Ch4+BensonR

= Wiki Chapter 4 = toc

Section 1 What do you see? A person is pushing a boy in a chair with a blindfold on, in order to simulate a roller coaster. He is picturing a roller coaster as she moves him about. What do you think? The part of the roller coaster right before the roller coaster comes to a sudden drop as it approaches max speed. This is because the anxiety of knowing you are about to drop or starting to drop and plummet towards the earth builds up until its almost unbearable. Also many people don't like height so seeing the ground from max height is a little dizzying. HW Steel Dragon 2000 Intimidator 305 A Giga Coaster is a complete-circuit roller coaster with a height between 300 and 399 feet. The term was coined by a Cedar Point and Intamin AG partnership after the construction of Millennium Force. There are three Giga coasters worldwide: Millennium Force at Cedar Point, Steel Dragon 2000 at Nagashima Spa Land in Japan, and Intimidator 305 at Kings Dominion. Millennium Force and Intimidator 305 were built by Intamin AG while Steel Dragon 2000 was built by Chance-Morgan. What do you think now? The parts that will emulate the greatest thrills are the parts where there is a change in acceleration and direction. Where people feel the greatest thrill, there is a lot of screaming. They will experience acceleration on and sloped parts of the ride as well as coming out of a loop.

What do you see? There are people riding a roller coaster the people going down the steep incline are excited and thrilled while the ones rolling on the flat section are asleep and bored. What do you think? The steel roller coaster will give a bigger thrill because the angle of the roller coaster is much higher, meaning higher acceleration and thrill. PTG 1. The assuming there is no friction speed at the bottom of the track will be equal for both a and b because speed is relative to initial height, which is equal. 2. The biggest thrill assuming there is friction would be track B because it is steeper thus has a higher acceleration. **Physics To Go** 5. Total energy present in the first hill must be greater than the energy in the second hill. 6. Energy is lost due to friction and air resistance. 7. GPE=mgh GPE=(300)(9.8)(15) GPE= 44100 J 8a. KE=(1/2)(m)(v^2) KE= 45000 J 8b. If KE is 0, GPE= 45000 J 8c. GPE=mgh 45000= (400)(9.8)(h) 11.48m= h 9. GPE is increasing 10. The same- they all have the same maximum height and equal mass 11a. Yes 11b. GPE=EPE mgh=EPE (0.020)(9.8)(0.4)=EPE 0.0784 J=EPE 11c. 0.0784=GPE 0.0784=mgh 0.0784=(0.06)(9.8)(h) 0.13m=h 12a. GPE=EPE 52920=(1/2)(k)(x^2) 6615 N/m= k 12b. GPE=EPE 70560=(1/2)(k)(x^2) 4.6m = x 13. EPE=KE (1/2)(k)(x^2)=KE 1.8 J = KE What do you think now? The conservation of energy from GPE is transferred into KE which is than transferred into GPE when reaching max height. Yes it costs more to lift more people because there is more force needed to reach max height, the more GPE, the more work needed to get to max height, thus costing more money in electricity. = Section 4 = What do you see? There are identical roller coasters on the moon and jupiter, the people on jupiter are having more fun because there is a higher gravity on Jupiter resulting in more force and acceleration.

What do you think? Gravity is directed towards the center of the earth so people in australia are held towards the ground even though they are "upside down" because gravity pushes them towrds the core of the earth not in one single direction. = Section 5 = What do you see? A butcher shop weighing meat by the pound or kilogram and a science lab using newtons to calculate the weight of the meat. What do you think? You cannot use the same scale because different scales are rated for certain weights. If a scale able to weigh an elephant weighs a canary, it might not be able to detect the weight. If a scale that is able to weigh a canary is used to weigh an elephant, the scale would break. A bathroom scale works by having sensors in the legs that measure the amount of force applied to the legs when stepped on. Section 6 What do you see? Two people are in elevators, one moving up one moving down. The lighter person is in the elevator going up yet the scale is reading a big number. In the elevator going down, the scale is reading 0 even though the man is large. What do you think? Your weight changes due to your position and motion on a scale, but your mass does not change.

PTG Section 6, PTG #4
 * **Motion of the Elevator** || **Acceleration (up, down, zero)** ||  || **Relative Scale Reading (greater, less or equal to weight)** ||
 * At rest, bottom floor || 0 ||  || equal ||
 * Starting at Rest, Increasing Up || v=up a=up ∑=up ||  || greater than weight ||
 * Continuing to move, Constant Up || 0 ||  || equal ||
 * Slowing down to top floor, Decreasing Up || v=up a=down ∑=down ||  || less than weight ||
 * At rest, top floor || 0 ||  || equal ||
 * Starting at rest, Increasing Down || v=down a=down ∑=down ||  || less than weight ||
 * Continuing to move, Constant Down || 0 ||  || equal ||
 * Coming to a stop on the ground floor || v=down a=up ∑=up ||  || greater than weight ||

Section 6
**What do you See?** There are two people standing in an elevator, one is heavier than the other. The heavier one is going down in the elevator and his weight is 0. The lighter person is going up in the elevator and weighs 200 pounds. **What do you Think?** Weight changes as you position in relation to sea level changes. It is documented that in certain places you weigh differently due to the force of gravity in the area.

**Physics Talk Summary** An object at rest has zero net force. Newton’s first and second law describe this because there is no acceleration. Force must equal zero in regards to the second law and an object in motion stays in motion or an object at rest stays at rest unless acted upon by a force. It is the same as an object in constant speed. There is no net force because there is no acceleration. At constant speed or at rest, there is the same amount of force acting on you as the force of weight that you are providing. If you are accelerating, like accelerating up on a roller coaster for example, there is a net force acting on you. If you are accelerating up, the force of gravity isn't as strong on you so it appears that you weigh more. F=ma- to calculate acceleration Fscale= weight due to scale -ma When you are accelerating upward you feel you are heavier because of the drop of your stomach and your nerves. When an elevator is accelerating down, you feel that you weigh less. Everything on earth has an acceleration of 9.8 m/s squared in free fall but that is ignoring air resistance. Air resistance slows something down. It is always there are it is hard to ignore. Wind is an example of air resistance.

**Checking up Questions** ** 1.When at constant speed, net force is 0. ** ** 2.The person is accelerating upwards on a roller coaster making normal force greater. ** 3. You feel heavier when on a roller coaster when the cart is pushing up on you. There needs to be a certain amount of force on you in order to keep you from falling out and to keep you innards in place. The force exerted by the cart is greater than weight. 4. In free fall objects are moving a the same rate thus the contact force on the scale would be 0. 5. It slows down due to air resistance.

**Physics to Go** ** 1. ** ** a)vf= vi+at **  ** 0 +9.8*2= 19.6 m/s **  b)** vf=* **5= 49 m/s c)** vf= vi+at ** 0+9.8*10= 98 m/s  ** 2. **  ** a)vf= vi+at ** ** 1.6*2= 3.2 m/s ** ** b)vf= vi+at ** ** 1.6*5= 8 m/s **  ** c) vf= vi+at ** ** 1.6*10= 16 m/s ** ** 4.) ** ** 5. f=ma **  ** 137-140=0 **  ** The elevator is increasing down or decreasing up. **  6. The person will feel heavier because Normal>Weight, as the elevator accelerates more the weight will increase. 7a.) The scale will read lighter than their normal weight. 7. b) F= ma  n- mg=ma  N=ma+mg  N= (50x-1.5)+(50x9.8)  N= 415 N  8.  a) 1=mg W=9.8*50 w=490 N b) N-W=ma  N=mg+ma  N=(50 x9.8) + (50x 2)  N=590 N  9. In the first cartoon, the person on the elevator is moving at constant speed, if he is at constant speed there is no change in velocity or acceleration thus there is no change in net force. In the first sketch the person on the elevator is moving at a constant speed. Apparent weight is equal to normal weight.  In the second cartoon, the person is increasingly accelerating down. They are in freefall which means all objects are falling at the same rate and the contact force between the person and the scale. There is no normal force.  In the last cartoon, the elevator is accelerating upwards so the person feels heavier. Normal force is greater than weight, which is apparent because the person weighs 100N more than his mass. Therefore apparent weight is greater than normal weight. The floor is exerting 100 N more mass than the person is on the scale. Their normal force is higher than their weight and therefore their apparent weight is more than their normal weight.
 * **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 ||

10. Our roller coaster acceleration should be high because the initial height is very high and is intended for adults. In order to be safe, acceleration due to gravity would have to be less than 5 G’s because anymore and it would be dangerous for a person.

**What do you Think Now?** Apparent weight changes but actual weight does not change when riding on a roller coaster. You feel like your weight is changing but it really isn't, your weight if measured on a scale during the coaster would change. When you are going up a hill you feel heavier then when you are at the bottom of a hill, and your weight on a scale at the top of the hill would be heavier. This is because normal force is greater than weight at the top compared to the bottom.

Section 7
What do you see? There is a roller coaster where the cart is going up and down hills and through loops. At a curve, the cart and people begin to topple over.

What do you think? You don't fall out of a cart during a loop because the speed and momentum of the cart keep the objects in it, in motion.

Physics Talk -centripetal force is any force that points to the middle of the circle. -centripetal acceleration always points to the center -tangential velocity -speed is usually constant but there is always acceleration if ac is = to 0 then you are moving in a straight line. equation is EFc=mv^2/R= Ac -increase in radius makes centripetal force go down -when the mass is increased, the force increases -increase in velocity =increase in force as well. -to find apparent weight - identify the acceleration, find the force. Ac+F=the bigger force -less than 4G’s of force is safe for humans, anything more and you could be injured clothoid loop- at the top the radius is smaller and bigger at the bottom.

Checking Up 1. In order for an object to travel in a circle it needs to have centripetal force. 2. When you travel in a circle, your direction constantly changes thus you are accelerating centripetaly 3. At top of a loop, the weight and normal=Fc. 4. Your apparent weight is due to normal force. 5. Centripetal force is larger when speed is increased (direct), mass is increased (direct), and radius is shorter (inverse).

PTG

1. a. The path of the car would be circular.

b. The car would travel in a path tangent to the point it was traveling at when the string broke.

2. a. Friction replaced the string of the toy car.

2. b.    a. The speed of the roller coaster stayed at 20 m/s. b. The velocity changed because direction changed. c. ∆ velocity=28.2 m/s 45 degrees NW V2 - V1 = change in V  20m/s ^, 20 m/s < 20^2 + 20^2 = c ^ 2 c = 28.2 m/s tan(x) = 20/20 = 45 7. Ac = v^2 / r  = 20^2 / 200 = 2 m/s^2 10. Fast Moving Roller Coaster Slow-moving roller coaster 13. a. Bottom of hill #1- heavier b. Top of vertical loop- uncertain c. Bottom of vertical loop- heavier d. Bottom of hill #2- heavier e. Lift hill (going up at constant speed)- normal
 * || Required Fc || Force of gravity (weight) || Normal force (the force of the track on the car) ||
 * Top of the loop || 4000 N || 500 N || 3500 N ||
 * Bottom of the loop || 6000 N || 500 N || 6500 N ||
 * || Required Fc || Force of gravity (weight) || Normal force (the force of the track on the car) ||
 * Top of the loop || 800 N || 500 N || 300 N ||
 * Bottom of the loop || 2800 N || 500 N || 3300 N ||

14. a. Bottom of hill #1- up  b. Top of vertical loop- down c. Bottom of vertical loop- up d. Bottom of hill #2- up  e. Lift hill (going up at constant speed)- zero f. Horizontal loop- center g. Back curve- center

Physics Plus 1. a. Fnet increases. The mass increases but the velocity stays the same and the radius stays the same, thus increasing the net force. b. If the velocity increases, the Fnet also increases because it has a direct squared relationship with V. 2. The strength of the track must be quadrupled. 3. The Fnet gets smaller if the radius gets larger because they are indirectly proportional. 4. The larger the radius of the curve, the smaller the force required to keep the car moving along the curve assuming speed increases at the same ratio. If the radius of the curve is small, then a larger force is required. 5. If you were to let go of the stopper, it would continue in a straight line of motion without any force tangent to the point where it was traveling when it was let go.

What do you think now? You don't fall out of a roller coaster car when you are upside down because net force along with centripetal force points toward the center but you are not upside down long enough to move because you are already on another part of the circle. You feel this in your stomach because you are pressed into your seat by inertia.

Chapter 4- Section 8
**What Do You See?** There are carts climbing a big hill on the left and as they approach a big drop they appear nervous. The slope is so steep on the way down that their hats are blown off. **What Do You Think?** Work= Force*Distance, so it should not require more work to pull a cart up a steep slope than on a gentle slope because distance is constant and so is force. It is more difficult to go up a steep slope because it requires you to travel more distance in less time.

**Physics Talk** 4/12/11 **Summary** Displacement is parallel to force in a work equation. As incline increases, force needed increases but the distance width-wise is shorter. Work along an incline is always constant. KE is transferred to EPE when the cart hits the brakes or springs in order to stop. Power=Work/Time or P=W/∆ T Power= speed from which the work is transferred into energy. Power is measured in watts (J/s).

**Checking Up Questions** 1. The energy at the top is transferred into GPE. 2. Work is converted to GPE while the cart climbs the hill until it plateaus, where GPE is the total energy. 3. Truckers use a ramp because they need less force for a longer distance. 4. Ke is transferred to work due to friction and KE decreases. 5. The unit for power is watts.

**PTG** 4/16/11 1.  a)At the top, GPE is full and at the bottom it has less.  b) Work=∆GPE. c) Work=EPE d) EPE=1/2kx^2 e) Because it is not all the way at the bottom, Total energy= mostly kinetic but a little GPE. f) It decelerates when it first hits the spring. 2. a) The work=0, force and distance are not perpendicular.  b) W=F*d =(60)(.5) =30 J  c) W=F*d  =(75)(40)  =3,000 J  d) W=F*d =(500)(.7) = 350 J  3. Too much using, is abusing. Decrease energy consumption, don't waste energy. 4. There would be more GPE because if mass increases, the necessary force increases which means work increases. 5. a) W=F*d  =(10,000)(20)  =200,000 J  b) P=W/t =20,000/150 =1,333.33 W  6. To get up the first incline, work has to be done which is converted into GPE as it approaches the top. At the top GPE=total energy. As it begins to fall, GPE is converted into KE where at the bottom of the first hill KE= total energy. As it approaches the vertical loop Ke is converted into GPE, then back to KE as it passes through the top of the loop to the bottom. There is still A little GPE as it enters the back curve but still mostly KE as it is low to the ground and in the horizontal loop what little GPE there was is converted to KE which hits the braking system and conis converted into work due to EPE.

**What Do You Think Now?** 4/16/11 It takes less time but more energy to move a roller coaster cart up a steep incline than a gentle incline. The amount of distance traveled in a certain amount of time is greater. Due to Newton's law of conservation, Work=GPE. Mass is a factor in this equation as GPE=mass*gravity*height. Thus it is less difficult to walk up a gentle slope because more force is needed to travel over the same distance in larger increments. Height = distance in these problems. There is an inverse relationship between force in distance when traveling up an incline.

Section 9
What do you think? Knowing that people died will probably induce more endorphins when going on the ride thus increasing thrill because you know you might die. My answer does not change, would I personally go on the ride? No.

What do you see? There is a girl and a boy, the girl is thinking in energy and has a lot written down. The boy is thinking in force and is struggling to write anything down.

What do you think? Thrill is caused mostly in part by change in acceleration, thus the parts of the snake that will be the most exciting will be the turns, hills and loops. People find thrill in speed and acceleration, so as the coasters speed increases so does thrill. If the speed stayed the same the whole ride, the coaster would be very boring.

Physics Talk - barring friction, the mechanical energy, GPE+KE, is equal at any point on the coaster. - if 2 points on a coaster have the exact same height, mechanical energy is equal and so is speed - on a straight line gravitational force and normal force remain constant in the same direction - a car has an acceleration remaining constant in magnitude as well as direction - a curved line has a normal force that changes direction and magnitude which creates large thrills for the riders - scalar: size; speed, energy, mass, time - vector: has direction and size; force, momentum, acceleration, velocity - vector addition, use Pythagorean theorem to find the resultant and trigonometry to find the angle - force in the direction of motion= work

Checking Up 1. Pythagorean Theorem. 2. Energy is scalar, force is vector. 3. GPE is only height dependent since gravity is unchanging and so is mass, if two points on a coaster are equal in height they are equal in speed as well. 4. The path does not affect it. 5. Work or any type of force is required.

PTG 1a. a2 +b2=c2 25+25=c2 50=c2 c= 7.07m/s SW 1b. tanx= 5/5 x= 45 degrees 2. These coasters have the same GPE= same KE= same Velocity 3. a) distance: scalar  b) displacement: vector c) speed: scalar d) velocity: vector e) acceleration: vector f) force: vector g) KE: scalar h) GPE: scalar i) work: vector 4a) scalar b) vector c) scalar d) vector 5. In order to get up a hill, KE, work and mechanical energy are needed, once at the top these energies are converted into GPE and is it falls down the hill GPE is converted into KE. At the bottom of hills Normal force is greater but as you approach the top Weight is greater than Normal as your body wants to keep rising but the cart stays on the track. This feeling feels like free fall.6.  c) Normal force is always perpendicular to the object it is being measured on, therefore it is easier to measure the roller coaster in force rather than scalar.

b) The points have the same height = equal amount of energy. c) The amount of energy will be the same as GPE at the top is the same so KE at the bottom of the hill will be the same as well. d) They all have the same amount of energy so you do not need to look at the other points. Mass Gravity and Height are the same so the answers at every single point will be equal.

What do you think now? Quick changes in direction and acceleration will be the most exciting feature for thrill seeking roller coaster riders. This is because change in direction, speed and acceleration cause thrill. If speed stays constant, the ride can still be thrilling if there are changes in direction like loops, back curves and corkscrews because although the speed doesn’t change direction is changing which also means acceleration is changing.

Section 10
What do you see? The roller coaster has no safety railings or equipment and has many issues with staying on the track. There are people falling out, carts falling off the tracks, and the acceleration is extremely high at points. Physics Talk - safe acceleration for humans is under 4g - free fall causes an acceleration of 1g - roller coaster inclines are not straight drops so they do not induce freefall, therefore you cannot accelerate more than 1g on a straight track - When on curved tracks and loops acceleration can exceed 1g - Centripetal acceleration is a= v^2/r - Acceleration can be modified decreasing speed or increasing the radius of the curve - largest centripetal acceleration is felt at the bottom of the loop - Total force is a combination of weight of the cart and normal force exerted from the track. - normal is required when it is moving in a circle at the bottom of the loop it is much greater than the normal force needed when it is at rest at the bottom of an incline - when moving in a vertical circle, centripetal force is required - centripetal force is fnet= ma or Fnet= mv^2/r - support force, is normally equal to your weight - if you experience 2gs= double your weight because support force is double your weight - heaviness is based on support force - free fall= weightless because there is no support force - acceleration at the top of a loop must be at least 1g, or you will start to free fall.

Checking Up 1. 4gs is the maximum safe acceleration. 2. Acceleration can be decreased by a decrease in speed or increase in radius. 3. At the bottom of the loop. 4. At the top of the loop.

PTG 1. In order to make a roller coaster safe, I would check where acceleration is greatest ie. the bottom of loops and hills and at the top of the loops to ensure acceleration is at least 1g. The points where acceleration can be great should not exceed 4gs as a human may pass out due to the blood rush. 2 a) mgh+1/2mv^2  = 20m  b) a=v^2/r a= 20^2/12 a= 33.33 m/s^2 c) Yes, it does not exceed 4g. d) a=v^2/r 36.9= v^2/12 v= 22m/s e)a=v^2/r 39.6=v^2/7  v= 17m/s  3.  a) a=v^2/r a= 35^2/10 a= 62.5m/s^2 b) No, it exceeds 4g. 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) v= square root of 49.02 (10) v= 22.12m/s d) a= v^2/r a= 24^2/10  a= 58 m/s^2  e) This roller coaster is unsafe because at the bottom of the loop the acceleration is greater than 4gs. 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(8.9)^2+9.8(16) h= 20.1m 6. a) a=v^2/r  a= 12^2/18  a= 8m/s^2  b) Fv=mv^2r Fc= 900(12)^2/18 Fc= 7200N c) The friction from the track on the wheels. 7.  a) a=v^2/r a= 20^2/15 a= 26.7m/s^2 b) Fc=mv^2/r 900(20)^2/15  Fc= 24000N  c) The coaster can withstand 25000N, this means it is able to support the 24000N force. 8 a) No, it is not mass dependent, it’s not in either formula.  b) No, mass cancels out c) When the weight gets larger the normal force must compensate and increase, the strength of the track is solely dependent on the weight it is rated to withstand.

Physics Plus

What do you think now? If I knew a roller coaster could cause injury and/or death i would not ride it, I ride roller coasters for thrill knowing I will be safe no matter what, not to put my life at risk. This goes along with if I knew half the people that rode a certain ride died, 50% is a HUGE percentage of death. This percentage is big an due to how unsafe the roller coaster is, it might be shut down by the countless amount of lawsuits from the loved ones of the deceased. An acceleration higher than 4g can cause unnecessary altercations and although it would seem awesome to go at such a high rate of acceleration, it would not be fun to see everyone next to you pass out or die as you begin to black out. You want to go at a low enough G to keep people from injury, but high enough to be able to complete a loop without falling.