Chapter+4+wiki

toc Chapter 4

=Section 1:=

What do you see? A woman is pushing a man in a zig-zagged path. The man is imagining that he is on a rollercoaster. I think that the drops on a rollercoaster cause the loudest and most frequent screams. It is the part of the rollercoaster that scares people the most and as you are going down the drop you have to scream.

Roller Coaster Design

Physics Talk Scaler- no direction, but quantity. Vector- magnitude and direction. Displacement- The actual distance traveled from point to point.

Checking Up 1) Scaler shows no direction while displacement is a vector and does show direction. 2) If you go any amount for distance and end up in the same spot as where you started the displacement is always 0. 3) To find the speed of something you take its distance and put it over the total time. To find velocity you take the displacement and put it over time. 4) Acceleration is the change in velocity over the total time it takes.

Physics To Go 1) In the side view you can't tell the direction( right or left) that the roller coaster track is going. 2) The biggest thrill would come from when the acceleration is the greatest. When you are going around curves quickly or speeding up a lot at one time. 3)a) La Paz is going the fastest because it covers the most distance in 24 hours. b)v=d/t 40000/24= 1666.7km/h c) SInce it is constantly moving we don't feel it. 4) a=16-4/3 a=4 m/s 5)a) speed b) velocity c) acceleration d) velocity, displacement e) displacement 6) v= .1/2 v= .05m/s 7) .05= .05/s s=1 8) a= 25/10 a= 2.5 m/s^2 10)a) To make a ride more suitable for children i would take away some of the major drops and make the turns less sharp by making the diameter wider.

=Section 2= What do you see? The people who are going down the steeper slope will get a greater amount of thrill because the more steep the angle the more acceleration there.

Physics Talk The energy transformations in a Roller Coaster are gravitational potential energy and kinetic energy. gpe is the energy that your body possesses dependent on where you are on a gravitational field. ke is the energy that an object has depending on how fast it is going. Energy at the bottom is equal to energy at the top.

Checking Up 1) The higher the point the ball is released from, the faster its final speed is. 2) GPE increases as the height increases. 3) KE increases as the speed of an object increases. 4) As it rolls down the hill the cart loses GPE but gains KE. 5)

Physics To Go 8) It will not change because the masses in the two equations cancel out anyway. Roller Coasters are not mass dependent. 9)a) B has the least GPE because it is the time when the Roller Coaster is at its lowest point. b) C and F because they are at the same exact level therefore have the same speed. c) B because it is the lowest and therefore has the least amount of GPE. When GPE is at its lowest KE is at its highest.

What do you think now?

Reflecting on the section

=Section 3= What do you see? Kids are playing with a popper toy. As it pops up they are measuring the height of the pop along with the speed it pops with. As the mass of the roller coaster increases so does the GPE. As GPE goes up, the work needed to pull the roller coaster to the top of its drop goes up. S it does cost more.

Physics Talk SPE- spring potential energy- the energy that is stored due to its compression or stretch (SPE= 1/2kx^2) Mechanical Energy- the sum of KE and PE. Mechanical energy at the highest point is equal to mechanical energy at the lowest point.

Checking up 1) As it pops off a table, the poppers SPE increases. 2) Since PE=2J then the GPE= 2J 3) At max height the GPE will be 2J 4) K is the spring constant and x is the distance the spring is compressed.

Physics To Go 5) You can not make it any higher because the initial height is the max height. It will not have enough GPE to reach the second peak. 6) Since there is friction acting on the roller coaster, the friction will stop it. There is work ebing done witch decreases GPE. 7) GPE = mgh GPE = (300) (9.8) (15) GPE = 44,100J 8) a) KE= 1/2 mv^2 KE= 1/2 (400) (15)^2 = 45,000J b) KE=GPE 45,000 J c) 45,000= (400)(h)(9.8) height= 11.48 9) When you throw a ball up and icrease the height, you also increase the GPE. 10) It will be the same for all the paths because they will all have the same GPE because all of the heights are the same. 11) a) GPE should equal KE GPE = mgh GPE = (0.02)(9.8)(.4) .078J b) KE = SPE 1/2 mv^2 = SPE SPE = 1/2 (0.020) (2.7)^2 SPE = 0.073J c) KE = GPE 1/2mv^2 = mgh 1/2 (.006) (2.7)^2 = (.006) (9.8)h height=.13m 12) a) GPE = SPE mgh = 1/2kx^2 300(9.8)18 = 1/2k(4^2) k = 6615 N/m b) GPE = SPE GPE = mgh GPE = 70,560 J 1/2(6,615)x^2 = 70,560 x = 4.62m 13) KE= SPE KE= 1/2kx^2 KE=1/2 40(.3)^2 KE= 1.8J

What do you think now? Roller coasters use cables and motors to pull the cars up to the top. It does make the cost of a roller coaster more because the GPE does go up and therefore so does Work. As work is increased the more is needed to pull the roller coaster up.

=Section 4= What do you see? The kids who are on the roller coaster on Jupiter are having a lot more fun that the kids who are on the roller coaster on the moon. This is because Jupiter has a lot more gravity than the moon does. The direction of Earth's gravity is towards its core. The people in Australia who are at the bottom of the globe are held onto the Earths surface because gravity is pulling them towards its center.

Physics Talk A gravitational field is the gravitational influence in the space around a massive object. Earth is the source of a gravitational field. Gravity becomes less powerful the further you travvel away from the source. Inverse square relationship is the relationship between the magnitude of a gravitational force and the distance from the mass. Newtons law of universal gravitation is all bodies with mass attract all other bodies with mass; the force is proportional to the product of the two masses and gets stronger as either mass gets larger; the force decreases as the square of the distances between the two bogies increases. Fg = (Gm1m2)/r^2

Checking up questions 1) the direction of the gravitational field of the classroom is downward towards the ground. 2) The closer you are to the surface fo the earth, the stronger the gravitational field is. 3) If the distance is tripled, the force is 1/9th of what it was originally. 4) Gravity holds the moon in its orbit around the Earth. 5) The shape that the orbit takes around the sun is elliptical.

Physics To Go 1) If the force between 2 asteroids is double the new force would be 1/4th of what it was originally. 1/4th of 500 is 125. 125N  2) a) Fg= 1/4th  b) Fg= 1/9th c) Fg= 1/16th 3) Gravity will always be trusted because it is the force that allows us to stand without floating off somewhere uncontrollably. As long as there is mass, there will be gravity. 4) Acceleration due to gravity is less at the very top. 5) a) The water thats on the side of the earth is closer to the moon than the middle of the earth is.  b) there are high tides present when the body of water is facing the mood. Gravitational fields are attracted to water so the water rises and causes larger waves. c) The distribution of water on the Earths surface is uneven because there are small islands and peices of land throughout the oceans. The water is also all at different distances from the moon so there is different amounts of force acting on it. 6) a) All the fish would die because there would be nothing keeping them in the water. They would just float up into the air and die.  b) Because the fish's mass is less than the Earht's the Earth is able to keep it down in the water. 7) a) 1/4th b) 1/9th c) 1/16th d) 4 times 8) a) 2 times  b) 3 times c) 4 times d) 1/2 times 9) a) 4 times b) 9 times c) 16 times d) 1/16 times 10) a) 2 times  b) 9 times c) 6 times

Physics Plus 1) a= v^2/r 2) v=d/t v= 2(pi)(3.84)(10)^8/ 2440800 v= 998.5 m/s 3) a= v^2/r a = 998.505^2 / 3.84x10^8  a= .0025 m/s^2

What do you think now? Gravity definatey does have direction. Gravity is directed towards the center of the earth because thats the largest mass. People in Australia are able to stand upside down because gravity always points towards the center of the Earth so they are attracted to the Earths surface.

= Section 5 = What do you think? There are two different scales being shown. I dont think you could use the same scale because one weighs so much more than the other. A bathroom scale works by taking the compression of a spring inside and then multiplying it by gravity.

Physics Talk Hooks Law is the restoring force exerted by a spring is directly proportional to the distance of stretch or compression of the spring. The more force you apply on a spring the farther the spring stretches. F=-kx Scales work by calculating the compression of the spring inside it.

Checking Up 1) The stretch is 5 times as far. 2) The spring constant is the amount of weight a stretch can hold. the higher it is the more weight it can hold. 3) Youhave to multi[ly the amount by the gravity, 9.8. 4) The more you weight he more compressed the spring is, thus the larger number shown on the scale.

Physics To Go 1) a)w=mg w=100(9.8) w=980N b) w=mg w=10(9.8) w=98N c) w=mg w=60(9.8) w=588N 2) a)520N b)4000N c)200N 4) F=-kx 12=-.03k 400N=k 5) He means that as the force increases the stretch increases, and as it decreases the stretch decreases. 6) The 15N/cm spring because the higher the constant the stronger the spring. 7) F=kx 3=.02k 150N=k 8) The spring compresses as weight is placed on the scale. The compression is multiplied by k(the spring constant)

What do you think now? It would not be able to weigh those two things because they are such completely different weights. If an elephant were being weighed on the same scale and the canary was weighed correctly, the elephant would break the scale. If an elephant were weighed correctly and then the canary got on the same scale the spring would not even compress in the scale and you wouldn't get a weight A scale works by taking the amount of compression of the spring and then multiplying it by the spring constant.

=Section 6= What do you think? One large man is standing on a scale and the scale is reading 0. This is because the man is on an elevator moving downwards so gravity is negated. The other picture is of a small kid whos weight reads a high number because the elevator is moving up. No, because you are still going to be the same mass as when you started and the gravity is going to remain the same. Yes, as you ar going up a lift it would read a higher number than if you were going downhill.

Physics To Go 1) a) Vf= Vi+at Vf= 2(9.8) Vf= 19.6m/s b) Vf= Vi+at Vf=5(9.8) Vf=49m/s c) Vf= Vi+at Vf=10(9.8) Vf= 98m/s 2)a) Vf= Vi+at Vf=2(1.6) Vf=3.2m/s b)Vf= Vi+at Vf=5(1.6) Vf=8m/s c) Vf= Vi+at Vf=10(1.6) Vf=16m/s

4)

5) If someone who is actually 140lbs weighs 137lbs on a scale on an elevator, the elevator is accelerating downwards or decreasing speed upwards. Since the persons weight is down that means the acceleration has to increase downwards or decrease upwards. 6) As they accelerate upwards they will realize that they heavier than when the elevator was not moving. This is because as the acceleration upwards increases the force on the scale is greater. 7)a) While the elevator is moving downward the persons weight will appear lighter on the scale. b)W-F=ma 490-F=75 F= 415N 8)a) b)W-F=ma 490-F=100 F= 390N c)At a constant speed there is no acceleration so the weight read on the scale would be the persons normal and actual weight. 9)a) Without motion the forces up and down are equal so there is no change to the actual weight. b)When in a free fall there is only one force with any power. The force of weight going down is greater than the scale force pushing up so the scale would be 0. c} When there is acceleration upwards acceleration is positive. As acceleration goes up, so does the scale force and thats why the weight reads heavier than normally. 10) When you are inside of a loop there is always a change in acceleration and the people in the loop feel like they are hevier. This increases the thrill.
 * **Motion of the Elevator** || **Acceleration (up, down, zero)** ||  || **Relative Scale Reading (greater, less or equal to weight)** ||
 * At rest, bottom floor || Zero ||  || Equal ||
 * Starting at Rest, Increasing Up || Up ||  || Greater ||
 * Continuing to move, Constant Up || Zero ||  || Equal ||
 * Slowing down to top floor, Decreasing Up || Down ||  || Less ||
 * At rest, top floor || Zero ||  || Equal ||
 * Starting at rest, Increasing Down || Down ||  || Less ||
 * Continuing to move, Constant Down || Zero ||  || Equal ||
 * Coming to a stop on the ground floor || Up ||  || Greater ||

What do you think now? No, your actual weight does not change. Even though your apparent weight may change your actual weight stays the same. Yes, because your apparent weight would change dependent upon the accelerations of the roller-coaster. Whether it is accelerating up or accelerating down your weight on the scale would change. When you first begin to increase speed up an incline you would be heavier. As you are slowing down at the top of an incline you would feel lighter because your acceleration goes down.

=Section 7= What do you think? There is a cart traveling a path and when it gets to the first curve it is goin to fast and the cart almost tips completely over. You stay in a cart while going through a loop because you are accelerating a lot and feel a lot heavier than normal.

Physics Talk Centripital acceleration always points to the center. Always acceleration. If equal to 0m/s^2 then you are moving in a straight line. Tangental velocity is mostly constant. (uniform circular motion) Equation= Fc=mv^2/R. By increasing R you lower Fc. By increasing mass you increase Fc. By increasing velocity you increase Fc. Safe accelerations are less than 4gs. Trained people have a maximum of 6gs. Circular loop's radius is always the same. Clothoid loop's radius changes throughout the loop. High speed and small radius is dangerous.

Checking up questions 1) Centripital force 2) Yes because you are always changing your direction. 3) Weight and normal forces are the forces that effect it. 4) Normal force determines your actual weight. 5) Direct relationship with mass. inverse with Radius. Direct square with velocity.

Physics To Go 1)a) It would travel in a circle. b) When the string makign it go in a circle broke it would continue in a straight path tangent to the circle. 2)a) Friction takes its place. b) Since there is no friction on a patch of ice you would no longer have a force to keep you moving in a circle so you would end up going stright instead of in a circle. 6)a) No, it doesn't change. b) Yes, because its direction changed. 7) Ac=v^2/r Ac=400/200 AC= 2m/s^2 10)a) A really fast coaster. b) A slow roller coaster
 * || Required Fc (N) || Required Weight (N) || Normal Force (N) ||
 * top of the loop || 4000 || 500 || 3500 ||
 * bottom of the loop || 6000 || 500 || 6500 ||
 * || Required Fc (N) || Required Weight (N) || Normal Force (N) ||
 * top of the loop || 800 || 500 || 300 ||
 * bottom of loop || 2800 || 500 || 3300 ||

13)a) Heavier b)Can't tell c) Heavier d) Heavier e) Same 14)a) Up b) Down c) Up d) Up e) None f) Towards the center g) Towards the center

Physics Plus 1)a) When the F force increases the mass increases, the velocity stays the same, and its radius stays the same. b) It is relationship is squared so if the velocity doubles, it quadrouples. 2) The force would be quadrupled. 3) It is indirectly proportional so as one gets bigger the other gets smaller. 4) The wider the turn the less force is needed to keep the cart on the track and vice-versa. 5) I f you were to let go of the stopper, it would continue in a straight line motion without any force.

What do you think now? What causes you to stay in the seat during a rollercoaster irde is inertia. When you go through a loop you feel heavy and pressed down into your seat so you are safe.

=Section 8=

What do you think? There is a roller coaster cart going up a steep incline and people are pulling it up. the people are struggling and they are sweating. It is a lot harder to pull something up a steep incline because when you are pulling it up a steep incline more of the weight is pointing straight down and not to one side.

Physics Talk Work is the product of displacement and the force in the direction of the displacement; the energy transferred to an object. Force is larger on a steeper incline but the distance along the incline was smaller vertical displacement is the height that it must be lifted W is the same regardless to the angle of the incline

 Checking Up Questions 1) The energy at the top is transferred into GPE.  2) The coaster gets its GPE from the work that the cart has while getting up the hill.  3) Truckers use a ramp because they need less force for a longer distance.  4) The roller coaster's kinetic energy is transferred into work because of the friction.  5) J/s, also known as watts.

 Physics To Go 1)a) The cart only has GPE at the top before it is moving but at the bottom of the ramp there is no GPE. <span style="color: #000000; font-family: Arial,Helvetica,sans-serif; font-size: 110%;"> b) All the work is done by gravity. <span style="color: #000000; font-family: Arial,Helvetica,sans-serif; font-size: 110%;"> c) All the work is done by the spring <span style="color: #000000; font-family: Arial,Helvetica,sans-serif; font-size: 110%;"> d) 1/2 kx^2 <span style="color: #000000; font-family: Arial,Helvetica,sans-serif; font-size: 110%;"> e) The energy is kinetic and GPE. <span style="color: #000000; font-family: Arial,Helvetica,sans-serif; font-size: 110%;"> f) The cart begins to slow down as it starts compressing the spring <span style="color: #000000; font-family: Arial,Helvetica,sans-serif; font-size: 110%;"> 2)a) zero because it is perpendicular work not parallel <span style="color: #000000; font-family: Arial,Helvetica,sans-serif; font-size: 110%;"> b) w=fd <span style="color: #000000; font-family: Arial,Helvetica,sans-serif; font-size: 110%;"> w= 60(.5) <span style="color: #000000; font-family: Arial,Helvetica,sans-serif; font-size: 110%;"> w=30J <span style="color: #000000; font-family: Arial,Helvetica,sans-serif; font-size: 110%;">c) w=FD <span style="color: #000000; font-family: Arial,Helvetica,sans-serif; font-size: 110%;"> w= 75(40) <span style="color: #000000; font-family: Arial,Helvetica,sans-serif; font-size: 110%;"> w= 3,000J <span style="color: #000000; font-family: Arial,Helvetica,sans-serif; font-size: 110%;"> d) w=FD <span style="color: #000000; font-family: Arial,Helvetica,sans-serif; font-size: 110%;"> w= 500(.7) <span style="color: #000000; font-family: Arial,Helvetica,sans-serif; font-size: 110%;"> w= 350J <span style="color: #000000; font-family: Arial,Helvetica,sans-serif; font-size: 110%;"> 3) A better way of saying conserving energy is saying don't waste it. The law of conservation of energy says to convert it into different forms. Energy is never wasted. <span style="color: #000000; font-family: Arial,Helvetica,sans-serif; font-size: 110%;"> 4) The mass on the cart would have changed because of the clay people so it would need more force to bring the cart up. There would be more work done and the GPE would be more. <span style="color: #000000; font-family: Arial,Helvetica,sans-serif; font-size: 110%;"> 5)a) w=FD <span style="color: #000000; font-family: Arial,Helvetica,sans-serif; font-size: 110%;"> w= 10,000(20) <span style="color: #000000; font-family: Arial,Helvetica,sans-serif; font-size: 110%;"> w= 200,000J <span style="color: #000000; font-family: Arial,Helvetica,sans-serif; font-size: 110%;"> b) P= W/T <span style="color: #000000; font-family: Arial,Helvetica,sans-serif; font-size: 110%;"> p= 20,000/150 <span style="color: #000000; font-family: Arial,Helvetica,sans-serif; font-size: 110%;"> p= 133.3 W (J/s) <span style="color: #000000; font-family: Arial,Helvetica,sans-serif; font-size: 110%;"> 6) Up the first incline, there is work which changes to GPE at the top. Down the hill there is KE which is changed into KE and GPE when going through a loop. It changes to KE when you are going through the horizontal loop. WHen you get to the second hill there is GPE and KE, and finally there is work done at the end to stop the cart.

<span style="color: #000000; font-family: Arial,Helvetica,sans-serif; font-size: 110%;"> What do you think now? <span style="color: #000000; font-family: Arial,Helvetica,sans-serif; font-size: 110%;"> It does take more energy to pull a cart up a steeper incline. The steeper the incline, the more force is neede, and therefore there is more energy used. =Section 9=

What do you think? The part of the snake that s going to be the most thrilling will be the points where there is a high velocity and a high accelerations. so the points where there are sharp turns and steep slopes will be the most thrilling. If it stays at the same speed the roller-coaster will still be fun when there is a sharp change of direction. the inclines will also still be fun because of the change in acceleration.

Physics Talk A number with both quantity and direction is called a vector quantity. Distance and speed are scalar quantities. To solve for a vector you use pythagorean theorem. Energy is a scalar quantity because to find the total energy you just add all the energies of the system together. A roller coaster cart at the same heights will have the same speed. The steeper the slope, the more gravitational force pointing down and so the bigger the acceleration is. On a straight incline, the normal and weight force are constant and so is the acceleration.

Checking Up Questions 1) Pythagorean theorem. 2) Energy is a scalar quantity and force is a vector. 3) It tells you that on a ride where friction is insignificant, KE+GPE will always equal the same thing, gravity and mass are constant so the GPE is depended on its height, and if the roller coasters are at the same height, they will be going at the same speed too. 4) The path doesn't effect it  5) Friction must take place.

Physics To Go 2) They have the same gravitational potential energy at the top because they start at the same height so at the bottom they will have the same kinetic energy, and therefore the same velocity. 3)a) distance- scalar  b) vector c) scalar d) vector e) vector f) vector g) scalar h) scalar i) work- vector 4)a) scalar  b) vector c) scalar d) vector 5) The roller coaster comes the first hill, it uses kinetic energy and work to get up the hill. When it is at the top of the hill the energy is converted into GPE. As is goes down the hill the GPE becomes less and the KE is greater. ﻿b) They are all the same speed because the GPE does not change.

c) Since the GPE does not change and the mechanical energy is always the same, this means the the KE is the same.

d) Nothing else matters other than the height because gravity and mass are always constant throughout a ride, so the only thing that changes GPE is height. If GPE is

equal at all three points the KE must be equal at those 3 points as well

What do you think now?

The most thrilling part would be the turns. Since the speed remains the same throughout the ride, the most thilling part would be the change in acceleration witch would

be during the turns.

= Section 10 =

What do you think? The picture shows a large roller coaster with a lot of carts on it. The ride is very dangerous because there are people falling off the ride. I feel like if i knew that people were falling off the roller coasters and getting severely injured i would not want to go on the ride, no matter how thrilling it would be.

Physics Talk Safety is the most important thing that a roller coaster can possess. In order for a roller coater to be rendered safe there must be no point on the roller coaster in witch the force of gravity is higher than 4 g's. Greater accelerations cause more g's. To lessen the amount of g's you must lessen the amount of acceleration. To do this you can decrease the speed, or increase the radius of turns. No matter where on a roller coaster there is always forces N and W acting on it.

Checking Up Questions 1) The max amount of g's a human can endure is 4. 2) You can decrease the speed the cart has entering the loop by making the drop that leads to the loop. Another thing you can do is increase the radius of the loop. 3) When the cart is at the top of the loop. 4) When its at the bottom of the loop.

Physics To Go 1) To make sure that a ride is safe i would find the centripetal acceleration on all the curves, and then divide it by gravity. If this number is under 4 g's the turns are safe and then i would go on the roller coaster. 2)a) b) a=v^/r a=20^2/12 a= 33.3m/s^2 c) Not safe, it is over 4 g's. d) 39.2=v^2/12 39.2(12)=v^2 470.4=v^2 21.69m/s=v e) 39.2=v^2/7 39.2(7)=v^2 274.4=v^2  16.57m/s=v  3)a) a=v^2/r  a= 25^2/10  a= 62.5m/s^2  b) Yes 4)a) GPE=KE mgh= mv^2 9.8(50)= v^2 490=v^2 v=31m/s b) a=v^2/r a= 22.12^2/10 a= 96m.s^2 c) d) a=v^2/r 24^2/10 a= 58 m/s^2 e) No, it is not safe because it is higher than 4 g's at the end of the roller coaster. 5)a) a=v^2/r 9.8= v^2/8 8.9m/s=v b) GPE=KE+GPE mgh=1/2mv^2+mgh 9.8h=1/2(9.8)^2+9.8(16) h=20m 6)a) a=v^2/r a= 12^2/18 a= 8m/s^2 b) Fc=mv^2r Fc= 900(12)^2/18 Fc= 7200N c) The normal force and the friction of the wheels on the track. 7) Yes, it is safe because the roller coaster can hold 25000N and the force is only 24000. 8)a) A change in mass will not change the Centripetal acceleration because is not used to calculate it. b) It will not matter because since there is mass on both sides of the equation the amounts cancel out. c) The weight effects the strength of the track.

What do you think now? I still think that if a roller coaster has a death toll i would not go on the roller coaster. I would not put my life on the line just to get a thrill from a roller coaster, i would much rather live. The thing you have to be the most careful about is the loop on a roller coaster. This is where the acceleration is the greatest and therefore the ride is the most dangerous. If the roller coaster has a part of it where the acceleration is greater than 4 g's it is dangerous.