Andrea+and+Maddi

ACTIVITY A: The First Drop of a Roller Coaster Rollercoaster: Nitro

PART A) At the park 1) Estimate distances and angles the Bottom of the Hill || Radius of curve at the Bottom of hill || Angle of Initial Incline up and the Angle of the Initial incline down ||
 * Height of Starting Point || Height of the Top of the Hill || Height of
 * 0m || 71m || 5m ||  || 68 ||

2) Measure time
 * Trials: || <span style="font-family: Tahoma,Geneva,sans-serif;">To Travel up First Hill(s) || <span style="font-family: Tahoma,Geneva,sans-serif;">To Travel Down First Hill (s) ||
 * <span style="font-family: Tahoma,Geneva,sans-serif;">Trial 1: || <span style="font-family: Tahoma,Geneva,sans-serif;">47.9 || <span style="font-family: Tahoma,Geneva,sans-serif;">6.9 ||
 * <span style="font-family: Tahoma,Geneva,sans-serif;">Trial 2: || <span style="font-family: Tahoma,Geneva,sans-serif;"> 48.1 || <span style="font-family: Tahoma,Geneva,sans-serif;">6.5 ||
 * <span style="font-family: Tahoma,Geneva,sans-serif;">Trial 3: || <span style="font-family: Tahoma,Geneva,sans-serif;">48 || <span style="font-family: Tahoma,Geneva,sans-serif;">6.9 ||
 * <span style="font-family: Tahoma,Geneva,sans-serif;">Trial 4: || <span style="font-family: Tahoma,Geneva,sans-serif;"> 48.3 || <span style="font-family: Tahoma,Geneva,sans-serif;">6.7 ||
 * <span style="font-family: Tahoma,Geneva,sans-serif;">Trial 5: || <span style="font-family: Tahoma,Geneva,sans-serif;"> 48.2 || <span style="font-family: Tahoma,Geneva,sans-serif;">6.6 ||

<span style="font-family: Tahoma,Geneva,sans-serif;">3) Diagrams <span style="font-family: Tahoma,Geneva,sans-serif;"> <span style="font-family: Tahoma,Geneva,sans-serif;"> <span style="font-family: Tahoma,Geneva,sans-serif;"> <span style="font-family: Tahoma,Geneva,sans-serif;"> <span style="font-family: Tahoma,Geneva,sans-serif;">d. Take a clear side view picture <span style="font-family: Tahoma,Geneva,sans-serif;"> <span style="font-family: Tahoma,Geneva,sans-serif;">http://mojraj.wordpress.com/2010/05/23/six-flags-great-adventure/

<span style="font-family: Tahoma,Geneva,sans-serif;">e. Take a short video of the relevant segment for future reference

media type="file" key="IMG_1436.3gp" width="300" height="300"

<span style="font-family: Tahoma,Geneva,sans-serif;">a. Create d vs. t, v vs. t and a vs. t graph for the motion this segment of the ride. <span style="font-family: Tahoma,Geneva,sans-serif;"> <span style="font-family: Tahoma,Geneva,sans-serif;">b. Create a thrill vs. acceleration graph for this segment of the ride.
 * <span style="font-family: Tahoma,Geneva,sans-serif;">4) Graphs **



<span style="font-family: Tahoma,Geneva,sans-serif;">a. Safety: What features were in place? <span style="font-family: Tahoma,Geneva,sans-serif;">b. Describe the weight sensations on the way up, on the way down, and at the bottom of the first hill: did you feel lighter, heavier, or normal? <span style="font-family: Tahoma,Geneva,sans-serif;">c. Describe the excitement level: on the way up, on the way down, and at the bottom of the first hill. <span style="font-family: Tahoma,Geneva,sans-serif;">d. Describe the thrill factors that may contribute to those feelings (besides the #g’s)
 * <span style="font-family: Tahoma,Geneva,sans-serif;">5) Evaluate **
 * <span style="font-family: Tahoma,Geneva,sans-serif;">There was a bar lap that prevented the passenger from flying out the ride. You couldn't get out of the seat because it was tightly around you.
 * <span style="font-family: Tahoma,Geneva,sans-serif;">You felt heavier on the way up because you were pushed back. On the way down, you felt lighter. At the bottom you feel normal because the normal and weight forces are equal.
 * <span style="font-family: Tahoma,Geneva,sans-serif;">The passenger feels anxious on the way up because the big drop is coming so the excitement level is low. Going down the hill is when the excitement level is at its highest and your adrenaline is kicking in. On the way up, you feel anxious for the upcoming drop. It is less exciting and slower. The bottom of the hill also has low excitement and not that much thrill.
 * <span style="font-family: Tahoma,Geneva,sans-serif;">The thrill factors are speed, height, the high drops, hills, and all different twists and turns on Nitro.

<span style="font-family: Tahoma,Geneva,sans-serif;">Part B) Back at School <span style="font-family: Tahoma,Geneva,sans-serif;">1) Calculate Experimental Values <span style="font-family: Tahoma,Geneva,sans-serif;">a. Speed at bottom of the first hill <span style="font-family: Tahoma,Geneva,sans-serif;"> <span style="font-family: Tahoma,Geneva,sans-serif;">b. Acceleration down the first hill <span style="font-family: Tahoma,Geneva,sans-serif;"> <span style="font-family: Tahoma,Geneva,sans-serif;">c. Power needed to get up the hill <span style="font-family: Tahoma,Geneva,sans-serif;">

<span style="font-family: Tahoma,Geneva,sans-serif;">a. Speed at bottom of the first hill <span style="font-family: Tahoma,Geneva,sans-serif;"> <span style="font-family: Tahoma,Geneva,sans-serif;">b. Acceleration down the first hill <span style="font-family: Tahoma,Geneva,sans-serif;">
 * <span style="font-family: Tahoma,Geneva,sans-serif;">2) Calculate Theoretical Values **

<span style="font-family: Tahoma,Geneva,sans-serif;">c. Power needed to get up the hill <span style="font-family: Tahoma,Geneva,sans-serif;">
 * <span style="font-family: Tahoma,Geneva,sans-serif;">3) Evaluate Accuracy of the 3 calculations above **



<span style="font-family: Tahoma,Geneva,sans-serif;">a. Calculate #g’s on the way down the hill and at the bottom of the hill. <span style="font-family: Tahoma,Geneva,sans-serif;"> <span style="font-family: Tahoma,Geneva,sans-serif;">b. Were #g’s within safe limits? <span style="font-family: Tahoma,Geneva,sans-serif;">c. Was there correlation between #g’s and excitement level? Explain, providing evidence.
 * <span style="font-family: Tahoma,Geneva,sans-serif;">4) Evaluate Safety **
 * <span style="font-family: Tahoma,Geneva,sans-serif;">Yes because it was within the safe limit of 4 g's.
 * Yes there is a correlation because as the number of g's increase, so does the excitement level. When the passenger is on the way up the first hill, there is no acceleration so the excitement level is low as the number of g's is 0. Yet, on the way down, there is an increased acceleration and the ride gets more exciting.

<span style="font-family: Tahoma,Geneva,sans-serif;">5) Thinking about Physics <span style="font-family: Tahoma,Geneva,sans-serif;">a) Explain the behavior of the mass on the string. Did the FBD of the car correlate to that of the mass? Why or why not? <span style="font-family: Tahoma,Geneva,sans-serif;">b) Did the #g’s correlate to the sensation of weight? <span style="font-family: Tahoma,Geneva,sans-serif;">c) Discuss the graphs that you created and why they curve the way that they do. > __A vs. T__: At first, the acceleration graph is a horizontal line at zero because the coaster cart is being tugged up the hill at a constant velocity. Next, the acceleration graph is a horizontal line at a higher value. This is because the velocity is increasing, but at a constant rate.
 * The mass went towards you as you went up the hill, then at the top of the hill, the mass was aligned with your body, not leaning toward or away. As we went down the hill, the mass leaned away from you. The FBD of the car correlates to that of the mass as the mass on the string acts as an aplomb.
 * <span style="font-family: Tahoma,Geneva,sans-serif;">Yes. While riding a roller coaster, you always feel the push of acceleration coming from the opposite direction of the actual force accelerating you. For this reason, as the # of g's increases, a person will either feel very heavy or light (heavy when accelerating up a hill, light when accelerating down a hill). As the g's increase, so does the apparent weight, and vice versa.
 * <span style="font-family: Tahoma,Geneva,sans-serif;">__D vs. T__: At first, the coaster cart is being tugged up the hill at a constant rate, and is therefore covering the same amount of distance per unit of time. For this reason, the graph is linear and increasing. Next, the coaster cart plummets down the first hill and quickly gains speed. The graph makes a j-curve, because the cart is covering increasing distances per unit of time (due to the increasing speed).
 * __V vs. T__: At first, the coaster is being tugged up the hill at a constant rate. Therefore, the velocity graph is a horizontal line. Next, the cart drops down the first hill and gains speed at a constant rate. Therefore, the velocity graph is increasing and linear.
 * __Thrill vs. A__: When the coaster is being tugged up the hill at a constant rate (no acceleration), there is no thrill. However, when the coaster plummets down the hill and continuously gains speed, acceleration increases drastically from zero (because velocity is no longer constant). As the acceleration increases, the thrill increases.

<span style="font-family: Tahoma,Geneva,sans-serif;">ACTIVITY B: A Vertical Loop of a Roller Coaster

<span style="font-family: Tahoma,Geneva,sans-serif;">Rollercoaster: Green Lantern

<span style="font-family: Tahoma,Geneva,sans-serif;">PART A: At the park:


 * <span style="font-family: Tahoma,Geneva,sans-serif;">1) Estimate distances and angles **

<span style="font-family: Tahoma,Geneva,sans-serif;">a. Height of top of loop (above the ground)
 * <span style="font-family: Tahoma,Geneva,sans-serif;">37.06 m

<span style="font-family: Tahoma,Geneva,sans-serif;">b. Height of first hill
 * <span style="font-family: Tahoma,Geneva,sans-serif;">47 m

<span style="font-family: Tahoma,Geneva,sans-serif;">c. Length of car
 * <span style="font-family: Tahoma,Geneva,sans-serif;">0.9144 m

<span style="font-family: Tahoma,Geneva,sans-serif;">d. Radius of loop
 * <span style="font-family: Tahoma,Geneva,sans-serif;">18.53 m


 * <span style="font-family: Tahoma,Geneva,sans-serif;">2) Measure time **

<span style="font-family: Tahoma,Geneva,sans-serif;">a. For the single car to travel past the top position on the loop


 * <span style="font-family: Tahoma,Geneva,sans-serif;">Trial || <span style="font-family: Tahoma,Geneva,sans-serif;">Time for Single Cart to Travel Past Top Position on Loop ||
 * <span style="font-family: Tahoma,Geneva,sans-serif;">1 || <span style="font-family: Tahoma,Geneva,sans-serif;">14.0 ||
 * <span style="font-family: Tahoma,Geneva,sans-serif;">2 || <span style="font-family: Tahoma,Geneva,sans-serif;">14.1 ||
 * <span style="font-family: Tahoma,Geneva,sans-serif;">3 || <span style="font-family: Tahoma,Geneva,sans-serif;">13.9 ||
 * <span style="font-family: Tahoma,Geneva,sans-serif;">4 || <span style="font-family: Tahoma,Geneva,sans-serif;">14.0 ||
 * <span style="font-family: Tahoma,Geneva,sans-serif;">5 || <span style="font-family: Tahoma,Geneva,sans-serif;">13.9 ||

<span style="font-family: Tahoma,Geneva,sans-serif;">
 * <span style="font-family: Tahoma,Geneva,sans-serif;">3) Diagrams **

<span style="font-family: Tahoma,Geneva,sans-serif;">d. Take a clear side view picture <span style="font-family: Tahoma,Geneva,sans-serif;"> <span style="font-family: Tahoma,Geneva,sans-serif;">http://www.nj.com/times-opinion/index.ssf/2011/05/hits_and_misses_green_lantern.html

<span style="font-family: Tahoma,Geneva,sans-serif;">e. Take a short video of the relevant segment media type="file" key="IMG_1434.3gp" width="300" height="300"

<span style="font-family: Tahoma,Geneva,sans-serif;">a. Create v vs. t, Fc vs. t and a vs. t graph for the motion this segment of the ride. <span style="font-family: Tahoma,Geneva,sans-serif;"> <span style="font-family: Tahoma,Geneva,sans-serif;"> <span style="font-family: Tahoma,Geneva,sans-serif;">b. Create a thrill vs. acceleration graph for this segment of the ride. <span style="font-family: Tahoma,Geneva,sans-serif;">
 * <span style="font-family: Tahoma,Geneva,sans-serif;">4) Graphs **

<span style="font-family: Tahoma,Geneva,sans-serif;">a. Describe the safety features on this coaster.
 * <span style="font-family: Tahoma,Geneva,sans-serif;">5) Evaluate **
 * <span style="font-family: Tahoma,Geneva,sans-serif;">There were seatbelts, harnesses that went over your shoulders, and warnings about keeping your limbs inside.

<span style="font-family: Tahoma,Geneva,sans-serif;">b. Describe the excitement level that you felt at the top, side and bottom of the loop.
 * <span style="font-family: Tahoma,Geneva,sans-serif;">At the bottom of the loop, there was the greatest excitement. The top was just as exciting because you are upside down. The side of the loop is the least thrilling.

<span style="font-family: Tahoma,Geneva,sans-serif;">c. Describe the thrill factors that may contribute to those feelings (besides the #g’s)
 * <span style="font-family: Tahoma,Geneva,sans-serif;">The thrill factors include weightlessness, height, corkscrews, and loops.

<span style="font-family: Tahoma,Geneva,sans-serif;">d. Describe the weight sensations at the top, side and bottom of the loop.: did you feel lighter, heavier, or normal?
 * <span style="font-family: Tahoma,Geneva,sans-serif;">Top: lightest
 * <span style="font-family: Tahoma,Geneva,sans-serif;">Bottom: heaviest
 * <span style="font-family: Tahoma,Geneva,sans-serif;">Side: normal weight

<span style="font-family: Tahoma,Geneva,sans-serif;">PART B) Back at School

<span style="font-family: Tahoma,Geneva,sans-serif;">1) Calculate Experimental Values

<span style="font-family: Tahoma,Geneva,sans-serif;">a. Speed at top of loop <span style="font-family: Tahoma,Geneva,sans-serif;"> <span style="font-family: Tahoma,Geneva,sans-serif;">b. Centripetal Acceleration <span style="font-family: Tahoma,Geneva,sans-serif;">

<span style="font-family: Tahoma,Geneva,sans-serif;">c. Apparent weight at top of loop

<span style="font-family: Tahoma,Geneva,sans-serif;">a. Minimum speed at top of loop <span style="font-family: Tahoma,Geneva,sans-serif;"> <span style="font-family: Tahoma,Geneva,sans-serif;">b. Speed at top of loop <span style="font-family: Tahoma,Geneva,sans-serif;"> <span style="font-family: Tahoma,Geneva,sans-serif;">c. Centripetal Acceleration <span style="font-family: Tahoma,Geneva,sans-serif;"> <span style="font-family: Tahoma,Geneva,sans-serif;">d. Apparent weight at top of loop <span style="font-family: Tahoma,Geneva,sans-serif;">e. #g’s <span style="font-family: Tahoma,Geneva,sans-serif;">
 * <span style="font-family: Tahoma,Geneva,sans-serif;">2) Calculate Theoretical Values **

<span style="font-family: Tahoma,Geneva,sans-serif;">a. #g’s were within safe limits?
 * <span style="font-family: Tahoma,Geneva,sans-serif;">3) Evaluate Safety **
 * <span style="font-family: Tahoma,Geneva,sans-serif;">Yes because the number was in between 1 and 4 g's.

<span style="font-family: Tahoma,Geneva,sans-serif;">b. Was there correlation between #g’s and excitement level? Explain, providing evidence.
 * <span style="font-family: Tahoma,Geneva,sans-serif;">Yes there is a correlation because as g's increase so does the excitement level. At the top of the bottom of the loop there are the most g's and the most excitement.

<span style="font-family: Tahoma,Geneva,sans-serif;">4) Thinking about the Physics

<span style="font-family: Tahoma,Geneva,sans-serif;">a) Explain the behavior of the mass on the string. Did the FBD of the car correlate to that of the mass? Why or why not?
 * They did not correlate because at the top of the loop you felt both weight and normal force acting on you

<span style="font-family: Tahoma,Geneva,sans-serif;">b) Did the #g’s correlate to the sensation of weight?
 * Yes.<span style="font-family: Tahoma,Geneva,sans-serif;"> However, the main factor that contributed to weight sensation was position in the loop. At the bottom, a person experiences the normal force of the cart pushing up on their body. During this time, a person feels heavier because their apparent weight is higher. At the top of the loop, normal force = zero. During this time, a person feels "weightless" because their apparent weight is lower.

<span style="font-family: Tahoma,Geneva,sans-serif;">c) Discuss the graphs that you created and why they curve the way that they do.
 * __V vs. T__: When the coaster descends down the first hill before entering the loop, it is speeding up at a constant rate in the negative direction. Therefore, the velocity graph is linear, below the x-axis, and moving away from the x-axis. When the coaster is making its way up to the top of the loop, it is slowing down at a constant rate in the positive direction. Therefore, the velocity graph is linear, above the x-axis, and is moving towards the x-axis. When the coaster is making its way down from the top of the loop, it is gaining speed at a constant rate in the negative direction. Therefore, the velocity graph is linear, below the x-axis, and moving away from the x-axis.
 * __Fc vs. T__: At first, when the coaster is descending down the first hill (before entering the loop) there is no centripetal force. Therefore, the graph is initially a horizontal line at zero. *It is important to note the equation **Fc = (mv^2)/r**. At the bottom of the loop, the velocity is greatest. Therefore, the centripetal force is greatest (mass = constant; radius = constant). At the top of the loop, the velocity is smallest. Therefore, the centripetal force is smallest. The graph is shaped like a parabola because of the v^2 relationship in the Fc = (mv^2)/r equation.
 * __A vs. T__: First, the coaster descends down a hill before entering a loop. During this time, the coaster is gaining speed at a constant rate in the negative direction. Therefore, the acceleration graph is a horizontal line at a negative value. Next, the coaster enters the loop and ascends to the top of it. During this time, the coaster is losing speed at a constant rate (*note: rate is lesser than that during initial drop down hill) in the positive direction. Therefore, the acceleration graph is a horizontal line at a lesser negative value. Then, the coaster makes its way back down to the bottom of the loop. During this time, the coaster is gaining speed at a constant rate (*note: rate going down = rate going up) in the negative direction. Therefore, the acceleration graph is a horizontal line at the same lesser negative value.
 * __Thrill vs. A__: When the coaster makes its initial descent (before entering the loop), its acceleration is a high negative value. During this time, the ride is most fun. When the coaster is in the loop, its acceleration is a lower negative value (because it is losing/gaining speed at a shallower rate). For this reason, the ride is not as thrilling in the loop. The more extreme the acceleration is in either direction (+ or -), the more thrill one experiences.