Roller Coaster Design Project HELP

[MissLlanas]

Roller Coaster Design Project...HELP!

okay so here we go. I'll give everything I have haha. & if anyone can help me out at all it would be greatly appreciated. I'm very much LOST!
BTW! I'm not asking anyone to do the project for me, don't get the wrong idea. I did attempt it, I got a little more than half way through & I realized i was doing it incorrectly.
so I'd appreciate any help! even if it's just on one problem :)
Objective:
Design a roller coaster and using the one meter of wire provided build a scale model of your roller coaster ride. Mount your coaster on something sturdy. Label at least 7 reference points.

Criteria
1. Coaster must be to scale (1:1000)
2. Fnormal on the rider must always be greater than or equal to zero.
3. Maxium acceleration on the rider = 6 g.
4. Design your coaster to include at least the following points;
(nvm that I'll skip it because I already have the design. It includes a first hill, a close to flat exit path, a second hill, and a loop..I also have that all measured to scale).
A picture illustrating the basic design I had in mind is attached.
the first hill being: 127 millimeter hence .127 meters
I'm not sure if I have to take measurement for the semi-flat exit path.
the second hill is 114.3 millimeters hence .114 meters
the loop 88.9 millimeters so .088 metersGiven
1. mass of coaster + passengers is 4500 Kg
2. Use gravitational field strength of 9.8 N/Kg

Calculation Questions:
1. Work done by the motor to bring the coaster to the top of the first hill
I realize W=Fd, however I'm used to being provided with at least two out of three of the values. I know my measured displacement is 127 m.m soo that's .127 meters...since I need to use meters. Hoowever I'm a little stuck on how to fidn the force? i initially attempted to use the given 4,500 Kg and multiply it by 60 m/s (because it is indirectly given in the criteria that acceleration must not exceed 6 g.) so upon solving it that way, I reached a solution of 34,290 J.

2. Total gravitational energy at the top of the first hill.
I know PEg = mgh, which would be 4,500 Kg) (9.8)(.127 m) = 5,600 J ?

3. Assume a 30 seconds for the car to reach the top of the first hill. Calculate the power expended by the motor.
P= W/t and so I would 34290 J/30 sec. = 1,143 W ?

4. Assume electricity costs $0.07 per kilowatt-hour. If the motor and lift system is 25% efficient, how much will the electricity cost to run one ride?
completely stuck here!

spreadsheet
6. Determine the total mechanical energy left as the coaster arrives at each reference point. (Hint: this equals the total energy at the top of the first hill (A) minus the energy dissipated by the friction force during the section of the track between A and your reference point.)
7. At each reference point calculate PE, KE, and speed.
8. Determine the number of g's on the rider at each point, following these steps:
a. draw a force diagram showing the normal force (from seat), gravitational force and direction of acceleration.
b. write the equation for Newton's 2nd law to calculate Fnet on the coaster at each reference point.
c. solve for normal force at each point.
d. number of g's = normal force/force of gravity
9. Compare the normal force and g' s to the criteria listed at the beginning of the assignment. Make adjustments to your design if these don't meet criteria.
10. At three reference points of your choosing, calculate the momentum of the coaster.
if you can help me at all PLEASE do. even if it's only one problem I definitely need the help!

 

[anathema]

Hi there,

I can definitely help you with some of these calculation questions. Let's go through them one by one:

1. Work done by the motor to bring the coaster to the top of the first hill:
You are correct in using the equation W=Fd. In this case, the force we are looking for is the net force on the coaster, which is equal to the force of gravity (weight) plus the normal force. So we can write the equation as W=(mg+N)d. The displacement is 0.127 meters, and the mass of the coaster is 4500 kg. The force of gravity can be calculated as mg=(4500 kg)(9.8 m/s^2)=44,100 N. And we know that the normal force must be equal to or greater than 0, so let's assume it is equal to 0 for now. This gives us a work done by the motor of W=(44,100+0)(0.127 m)=5600 J.

2. Total gravitational energy at the top of the first hill:
You are correct in using the equation PE=mgh. The mass is still 4500 kg, and the height is 0.127 meters. So the total gravitational energy is PE=(4500 kg)(9.8 m/s^2)(0.127 m)=5571.3 J.

3. Power expended by the motor:
You are correct in using the equation P=W/t. However, the time given in the problem is 30 seconds, not 60. So the power expended by the motor is P=5600 J/30 s=186.7 W.

4. Electricity cost to run one ride:
To find the electricity cost, we need to first convert the power from watts to kilowatts. So 186.7 W=0.1867 kW. The cost for 1 hour of electricity at $0.07 per kilowatt-hour is 0.1867 kW x $0.07/kW-hr = $0.01307. However, the motor and lift system are only 25% efficient, so the actual cost would be 0.25 x $0.01307 = $0.00327 for one ride.

6. Total mechanical energy at each reference point:
To find the total mechanical energy at each reference point, we need to consider the energy at the top of the first hill (A) and

 

[ogb p]

Hello! I understand that designing a roller coaster can be a challenging project. I am happy to provide some guidance and assistance to help you complete your project successfully.

Let's start by addressing the criteria for your roller coaster design. It is important to ensure that your coaster is to scale (1:1000) and that the Fnormal on the rider is always greater than or equal to zero. This means that the rider should experience a normal force pushing them into their seat, rather than being lifted out of it. Additionally, the maximum acceleration on the rider should not exceed 6 g, which is equivalent to 6 times the acceleration due to gravity (9.8 m/s^2).

Now, let's move on to the calculation questions. For the first question, you are correct in using the equation W=Fd. However, the force you need to use is the force exerted by the motor to bring the coaster to the top of the first hill. This can be calculated using the formula F=ma, where m is the mass of the coaster + passengers and a is the acceleration. Since you know the mass (4500 kg) and the acceleration (9.8 m/s^2), you can calculate the force and then use it in the equation W=Fd to find the work done by the motor.

For the second question, you have correctly used the formula PE=mgh to calculate the potential energy at the top of the first hill. However, the value you have calculated (5,600 J) seems a bit low. Make sure you are using the correct units (meters for height and kilograms for mass) and double check your calculations.

For the third question, you are correct in using the formula P=W/t. However, the work done by the motor is 34,290 J, not 34290 J. So, the power expended by the motor would be 34,290 J/30 sec = 1,143 W. Good job!

For the fourth question, you need to find the cost of electricity for one ride. To do this, you need to first calculate the energy used by the motor and lift system. Since the efficiency is given as 25%, you can use the formula E=0.25*P*t, where P is the power expended by the motor (1,143 W) and t is the time for one ride (30 seconds). This will give you the energy used in