(∆KE = work). The airbag increases the distance to stop, and since work has to be the same, the force will decrease with the airbag because (work = Fd), thus having a smaller force.
(small force = small injury = safer)
work = Fd <-- no airbag
work = fD <-- airbag
In terms of work and energy, why do gymnasts use mats?
Gymnasts use mats because they keep them safer. They will go from moving to not moving no matter how they're stopping because ∆KE is the same with or without a mat because (KE = .5mv^2) and
(∆KE = KE final - KE initial). Since the ∆KE is the same, the work is also constant because
(∆KE = work). The mats increase the distance to stop, and since the work has to be the same, the force will decrease with the mats because (work = Fd), thus having a smaller force.
(small force = small injury = safer)
work = Fd <-- no mat
work = fD <-- mat
Rotational Inertia is the property of an object to resist changes in the a spin. For example, an object with a smaller amount of rotational inertia is easier to spin than an object with a larger rotational inertia.
If you remember the Conservation of Linear Momentum that states (total momentum before = total momentum after), you will remember that momentum is ALWAYS conserved. So...
The Conservation of Angular Momentum is the law that states
(angular momentum before = angular momentum after).
The ice skater on the left has her arms out. This puts her arms' mass farther from her axis of rotation, giving her a larger rotational inertia and thus a smaller rotation velocity. The ice skater on the right has her arms pulled in. This puts her arms' mass closer to her axis of rotation, giving her a smaller rotational inertia and thus a larger rotational velocity. This is why ice skaters spin faster when their arms are pulled in to their chests.
Rotational & Tangential Velocities
Same rotational-different tangential --> Train wheels are designed to keep the train on the track by having the same rotational speed, but different tangential speeds. They're designed to have narrow edges on the outside and a wider wheel on the inside. This causes the wheels to have the same rotational velocities (moving the same distance over the same period of time) because they make the same amount of rotations. When the wider wheel ends upon the far side of the track then that side will be going faster and will cause the train to curve back towards the middle (self-correcting).
Different rotational-same tangential --> Gears are designed to have the same tangential speeds. Even when a smaller gear and a larger gear are connected, they are going the same speed. Although, the smaller wheel isn't making as many rotations as the larger gear, thus giving the two gears different rotational velocities (the amount of rotations made during a period of time).
Torques
A torque is a force acting over a perpendicular distance (lever arm), and it is caused by rotation. A torque happens when an object's center of gravity goes outside of it's base of support.
This object's center of gravity is outside it's base of support, so a torque is caused. This object will be easy to knock over.
*An object will be more likely to have a torque if its base is narrow or if it has a high center of gravity, and will be less likely to have a torque if its base is wide or if it has a low center of gravity.
This object's center of gravity is inside it's base of support, so a torque is NOT caused. This object will be hard to knock over.
*An object will be more likely to have a torque if its base is narrow or if it has a high center of gravity, and will be less likely to have a torque if its base is wide or if it has a low center of gravity.
This system is balanced, because the torques are equal.
Torque = (force)(lever arm)
Counter-clockwise torque = clockwise torque
(F)(lever arm) = (F)(lever arm)
*It is important to remember that...
1) force does NOT = force
2) lever arm does NOT = lever arm
3) torque = torque
Centripetal Force
Centripetal force is the force that makes a body follow a curved path.
*Centrifugal force (the center fleeing force) is NOT a real force.
This ball is connected to a string attached to a ceiling. When the ball is pushed, it will continue moving in a circular path due to centripetal force, which causes the ball to rotate around its axis of rotation (where the string connects to the ceiling)
String = F tension
Ball = F weight
*The centripetal force is in the inward direction, because it will NEVER be outward.
Example: In a washing machine, there are little holes on the inside metal to let the water drain out of the clothes. The clothes have a centripetal force in addition to their tangential velocity. The water only has a tangential velocity, because it is small enough to fit through the holes. It will keep moving in a straight line through the holes due to its tangential velocity. If there were no holes, then the water would have a centripetal force and stay inside the washer.
Center of Gravity
Example: Wrestlers bend their legs when wrestling, because it lowers their center of gravity. This makes it harder to get their center of gravity outside of their base of support, thus making it harder to create a torque. It essentially makes them more stable.
Example: A handy-man has wrench on a stuck bolt and can't seem to get the bolt loose. How can he make his job easier? He should get a longer wrench, because that will create a longer lever arm (the distance from the force applied to the axis of rotation). Now there is a larger lever arm AND a larger force, so there is a larger torque. Torque = (F)(lever arm)
Example: If a steel ball and a tape roll were to race down a ramp, the steel ball would win. The steel ball's weight is evenly distributed throughout the object, while the tape roll has a hole in the center so its mass is farther from its axis of rotation, giving it a higher rotational inertia and thus a smaller rotational velocity. The steel ball will have a smaller rotational inertia and thus a larger rotational velocity.
Example: If a water bottle filled with frozen water and a water bottle filled with regular water were to race down a ramp, the regular water bottle would win. In the frozen water bottle, everything is rotating when the bottle rotates, because it is all frozen together. In the regular water bottle, the bottle is rotating around the water, because the water for the most part stays in place.
In class we were asked to find the mass of a meter stick by only using a meter stick and a 100g lead weight.
In this picture, the meter stick is balanced, so that means the torques are equal. The counter-clockwise torque equals the clockwise torque, because torque = (force)(lever arm)
In this picture, there is a 100g weight on the far side of the meter stick. The center of gravity stays the same, and the axis of rotation stays the same. The only thing that has changed is...
This picture demonstrates how to solve for the mass of the meter stick. We know gravity (9.8), the mass of the weight (100g or 1kg), how long the stick is (100m), the center of gravity (50m), the axis of rotation (70m) and the lever arms (20m and 30m). 50 is just the remaining mass of the meter stick, but it is not necessary to use in the equations for solving.
To solve for the mass of the meter stick, we first need to have to correct measurements. We know that the weight is 100g or 1kg, but weight is measured in Newtons so we need to do a conversion.
w=mg
w=(.1)(9.8)
w=.98N
So we now know that the weight weighs 9.8N, and we can use that information in our equation.
torque = (force)(lever arm)
counterclockwise torque = clockwise torque
(force)(lever arm) = (force)(lever arm)
(force) (20) = (.98) (30)
20force = 29.4
force = 29.4/20
force = 1.47N
The question asked for the MASS of the meter stick, so we need to convert 1.47N back to mass.
This video is about Rotational Inertia and Angular Momentum. I like this video for multiple reason; it makes the definitions easy to understand, teenagers created it and it has examples that we have used in class, both of which make it relatable. Rotational inertia is the amount of resistance an object has to rotate. The video related rotation inertia to mass by saying, "rotational inertia depends on where the concentration of mass is. If it is close to the axis of rotation, it will have a small inertia and if it is far away, it will have a big inertia". I thought inertia was how big the object was, but that definition really cleared it up for me. The video also made clear that rotational inertia and rotational velocity are inversely proportional to each other, which makes the conservation of angular momentum law make sense (angular momentum before=angular momentum after). I found this video very useful.
This video explains the center of mass through acceleration and numbers, so if you wanted to know exactly how to solve for the center of mass you could use this video. Although, for our purposes the center of mass and center of gravity will almost always be the same.
This video gives one specific example of the center of gravity, and it completely changed how I saw it. After you watch the experiment, you will see how all three points of the wooden board meet at one point in the middle (the center of mass).
