Chapter+4

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=Section 1=

What Do You See?
toc I see a man blindfolded in an office chair being pushed by a girl. He thinks that he is on a roller coaster as he is being pushed in a random pattern.

What do you think?
The part that produces the most screams at the areas with the most G-forces, as g-forces are unusual to the body and most likely will cause the greatest scream.

Investigate- Part A
1a. 2a. We both have the same graph, so I think they are both accurate and depict the curve well. I also like how the drops are represented. 3a. The benefits of having two sketches are that the person viewing the diagram has a multi-dimensional view of what the roller coaster will look like. 4a.

Part B
1a. The person in the chair can fall out and be injured. The chair can flip over and the person in the chair can get crushed. High Speed Test- Part A- 3 Part B- 4 Part C- 5 Part D- 4 3a. There was change in reactions with every part of the test. 4a. The more velocity and change in direction, the more reactions. 5a. .4m/s 7b. Yes, there were always reactions.
 * = Category ||= Rating out of 10 ||
 * = Starts and Stops ||= 4 ||
 * = Spins ||= 4 ||
 * = High Speeds ||= 5 ||
 * = Slow, wide turns ||= 2 ||
 * = Collisions ||= 5 ||
 * = Turns ||= 3 ||
 * = Low Speeds ||= 2 ||

Checking Up
1. Displacement is the change in something position-wise. 2. Zero 3. Speed- how fast an object moves. Velocity- the rate that an object travels 4. Acceleration is the change in velocity divided by time.

Physics To Go
1. 2. The biggest thrills will be either on the largest drop or on the horizontal circle. They both produce the biggest change in acceleration and g-forces, respectively. 3a. Everything on the Earth is moving at a constant speed, so the Earth's spin is not noticeable. 3b. 40,000 km / 24 hr = 1,666.6 km/hr 3c. The speed isn't noticeable as everything is moving at it. 4. a=12m/3s a=4m/s 5a. Speed 5b. Velocity 5c. Distance 5d. Displacement 5e. Acceleration 6. Speed=10cm/2s Speed=5cm/s 7. 5=5t t=1s 8. a=25m/10s a=2.5m/s^2

=Section 2=

Physics Talk
If two objects leave the same height at the same time, GPE and Vf is the same, but the one with the steepest slope will reach the ground first. GPE = mgh KE= 1/2 mv^2

Checking Up
1). The change in incline has no affect on the final speed, but changes the time. 2). A change in height or mass increases or decreases GPE, they are in direct relation. 3). A change in velocity or mass will directly increase or decrease KE. 4). As GPE decreases, KE increases, they vary directly. 5). 30000J

Investigate

 * = Trial ||= Mass ||= Height (m) ||= GPE ||= Width of Ball ||= Time Through Gate ||= V at Bottom ||= KE at bottom ||= % Difference ||
 * = 1 ||= .226kg ||= 0.64m ||= 0.142J ||= .038m ||= .0379s ||= 1.003 ||= .114 ||= -19.7% ||
 * = 2 ||= .226kg ||= .147m ||= 0.326J ||= .038m ||= .0252s ||= 1.508 ||= .257 ||= -21.2% ||
 * = 3 ||= .226kg ||= .226m ||= 0.501J ||= .038m ||= .0203s ||= 1.872 ||= .396 ||= -21% ||
 * = 4 ||= .226kg ||= .324m ||= 0.695J ||= .038m ||= .0174s ||= 2.184 ||= .539 ||= -22.6% ||

Physics To Go
1) They are the same. 2) GPE and KE vary directly, when GPE goes down KE goes up. 3)

5)
 * height (m) || GPE (J) = mgh || KE (J) = 1/2mv^2 || GPE + KE (J) ||
 * 30 m || 60,000 || 0 || 60,000 ||
 * 0 m || 0 || 60,000 || 60,000 ||
 * 15 m || 30,000 || 30,000 || 60,000 ||
 * 7.5 m || 15,000 || 45,000 || 60,000 ||
 * height (m) || GPE (J) = mgh || KE (J) = 1/2mv^2 || GPE + KE (J) ||
 * 25 m || 75,000 || 0 || 75,000 ||
 * 0 m || 0 || 75,000 || 75,000 ||
 * 12.5 m || 37,500 || 37,500 || 75,000 ||
 * 5 m || 15,000 || 60,000 || 75,000 ||

=Section 3=

What Do You See?
I see a frog on a spring, and a person calculating how far the frog jumps in the air. On the table there are two children with a velocimeter, and a girl at the board writing equations.

What Do You Think?
Today, roller coasters get to their highest point either by using a chain or through hydraulics. I think that it costs more to pull a roller coaster car full of people than an empty car because the full roller coaster would have more mass.

Investigate
Find the GPE, SPE, KE and V of a ball launched by a spring launcher When the ball is launched upward by the spring launcher, the SPE of the spring converts to KE, giving the ball a velocity. In turn, the KE is converted to GPE giving the ball altitude, h. Lets find out if KE is actually converted to GPE by calculating the launch velocity and measuring the launch velocity using a velocimeter. In theory, KE initial is equal to GPE final. 1/2mv2=mgh --> v^2/2=gh --> v^2=2gh --> v=2gh^1/2 SPE=1/2kx^2 k= spring constant x= distance spring is compressed Overall, SPE=GPE 1/2kx^2=mgh Conclusion- Initial GPE is nearly equal to the final KE. This means that all energy is conserved.
 * = Trial ||= Mass ||= Height (m) ||= Mass of Ball ||= Spring Depression (m) ||= Width of Ball ||= Time (s) ||= V(initial) ||= V(final) ||= Percent Difference ||
 * = 1 ||= Ball ||= 1.06 ||= .0024 ||= .015 ||= .038 ||= .0072 ||= 4.56 ||= 5.28 ||= 13.6% ||
 * = 2 ||= Ball, 1 Nickel ||= .82 ||= .0074 ||= .015 ||= .04 ||= .0089 ||= 4.0 ||= 4.5 ||= 11.1% ||
 * = 3 ||= Ball, 2 Nickels ||= .69 ||= .0124 ||= .015 ||= .042 ||= .010 ||= 3.67 ||= 4.2 ||= 12.6% ||
 * = 4 ||= Ball, 3 Nickels ||= .55 ||= .0174 ||= .015 ||= .044 ||= .012 ||= 3.28 ||= 3.67 ||= 10.6% ||
 * = 5 ||= Ball, 4 Nickels ||= .43 ||= .0224 ||= .015 ||= .046 ||= .013 ||= 2.9 ||= 3.54 ||= 18.1% ||

Finding the spring constant- 1/2kx^2=mgh 1/2k(.015)^2=(.0024)(9.8)(1.06) .0001125k=.0249312 k=221.61
 * = Trial ||= x (m) ||= m ||= h ||= k ||
 * = 1 ||= .015 ||= .0024 ||= 1.06 ||= 221.61 ||
 * = 2 ||= .015 ||= .0074 ||= .82 ||= 528.50 ||
 * = 3 ||= .015 ||= .0124 ||= .69 ||= 745.32 ||
 * = 4 ||= .015 ||= .0174 ||= .55 ||= 833.65 ||
 * = 5 ||= .015 ||= .0224 ||= .43 ||= 842.80 ||

Physics Talk
Spring Potential Energy- SPE = 1/2kx^2 K is the spring constant and x is the amount that the spring is pushed in.

Checking Up
1. The SPE turns into GPE, when it falls it is converted into KE. 2. There is 2J of KE 3. There is 2J of GPE 4. The spring constant and the amount that the spring is compressed.

Physics To Go
1. The total amount of energy (KE+GPE) will always equal the same amount. 2. At launch- 25KE, 0GPE At Peak- 0KE, 25GPE At the end of the fall- 25KE, 0GPE 3. The mass would cause less energy. 4. The energy in your muscles turn into SPE, the SPE is turned into KE when you throw the ball. At the peak of the ball's trajectory, the KE is turned into GPE. As the ball falls, the GPE is turned into KE. 5. The second hill of a roller coaster can never be as high as the first because there is not enough KE to reach the same height. 6. There is friction between the roller coaster car and the track, as well as between the car and the air. 7.GPE=mgh GPE=(300kg)(9.8m/s^2)(15m) GPE=44,100 J 44,100 J of energy. 8a. GPE=mgh GPE=(400kg)(9.8m/s^2)(15m) GPE=58,800 J GPE=KE KE=58,800 J 8b. The GPE will be 58,800 J 8c. It must be less than 15 meters. 9. It Increases. 10. The increase is the same. 11a. GPE=mgh GPE=(.02kg)(9.8m/s^2)(.4m) GPE=.0784J KE=1/2mv^2 KE=(1/2)(.02kg)(2.7m/s)^2 KE=.0729J The KE and GPE are extremely close to being the same. 11b. SPE=1/2kx^2 The SPE should be equal to the GPE and the KE. 11c. GPE=mgh .0784 J=(.06kg)(9.8m/s^2)(h) .0784 = .588h h = .0784/.588 = .133m 12a. GPE=mgh GPE=(300kg)(9.8m/s^2)(18m) GPE=52,920J GPE=SPE SPE=52,920J SPE=1/2kx^2 52,920J=1/2kx^2 52920=(1/2)(k)(4^2) 52920=8k k = 6615 12b. GPE = mgh GPE=(400kg)(9.8m/s^2)(18m) GPE=70,560J GPE=SPE SPE=70,560J SPE=1/2kx^2 70,560J=1/2kx^2 70560=(1/2)(k)(4^2) 70560=8k k = 8820 13.SPE=1/2kx^2 SPE=(1/2)(40N/m)(.3m^2) SPE=(1/2)(40)(.09) SPE=1.8 J SPE=KE KE=1.8 J

=Section 4=

What Do You See?
I see two groups of people riding on a roller coaster. One is on the Moon, and the people are sleeping. The other is on Jupiter, and they are going very fast, most likely because of the difference in gravity.

What Do You Think?
Gravity can have a direction, it is pointing towards the center of a planet. People in Australia can be held "upside down" because they are pushed by gravity towards the center of the Earth, so everyone is being pushed in the same direction.

Physics Talk
Gravitational field- the gravitational influence in the space around a massive object. Inverse-square relationship- relationship between the magnitude of a gravitational force and the distance from the mass. Gravity- the force of attraction between two bodies due to their masses. Newton's law of universal gravitation- all bodies with mass attract all other bodies with mass. Inverse-Square relationship 2x the distance=1/4th the force 3x the distance=1/9th the force 5x the distance=1/25th the force 10x the distance=1/100th the force

Checking Up
1. Towards the center of the earth. 2. The one that is closest to the center of the earth. 3. 1/9th of the force. 4. Universal constance, 6.67 x 10^-11 N x m^2/kg^2 5. It's eliptical

Physics To Go
1. 125 N. 2a. 1/4th. 2b. 1/9th 2c. 1/16th 3. It isn't going to change because it is constant. 4. They will be exactly the same. 5a. The water is closer to the moon. 5b. The moon's gravitational force on the water, when the moon orbits the Earth it has an effect on the oceans. 5c. The moon's gravitational force pulls the water towards it, and there is gradually more water facing the moon than is on the opposite side of the Earth. 6a. A fish wouldn't go anywhere if there was no gravity. 6b. The fish would have nothing to move itself against if there was no gravity. 7a. 1/4th times less 7b. 1/9th times less 7c. 1/16th times less 7d. 4 times greater 8a. 2 times greater 8b. 3 times greater 8c. 4 times greater 8d. 1/2th times less 9a. 4 times greater 9b. 9 times greater 9c. 16 times greater 9d. 1/4th times less 10a. 2 times 10b. 9 times 10c. 6 times

=Section 5=

What Do You See?
I see two scenes, one with a butcher weighing meat, and in the other there are two scientists weighing meat with a spring scale.

What Do You Think?
I think that you can, but it won't be accurate as a scale to weigh an elephant would have to be heavy-duty. While a scale to weigh a canary would have to be able to weigh minute weights. The bathroom scale works by measuring the normal force that the floor exerts against you.

Investigate
A 1a. It's a measurement of weight 1b. Yes, it measures weight. 1c. Weight is mass 2a. 1078 vs 398 3a. Significantly less 4a. 107.8 4b. 2.45 5a. 375 newtons B 2a. The spring will pop back to its original shape. 3a. The spring bounces back towards it original shape. 4a. No, it springs back a little bit, but not all the way. media type="file" key="Movie 37.mov" width="300" height="300" 7a) 20g=1.3cm 50g=3.5cm 100g=7.4cm 70G estimate- 5.4- Actual-5cm 120-9cm 150- 11cm



Unknowns: "B"- Guess- 100g

Physics To Go
1a. 980N 1b. 98N 1c. 588N Weight = (mass in kg) x 9.8m/s2 ie: Fw=mg __Weight__ is measured in Newtons or pounds __Mass__ is measured in Kilograms or slug Conversion: 1kg=2.2lbs My weight in pounds: 159lbs My mass in kilograms: 72.3kg My weight in newtons: 708.54N 2a. 32.5N 2b. 250N 2c. 12.5N 3. 4. 12=1/2k(.03) k=26666N/m 5. As the force exerted on the spring increases, the stretch of the spring increases. 6. 15N/m 7. 1.5N/m

=Section 6=

What Do You See?
I see two elevators, one with a large man and it is descending, and one with a small child and it is ascending. The two are on scales, and the small child reads a weight of 100 because he is ascending and there is more g-force. The man reads a weight of 0 because he is in free fall

What Do You Think?
Your weight will not change, but you feel as if your weight is changing. Your apparent weight is changing. Yes, the bathroom scale would because the normal force is being exerted upon you is changing in areas such as drops and hills.

Investigate Part A 1a. 100 g 2a/b
 * || acceleration (up, down, zero) || scale reading (larger, smaller, equal to weight) ||
 * mass at rest || zero || equal ||
 * mass up at constant speed || zero || equal ||
 * mass accelerating upward || up || larger ||
 * mass at rest at top || zero || equal ||
 * mass moving down at constant speed || zero || equal ||
 * mass accelerating downward || down || smaller ||

3a. It gets smaller but at a constant speed, its equal 4a. 5a. Yes, because gravity goes towards the earth 5b. Yes, because of the Fnet 5c. No 5d. Yes, they are the same 6a. No, net force is acting on it

Part B 1a. The scale reading gets larger 1b. You are looking at apparent weight 1c. 2a. Yes 2b. Yes 2c. Yes, there is the hand pulling the weight up 2d. Same length 4a. Your weight would increase 5a. Mass will decrease slightly 5b. Our prediction is correct 6a. Mass will decrease 6b. Our prediction is correct 6c. It is going to go down 6d. Our prediction is correct 7a.

**Physics Talk**
Objects moving at a constant speed have a net force of 0. A = F/m -> F = ma F = mg -> m = F/g

==**Checking Up** == 1. 0 N 2. The scale would show a greater weight than the person's actual weight when accelerating upwards. 3. Because there is a force pushing up on you to accelerate you upwards. The force is pushing on you up, but you feel like you are pushing down into the force. 4. If you are in free fall while in an elevator, the scale will measure zero. 5. A rain drop is slowed by air resistance.

==**Physics To Go** == 1a. 2 sec x 9.8 m/s^2=29.4 m 1b. 5 sec x 9.8 m/s^2=147 m 1c. 10 sec x 9.8 m/s^2=539 m 2a. 2 sec x 1.6 m/s^2=4.8 m 2b. 5 sec x 1.6 m/s^2=24 m 2c. 10 sec x 1.6 m/s^2=88 m 3a. Yes 3b. Yes 3c. Yes 4. a. equal b. smaller c. equal d. greater e. equal f. larger g. equal h. smaller i. equal 5. The elevator is either starting to move down or slowing up. 6. The scale will measure something greater than 600 N when it starts accelerating upwards. 7a. Decrease 7b. Depending on direction7b. Depending on direction5. The elevator is either starting to move down or slowing up. 6. The scale will measure something greater than 600 N when it starts accelerating upwards. 8a. 50 kg 8b. > 50 kg 50 kg(9.8 m/s^2)=490 N 490-F=(50 kg)(2 m/s^2) F=490-100 F=390 N 8c. 50 kg 9a. The elevator is either not moving or it is a constant speed. The net force is 0. 9b. The elevator is in a free fall. 9c. The elevator is accelerating upwards. The man weighs more.

=Section 7=

What Do You See?
I see a roller coaster with a drop and loop, and different scenes as the coaster car travels along the track. The track is impossible because there is not enough inertia to make it up the first hill.

What Do You Think?
You don't fall out of the car because you are pushed into the roller coaster car seat when you go on a loop because of the centripetal force.

Investigate
Part A 1a. The car goes straight. 1b. The car goes around in a circle. 1c. The car will travel in a straight line tangent to the circle. 1d. My prediction is right. 2a. Centripetal force. 2b. It goes towards the center. Part B 1a. The string tightens and more force is needed. 1b. The faster the stopper went, the more force was needed. 2a. You need to apply A LOT more force. 2b. To compare force. 2c. The more mass, the more force. 3a. The longer the string the more force you need. 3b. You need to keep the mass constant. 4b. The force is more when the rubber is at the bottom but less when its at the top because gravity helps. 4c. Slacks near my fingers. 5a. To increase speed more force is needed. to slow up less force is being used. 5b. Yes, the more mass means more force to get it moving. 5c. A smaller radius needs less force. 5d. Use a stronger material. 6a. The force would need to be larger, because the car is moving at a faster speed. 6b. A small speed needs a small force.

**Physics Talk**
All objects moving in circles accelerate and require a force toward the center of the circle. The normal force is the force acting perpendicular to the surface. The force that keeps the object moving in a circle is called the centripetal force. The centripetal force is always directed toward the center. Centripetal Force- Fc = mv^2/r Where Fc is the centripetal force, m is the mass of the object, v is the speed and r is the radius of the circle.

**Checking Up**
1. Centripetal force is needed to make an object to move in a circle. 2. No, you are traveling at a constant speed. 3. The force of gravity and the force of the track on the cart. 4. The normal force and the force of gravity. 5. The greater the mass, greater the radius radius, and greater the speed are all factors that require more force to make the cart travel in a circle.

**Physics To Go** 1. Draw 2a. Friction 2b. It would keep going straight. 3. The force increases. 4. More difficult, as you need a greater force of friction. 5. F=total force m=mass v=velocity r=radius 6a. No, the speed had no change. 6b. Yes because the direction changed. 6c. 20m/s north. 8. The forces are normal force, gravitational force, and centripetal force. 9. All the forces that act on the object in a circle are the centripetal force.

=Section 8=

What Do You See?
I see a roller coaster, with one car on the hill that needs to be pushed by a group of people. The other car is descending down the slope and one person is flying out of the car. The car going up the hill has to overcome gravity, and the one going down the hill travels with it.

What Do You Think?
Yes, because you are close to free fall. You need more energy so it is more difficult.

Physics Talk
W=FD Power- the work done divided by the time elapsed - the speed at which work is done and energy is transferred. Watt- the SI unit for power, 1W=1J/s

Checking Up
1. It becomes GPE. 2. The Height, Mass, and Gravity. 3. It makes it easier to get the supplies there and lowers the force. 4. It stops because the velocity = 0. 5. The unit for power is a watt.

Physics To Go
1a. It's higher at the top. 1b. 9.8 1c. It's equal. 1d. GPE/X 1e. It is half KE half GPE 1f. As soon as it contacts the spring. 2a. 0, no work is done 2b. 30 2c. 3000 2d. 350 3a. A better way to say conserve energy would be to maintain energy. 4. It would have required more energy. 5a. 200,000 5b. 1333.333 watts

=Roller Coaster= Top of first drop: GPE=(15)(9.8)(.463) GPE=68.061J

Loop: GPE=(15)(9.8)(.23) GPE=33.81J

End of Turn 1: GPE=(15)(9.8)(.07) GPE=10.29J

Camelhump: GPE=(15)(9.8)(.09) GPE=13.23J

Bottom of first drop Coaster height- 46.355cm Marble Weight- 15g GPE=(15)(9.8)(.463) GPE=68.061J 68.061=1/2(15)v2 68.061=7.5v2 9.0748=v2 V=3.01m/s

Energy conservation: As the marble goes down the ramp it gains KE, which is when it goes into the vertical loop and out into the helix turn. The drop at the end of the helix gives it enough KE to make it back up the camelhump, which it then goes down into the full helix and hits the spring to stop it at the end of the track.

Power: The marble goes down the first drop, giving it enough speed and KE to go through the vertical loop.

Newtons laws: The marble will go down the ramp because there is no force to stop it. 2nd law: The first drop gives the marble plenty of KE and V to make it through the entire track. The second but smaller drop also gives it KE. 3rd law: During the track, the friction between the track and marble causes it to slowly lose energy.

Gravitation: Gravity and conversion from GPE to KE causes the marble to gain its energy and gravity also helps to keep the marble on the track and ensures it doesn't fly out.

Apparent weight:As the marble goes down drops, the g force and apparent weight of the marble is increased, as the marble goes up hills, the apparent weight decreases.

Hookes law: At the end of the rollercoaster there is a spring-like device that will help to stop the marble when it finishes the track.

Conclusion: Our rollercoaster, Captain America The Ride, is the rollercoaster you want to have in your park. It incorporates all fan-favorites, a vertical loop, helix turns and a camelhump, in a safe and efficient design.