Chapter+4

=Section 1= toc What do you think?
 * I think the taller steel roller coaster would produce more screams because they are able to use more technology to make the coaster scarier and more thrilling. There could be higher drops, more loops and a faster time on the ride. The part of the roller coaster that produces the loudest screams would be when there is the start of a drop or during a loop. This is because people aren't sure of where they are going or what's going to happen next.**

Physics Talk Summary
 * A scalar is a quantity that has magnitude (size/amount), but no direction. A displacement is the difference in position between a final position and initial position; it depends only on the endpoints, not the path; displacement is a vector quantity; it has magnitude (size) and direction. A vector is a quantity that has both magnitude (size/amount) and direction. Speed is the distance traveled divided by the time elapsed; speed is a scalar quantity. it has no direction. Velocity is the displacement divided by the time elapsed; velocity is a vector quantity, it has magnitude (size) and direction. Acceleration is the change in velocity divided by the time elapsed; acceleration is a vector quantity with magnitude (size) and direction.**

Checking Up 1. **Distance is the actual measurement of an entire path and is a scalar quantity. On the other hand, displacement is a measured distance a direction included, but only depends on the endpoints not the distance of the whole path.** 2. **You displacement is 0, because you started out at your house and came back to it, so the endpoints are the same.** 3. **Speed is the distance traveled divided by the time elapsed and is scalar, which means it has no direction. Velocity is the displacement divided by the time elapsed and included magnitude and direction.** 4. **You can find the acceleration of an object by finding the change in velocity by the time elapsed.**

Physics to Go 1. 2. **I think the biggest thrill on The Terminator Express would be the horizontal circle because it almost defies gravity. Not many horizontal circles are used on roller coasters so people would not expect it.** 3a. **Around the equator 40000/24 = 1667 km/h. Changing speeds causes thrills** 3b. **v=d/t** 3c. **There is no change in velocity or direction, because it is a constant speed that everyone is traveling at.** 4. **a = v/t** 5a. **Speed** 5b. **Velocity** 5c. **Acceleration** 5d. **Displacement and velocity** 5e. **Displacement** 6. **10/2 = 5 cm/s** 7. **5/t = 5 cm/s = 1 second.** 8. **2.5** 10a. **I would eliminate the higher hill and the horizontal circle and make the speed slower because preschool children need many more safety precautions because of their size.** 10b.
 * a = 8/3**
 * a = 2.6 m/s^2**

What do you think now?
 * When a person feels lightest on the roller coaster is when the most screams are produced. This can occur during a loop or when going down a steep hill. The acceleration of the roller coaster increases as the steepness of the hills increase.**

=**Section 2**= What do you think?
 * The roller coaster with the steeper angle of descent (the steel one) would produce more thrill to the riders because it has a higher velocity and acceleration that causes people's weight to seem to change while on the ride.**

Physics Talk
 * Gravitational Potential Energy (GPE) is the energy a body possesses as a result of its position in a gravitational field. GPE = mass of an object X strength of gravitational field X height or GPE = mgh. Kinetic energy (KE) is the energy an object posses because of its speed. KE = 1/2 X mass of an object X speed X speed = 1/2 X mass of an object X (speed)^2 or KE = 1/2mv^2. The concept of energy can be used to describe the relationship between height and speed of an object. Joule is the SI unit for all forms of energy. The units are equivalent to kg X m^2/ S^2 or N X m. Mechanical energy is the sum of kinetic energy and potential energy.**

Checking Up 1. **Changing the length of the incline will make the speed gradually increase more as it rolls towards the bottom.** 2. **GPE will change when height changes in the sense if the height is larger then the GPE will be as well. The same will happen for the mass of an object, but when doing an experiment mass is normally not a variable.** 3. **Kinetic energy will increase if speed increases because it is directly related to velocity. The same will happen with the mass but as stated before mass is normally not a variable during experiments. If the mass gets larger or smaller (in changing the object) the KE will change respectably.** 4. **The GPE that the roller-coaster "loses" will be transfered to the people, tracks or be lost as heat energy.** 5. **As seen in my chart below, it is 30,000 joules of kinetic energy**

Physics To Go 1. **Same because they have the same initial height** 3. 4. 5. 6. 7a. **1.47 Joules** 7b. **1.47 Joules** 7c. **.375 meters, half way down the track** 8. **No because the mass of the cart does not effect the speed of the roller coaster** 9a. **Between A and B** 9b. **Between C and D and between E and F because they have the exact same drops** 9c. **D because the drop before it causes it to have more speed** 10b. **H is so much higher because at the top of A that by the time you are halfway through H you have lost all of your KE and will stop moving forward and start moving.** 11.
 * **Position of Car (height m)** || **GPE (J) = mgh** || **KE (J) = 1/2mv^2** || **GPE +KE (J)** ||
 * top (30 m) || 60,000 || 0 || 60,000 ||
 * bottom (0 m) || 0 || 60,000 || 60,000 ||
 * halfway down (15 m) || 30,000 || 30,000 || 60,000 ||
 * three-quarters way down (7.5 m) || 15,000 || 45,000 || 60,000 ||
 * **Position of car (height m)** || **GPE (J) = mgh** || **KE (J) = 1/2mv^2** || **GPE + KE (J)** ||
 * top (25 m) || 75,000 || 0 || 75,000 ||
 * bottom (0 m) || 0 || 75,000 || 75,000 ||
 * halfway down (12.5m) || 37,500 || 37,5000 || 75,000 ||
 * three-quarters way down (5 m) || 15,000 || 60,000 || 75,000 ||
 * **Position of car** || **Height (m)** || **GPE (J) = mgh** || **KE (J) + 1/2mv^2** || **GPE + KE (J)** ||
 * bottom of hill || 0 || 0 || 50,000 || 50,000 ||
 * top of hill || 25 || 50,000 || 0 || 50,000 ||
 * top of loop || 15 || 30,000 || 20,000 || 50,000 ||
 * horizontal loop || 0 || 0 || 50,000 || 50,000 ||

What Do You Think Now? **A person on a roller coaster will experience more thrill during part B because one would experience more acceleration since the track is the steepest at that point on the track. The speed at the bottom of both tracks will have the same kinetic and gravitational potential energy because both of the tracks have the exact same initial height, the paths of the tracks do not affect the end result.**

= Section 3 = What Do You Think? **Today, most roller-coasters also start with a hill lift that has a chain or cable pulling it up to the first drop, or any of the other drops. It does not cost more to lift the roller-coaster if it is full of people because mass cancels out in the equation of GPE = KE.**

Physics Talk __**Spring Potential Energy:**__ **the energy stored in a spring due to its compression or stretch** **- SPE = 1/2kx^2** **- GPE + KE + SPE = constant** **(mgh + 1/2mv^2 + 1/2kx^2 = constant)**

Checking Up 1. **The spring potential energy of a "pop-up" toy after it leaps off the table increases** 2. **Potential and kinetic energy are equal so it will be 2J** 3. **When it reaches maximum height the GPE will be 2J**

Physics To Go 5. **The second hill can not be higher than the first hill because there is not enough gravitational potential energy to reach the top of the second hill** 6. **Work due to friction creates heat and thermal energy takes away GPE making it less available for Kinetic Energy.** 7. **GPE = electric energy** **(300) (9.8) (15) = electric energy** **44,100 J = electric energy** 8a. **KE = 1/2mv^2** **KE = 1/2 (400) (15^2)** **KE = 45,000 J** 8b. **GPE = KE** **GPE = 45,000 J** 8c. **45,000 = 400 (9.8) h** **h = 11.48 meters** 9. **GPE increases as height does when the ball is thrown upwards.** 10.**GPE will be equal at the end because paths of their movement do not matter, as long as heigh is equal..** 11a. **The results are similar .078 and .073** 11b. **KE = EPE** **1/2mv^2 = EPE** **1.2 (.020) (2.7^2) = EPE** **.0729 J = EPE** 11c. **.4/3 = .13 m** 12a. **EPE = 1/2kx^2** **52,920 J = 1/2 k (4)^2** **6,615 Nm/s = x** 12b. **GPE = SPE** **GPE = mgh** **GPE = 70,560 J** **1/2 (6,615) x^2 = 70,560** **x = 4.62 m** 13. **KE = SPE** **KE = 1/2 k x^2** **KE = 1/2 (40) (.3)^2** **KE = 1.8 J**

What Do You Think Now **As mass increased, the pop up toy's height decreases. When the mass of a roller-coaster increases, the GPE needed to pull the roller-coaster also increases. This shows that because a roller-coaster is pulled by cables and electricity that when it's mass increases it needs more electric energy in order to go through the ride at the normal speed. Also, this means that the heavier the coaster is, the more it costs for the company to be able to lift the roller-coaster.**

= Section 4 = What Do You Think **Gravity has a direction that pushes objects towards the core of the earth. Because gravity is always pushing inwards, people in Australia are able to be held on earth because gravity is always keeping them on the ground.**

Physics Talk >> **Earth is it's own source of its gravitational field** >> **The direction of the gravitational field is the same as the force on a mass** >> **The gravitational field is stronger where the lines are close together** >> **The gravitational filed is weaker where the lines are farther apart** >> **The gravitational field extends out to infinity** >> **All bodies with mass attract all other bodies with mass** >> **The force of a body 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 two masses between the two bodies decreases** >> **Fg = Gm1m2/r^2**
 * Field is an influence that one object sets up in the same around it**
 * A Response Object responds to the field & is used to test for the existence of the field and map ing it.**
 * Inverse-Square Relationship is the force of gravity between two objects decreases by the square of the distance between them**
 * Newton's Law of Universal Gravitation describes the gravitational attraction of objects for one another**

Checking Up 1. **Inwards to the center of the classroom** 2. **The center of the Earth** 3. **The force of gravity triples** 4. **Gravitational pull** 5. **An elliptical path**

Physics To Go 1. **1/4 of 500 - 125 N** 3. **Because we have never, not had gravity** 4. **Acceleration due to gravity is less at the top than the acceleration due to gravity at the bottom** 5a. **The water side of the earth is closer to the moon** 5b. **When a body of water is facing the moon there are higher tides** 5c. **There are lower tides when the water is on the earth is not facing the moon** 6a. **The fish would break the water bubble it swims in and then all the fish would die** 6b. **Gravity holds the** **water** **down so the fish can swim in it.** 7a. **Force decreases by 2^2** 7b. **Force decreases by 3^2** 7c. **Force decreases by 4^4** 7d. **Force decreases 1/2^2** 8a. **Double the force** 8b. **Triple the force** 8c. **Quadruple the force** 8d. **Half the force** 9a. **Force increases by 4** 9b. **Force increases by 9** 9c. **Force increases by 16** 9d. **Force decreases by 1/4** 10a. **Force doubles** 10b. **Force increases by 9** 10c. **Force increases by 6**

Physics Plus
 * FG = 1 /( 3.84x10^8)**
 * FG = 2.60916 x 10 ^-9**


 * C = 2πr**
 * Time = 2415793158 / 2440800**
 * v = 988.505 m/s**
 * a = 988.505^2 / 3.84 x 10^2**
 * a = .0025 m/s^2**

What Do You Think
 * Gravity's direction is inwards toward the center of the earth. Australians can be held on the earth even though they are "upside down" because gravity is holding them into the center.**

=**Section 5**=
 * What do you think? **
 * You cannot used the same scale to weigh a canary as you do an elephant. The magnets in the scale need to be able to balance the force and provide a net force for what is being weighed. All scales work the same by providing a net force for a returning force.**

Physics Talk
 * There are many different relationships that could be imagined between the applied force and the stretch of the spring. There is a linear relationship between the measured amount of force required for each stretch of the spring. Many springs have the property that the stretch of the spring is directly proportional to the force applied to it. This means if you double the force, so does the stretch of the spring. Hooke's Law describes spring sthat behave in this way. The alw explains very simply what restoring force a spring exerts if it is stretched.**
 * Force exerted by the spring = -spring constant (or compression) X spring stretch**
 * Fs = -kx. F is the force exerted by the spring, x is the stretch or compression of the spring and k is the constanst**

Checking Up 1. **5 times** 2. **Spring Constant means the compression of the spring** 3. **The weight in Newtons is much larger than the mass in Kilograms** 4. **It is the same**

Physics To Go 1a. **100 x 9.8 = 980 N** 2b. **10 x 9.8 =98 N** 3c. **60 x 9.8 = 588 N** 2a. **130 x 4.45= 578.6 N** 2b. **1000 x 4.45 = 4450** 2c. **50 x 9.8 = 222.5 N** 3. 3c. **The slope is .1491, also the spring force constant** 3d. 4. **F = k x** 5. **As the force** **increases** **so does the stretch****.** 6. **The spring with the k value of 15 N stretches easier** 7. **3-1 / .02-.007 = 153.84 N/m (slope and k value)** 8. **A spring scale works because a certain amount of weight pulls or pushes it down as equal force is returned. It al depends on how easily stretched the spring is. If a spring is very easily stretched, it takes less weight to stretch down to the same length than a spring that is hard to stretch.**
 * 12 = .03k**
 * k = 400 (N/m)**

What do you think now?
 * You cannot used the same scale to weigh a canary as you do an elephant. The magnets in the scale need to be able to balance the force and provide a net force for what is being weighed. All scales work the same by providing a net force for a returning force. Some of the springs could be stronger or weaker than others, causing inaccuracy while measuring objects that have such different masses and weights.**

=Section 6= What do you think?
 * No, weight does not change. The forces acting upon the rider changes, causing the rider to feel lighter or heavier. If they had a scale with them on the ride they would be able to see these force changes. Just because force changes does not mean weight does too.**

Physics Talk
 * When an object is at rest, the sum of the forces on that object equal zero. Newton's first (an object at rest stays at rest and an object in motion stays in motion unless acted upon by a force) and second law (a = F / m) can be used to explain this. You realize that the object is at rest and has zero acceleration and no net force. To find acceleration you must know mass and the net force and you can use Newton's Second Law. When an object accelerates there is a net force change acting up the object as well as when an object decelerates. Acceleration due to gravity is identical for all objects falling on Earth if there are no other forces acting on the object.**

Checking Up 1. **It is zero** 2. **The scale reading is greater than the actual weight** 3. **The scale that you're standing on is exerting a greater force on yourself than you are down.** 4. **Zero because the scale and you are in a free fall. You are falling at the same rate the scale is falling** 5. **Air resistance**

Physics To Go 1. **vf = vi + at** 1a. **vf = 0 + 9.8(2)** 1b. **vf = 0 + 9.8(5)** 2. **vf = vi +at** 2b. **vf = 0 +1.6(5)** 3a. **Yes because both of the lines are equal and oppositely pushing against the block** 3b. **Yes** 3c. **Yes** 4. 5. **The elevator is accelerating downwards** 6. **The person's weight will seemingly increase** 7a. **Increase** 7b. 8a. **50 kg - 490 N** 8b. **∑F = ma** 8c. **50 kg - 490 N** 9. **There is a different scale reading for the student in each elevator because the acceleration or gravitation in each picture is different. When the weight and gravitation are equal (along with acceleration being constant), the scale will read the students normal weight. When the acceleration is down in a free fall, the weight of the person will be zero. When the elevator is accelerating upwards with more energy than gravitation, the scale reads a higher weight.** 10.
 * vf = 19.6 m/s**
 * vf = 49 m/s**
 * 1c. vf = 0 + 9.8(10)**
 * vf = 98 m/s**
 * 2a. vf = 0 + 1.6(2)**
 * vf = 3.2 m/s**
 * vf = 8 m/s**
 * 2c. vf = 0 +1.6(1)**
 * vf = 16**
 * **Motion of the Elevator** || **Acceleration (up, down, zero)** || **Relative Scale Reading (greater, less or equal to weight)** ||
 * **At rest, bottom floor** || **v = 0; a = 0; ∑F = 0** || **N = W** ||
 * **Starting at Rest, Increasing Up** || **v is up; a is up; ∑F is up** || **N > W** ||
 * **Continuing to move, Constant Up** || **v = 0; a = 0; ∑F = 0** || **N = W** ||
 * **Slowing down to top floor, Decreasing Up** || **v is up; a is down; ∑F is down** || **N > W** ||
 * **At rest, top floor** || **v = 0; a = 0; ∑F = 0** || **N = W** ||
 * **Starting at rest, Increasing Down** || **v is down; a is up; ∑F is up** || **N < W** ||
 * **Continuing to move, Constant Down** || **v = 0; a = 0; ∑F = 0** || **N = W** ||
 * **Coming to a stop on the ground floor** || **v is down; a is up; ∑F is up** || **N < W** ||
 * N = w = mg**
 * N - w = ma**
 * N = ma + mg**
 * N = 50(2) + (50)(9.8)**
 * N = 590 N**

What do you think now?
 * When riding a roller coaster your weight will not change. The forces acting upon the rider changes, causing the rider to feel lighter or heavier. If they had a scale with them on the ride they would be able to see these force changes. Just because force changes does not mean weight does too. The springs in the scale would read the amount of force that the rider is exerting on it and the scale will return an opposite force (Newton's 3rd Law of Motion). Force is not the same as weight.**

=**Section 7**= What do you think?
 * There is not enough gravity to push you down when forces are acting upon you a different way. The forces will take over and gravity will pull you down, causing you to fall out of the roller coaster.**

Physics Talk
 * Normal force is the force acting perpendicular to the surface.**
 * Centripetal force is any force directed toward the center that causes an object to follow a circular path at a constant speed. The equation that represents centripetal force is F(c)= mv^2/r**
 * Centripetal acceleration is the acceleration directed toward he center of the circle experienced by an object traveling in a circular path at a constant speed**

Checking Up 1. **Centripetal force, normal force and the force of gravity** 2. **No there is not an acceleration** 3. **Normal force and the force of gravity** 4. **Normal force** 5. **If you have a bigger mass you need a bigger centripetal force. If your mass is bigger it does not affect the radius but you must go faster if your mass is bigger.**

Physics To Go 1a. 1b. 2a. **Friction in the tires** 2b. 6a. **No** 6b. **Yes** 6c. **vf + -vi** 7. **v^2/R** 10.
 * N20 + W20**
 * sqrt(20^2+20^2) = 28.3, 45degress**
 * 20^2/200 =2 m/s^2**
 * ~ Fast ||~ Moving ||~ Roller ||~ Coster ||
 * || Required Centripetal Force || Force of Gravity (weight) || Normal Force (track on car) ||
 * Top of Loop || 4000 N || 500 N || (4000-500) 3500 ||
 * Bottom of Loop || 6000 N || 500 N || (6000+500) 6500 ||


 * ~ Slow ||~ Moving ||~ Roller ||~ Coaster ||
 * || Required Centripetal Force || Force of Gravity (weight) || Normal Force (track on car) ||
 * Top of Loop || 800 N || 500 N || 300 ||
 * Bottom of Loop || 2800 N || 500 N || 3300 ||

13a. **Light** 13b. **Heavy** 13c. **Light** 13d. **Uncertain** 13e. **Uncertain** 14a. **Zero** 14b. **Down** 14c. **Up** 14d. **Zero** 14e. **Zero** 14f. **Sideways** 14g. **Sideways**

Physics Plus 1)a. **The Net Force decreases in an indirect relationship** 1b. **The velocity increases in a direct relationship** 2. **The track must be at least 4 times stronger** 3. **The Net Force also decreases with the radius of the curve.** 4. **The larger the radius for the curve, the** **larger** **the force required to keep the car moving along the curve. If the curve is tight than a** **smaller****force is required.** 5. **The more string let out into the curve the less force was needed to complete the circle.**
 * Sample Problem:**
 * a: a = v^2/r**
 * a = 12^2/20**
 * a = 7.2 m/s^2**
 * b: Fnet = ma**
 * Fnet = (300)(7.2)**
 * Fnet = 2160 N**

What do you think now?
 * There is a force that acts with your normal force and the force of gravity called centripetal force that causes the passenger on a roller coaster to stay inside the ride at all times. Centripetal force is a force that acts on a body moving in a circular path that directs all of the force towards the center around which the body is moving. This causes you to stay in the ride. Acceleration and Net force are down plus the force of the track are as big as your force that you are exerting on the seat causing you to stay in your seat**

=**Section 8**= What do you think?
 * It takes more energy to go up a steep incline rather than a gentle incline because there is more force and friction acting upon the object trying to move up the incline.**

Physics Talk
 * When you move a cart to the top of an inclined ramp by applying a force with a spring scale over a certain distance you find tht the product of the force applied and the distance remained the same, regardless of the slope of hte ramp. The product of force multiplied by distance is called work (W = Fd). *the definition of work involves only that part of the force that is in the same direction or opposite direction of the displacement.**
 * The vertical displacement is the height that is it must be lifted.**
 * W = Fd**
 * = weight x height**
 * = mgh**
 * The work done on the roller coaster is mgh. This is equal to the change in gravitational potential energy (GPE) of the roller coaster.**
 * Power shows how fast work is done****.**
 * power = work done/ time elapsed**
 * P = ∆t**
 * The SI unit for power is a watt. One watt = 1 J/s**

Checking Up 1. **The work turns into GPE** 2. **From the work done to pull it up the incline** 3. **There is less work required when using a ramp because it changes the distance moved** 4. **It escapes through heat** 5. **Watt or J/s**

Physics To Go 1a. **GPE will be larger at the top, where it will equal 0 at the bottom** 1b. **W = Fd** 1c. **w = lx** 1d. **.5lx^2** 1e. **all of the energy is built up in the spring so all of the work and GPE and SPE are in the spring constant** 1f. **As it reaches the top of the incline it will slow gradually** 2a. **W = Fd** 2b. **W = Fd** 2c. **W = Fd** 2d. **W = Fd** 3. **Instead of "conserving energy" you should be consistent with the amount of energy that you use at one point.** 4. **The force exerted on the cart changes, causing the forces given off by the track to change.** 5a. **W = Fd** 5b. **P = F/∆t** 6. **There is work needed to go up the first and second incline to get up the coaster. GPE energy is at the top. During the first drop GPE turns in to KE. The vertical loop has GPE and KE. The final double curve of our coaster has a little GPE and mostly KE because of all the built up energy before. At the end there is work due to friction causing the coaster to stop.**
 * W = lx**
 * 150 x 7**
 * w = 1050 J**
 * 60 x .5**
 * 30 J**
 * 40 x 75**
 * 3000 J**
 * 500 x .7**
 * 350 J**
 * 10000 x 20**
 * 200000 J**
 * 200000/150**
 * 1333.33 W**

What do you think now?
 * It takes more energy to go up a steep incline rather than a gentle incline because there is more force and friction acting upon the object trying to move up the incline.**

=Section 9= What do you think?
 * There is a boy and girl attempting to create roller coasters, but the boy is trying to use force when energy is an easier and more relevant term to use when making this. The part of The Snake that will be the most thrilling is when there is the turns, but they should be more narrow. Acceleration will change because direction changes.**

Physics Talk __**Vector**__
 * A vector description includes a number (magnitude) and a direction**
 * Force, speed**
 * Displacement is described by a vector**
 * To add vectors you must draw them and use vector addition**

__**Scalar**__
 * Scalar quantity is distance**
 * Energy- joules**
 * Total mechanical energy is the same at every point as long as frictin is not significant or motors do not add energy**
 * GPE depends only on the height from a reference position sicne mass and gravitational force remains the same**
 * if two points on a roller coaster have the same height, the roller coaster is moving at the same speed at those two points**
 * Energy paths are independent and will be the same no matter what point you are looking on while traveling**

Checking Up 1. **Vector addition is needed to add vector quantities. You may draw and label a diagram also.** 2. **Energy is a scalar quantity. Force is a vector quantity** 3. **Total mechanical energy is the same at every point as long as frictin is not significant or motors do not add energy** **GPE depends only on the height from a reference position sicne mass and gravitational force remains the same** **if two points on a roller coaster have the same height, the roller coaster is moving at the same speed at those two points** 4. **No, the energy of the roller coaster does not depends on the path** 5. **More energy**

Physics to Go 1a. 1b. 2. **Although these tracks have different angles, the only thing that determines speed is the original heigh of the cart.** 3a. **Vector** 3b. **Vector** 3c. **Scalar** 3d. **Vector** 3e. **Scalar** 3f. **Vector** 3g. **Vector** 3h. **Scalar** 3i. **Scalar** 4a. **Scalar** 4b. **Scalar** 4c. **Vector** 4d. **Vector** 5. **An energy ride would have more hills and turns while a force ride would have more twists and loops.** 6a. 6b. 6c. **It is easier to analyze the forces because there are no hills or loops** 7a. 7b. **All of the energies would be equal at all of these three points because they are at the same height** 7c. **KE would be equal at all of these heights because they are at the same height** 7d. **Because KE and GPE change respectably as the coaster changes but there is never lost energy because it is impossible to destroy energy.**
 * 7 m/s**

What do you think now?
 * When The Snake is running, the most thrilling part of the coaster will be the turns. It will be fun because the turns could be shapr and when you make a turn and velocity is changing. The ride could also be fast, making it more thrilling with speed. If noise was added there would be even more fear from the passengers if scary dialogue was added to the ride.**

=Section 10= What do you think?
 * Yes I think that if people know that their lives are in danger they automatically get scared and more thrilled by the ride. It is also an exciting story to tell their friends when they tell them that they "survived" the deadly coaster. If one half of all roller coaster riders died it would be a more normal thing, but still thrilling to ride the ride and not die. Also, if there was a high death rate because of riding a roller coaster I would presume that there would be less willing riders. **

Physics Talk
 * Depending on where you are on the roller coaster during the ride, the amount of g's change. When analyzing the acceleration at any point the centripetal acceleration must be toward the center of the circle. **
 * a = v^2/r **


 * Qualitative (no numbers): decreasing the speed at that point will lower the acceleration when you change the height from which the coaster descends. Less GPE will result in less KE and the lesser of these two energies will create a lower total energy, decreasing the speed. **


 * Centripetal force can also be calculated by using Newton's Second Law: F(net) = ma or in this case F(net) = mv^2/r **

Checking Up 1. **The maximum safe acceleration for a roller coaster is under 4 g's** 2. **Two ways to keep the acceleration of the coaster cart low enough is by decreasing total GPE and KE which can be done by changing the initial height or widening a turn.** 3. **The top of the loop of a roller coaster cart has the greatest acceleration** 4. **Normal force is the greatest at the top of the loop.**

** Physics To Go: ** 1. **The amount of force at each point of the roller coaster, (GPE and KE), all g's are under 4, track must best be strong enough to hold the forces.** 2a. **mgh = 1/2mv^2** 2b. **a = v^2/r** 2c. **Yes** 2d**. v^2/12 = 39.2** 2e. **v^2/7** 3a. **a = v^2/r** 3b. **No because it is over 6 g's when the safe amount of g's is 4** 4a. **mgh = 1/2mv^2** 4b. **a = v^2/r** 4c. **Ac = v^2/r** 4d. **58 m/s** 4e. **The acceleration is safe at the top and bottom of the link.** 5a. **mgh = 1/2mv^2** 5b. **mgh = 1/2mv^2** 6a. **a = v^2/r** 6b. **mv^2/R** 6c. **The track on the wheels** 7a. **a = v^2/r** 7b. **mv^2/R** 7c. 8a. **No because mass is not a factor in finding centripetal acceleration.** 8b. **Same** 8c. **Yes because the normal force from the track needs to be greater.**
 * 9.8(h) = 1/2(20)^2**
 * 20 m**
 * a = 20^2/12**
 * a = 33 m/s^2**
 * v = 21.6 m/s**
 * v =17 m/s**
 * a = 62.5 m/s^2**
 * 9.8(5) = 1/2v^2**
 * 31 m/s**
 * a = 31^2/10**
 * a = 96.1 m/s^2**
 * 96 = v^2/10**
 * v = 24 m/s**
 * 9.8(16) = 1/2v^2**
 * v = 8.9 m/s**
 * 9.8h = 1/2(8.9^2)**
 * h = 20 m**
 * a = 8 m/s^2**
 * 900(12)^2/18**
 * = 7200 N**
 * a = 26.6 m/s^2**
 * 900(20)^2/15**
 * = 24,000 N**

Physics To Go

What do you think now?
 * Yes I think that if people know that their lives are in danger they automatically get scared and more thrilled by the ride. It is also an exciting story to tell their friends when they tell them that they "survived" the deadly coaster. If one half of all roller coaster riders died it would be a more normal thing, but still thrilling to ride the ride and not die. Also, if there was a high death rate because of riding a roller coaster I would presume that there would be less willing riders. The cost and insurance policies of the rides would be at a greater cost, and with less riders I think overall the roller coasters would shut down. Safety is extremely important while on any ride, especially one that is going 40 meters per second or possibly upside down. Riders would most likely second guess riding a roller coaster if they had previous knowledge that it was not safe. **