Calculate Speed at Top of Roller Coaster 2nd Hill (5.5m)

In summary, the mass of the coaster is 800 kg and it goes up a lift hill of 18 m at a speed of 2.50 m/s. The second hill is 5.5 m high and the person wants to know the speed at the top of the second hill. Using the equations for potential and kinetic energy, the speed at the top of the second hill is calculated to be 15.9 m/s. The mass of the coaster does not affect this calculation as the coaster is under constant acceleration due to gravity.
  • #1
cowgiljl
63
1
The mass of the coaster is 800 kg
The lift hill is 18 m highabd it goes up the lift hill at 2.50 m/s
The second hill is 5.5m high.

Wants to know the speed at the top of the second hill.
do i really care about the weight of the car?

This is what i have so far

PEtop1 +KEtop1 = KE bott
2*9.80*18 +2.5^2 = v^2 bott
V bott = 18.9 m/s

second formula was
Ke bott - Pe top1 = KE top 2
18.9^2 - 2*9.80*5.5 = V^2 top 2

Vtop 2 = 15.9 m/s and that is my final answer is that look right

thanks
 
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  • #2
Yep...answer looks right to me.
 
  • #3
thanks

thanks hindi
 
  • #4
I believe the mass doesn't matter in this problem because the coaster is under constant acceleration for the whole run (gravity).
 

1. How do you calculate the speed at the top of the second hill on a roller coaster that is 5.5m tall?

The speed at the top of the second hill can be calculated using the formula v = √(2gh), where v is the velocity, g is the acceleration due to gravity (9.8m/s²), and h is the height of the hill (5.5m). So, the speed at the top of the second hill would be v = √(2 x 9.8 x 5.5) = √107.8 = 10.38m/s.

2. What is the significance of calculating the speed at the top of the second hill on a roller coaster?

The speed at the top of the second hill is important because it determines the amount of potential energy that is converted into kinetic energy. This affects the overall speed and thrill of the roller coaster ride.

3. Can you use any other formula to calculate the speed at the top of the second hill?

Yes, another formula that can be used is v = √(u² + 2as), where v is the final velocity, u is the initial velocity (which would be 0m/s at the top of the hill), a is the acceleration (which is equal to the acceleration due to gravity), and s is the displacement (which would be the height of the hill).

4. How does the speed at the top of the second hill affect the safety of a roller coaster?

The speed at the top of the second hill must be carefully calculated and controlled to ensure the safety of the riders. If the speed is too low, the roller coaster may not have enough momentum to make it over the hill and could potentially stop or even roll backwards. If the speed is too high, it could cause discomfort or injury to the riders.

5. Is there a maximum or ideal speed for a roller coaster at the top of the second hill?

There is no specific maximum or ideal speed for a roller coaster at the top of the second hill as it depends on various factors such as the design and layout of the roller coaster, the weight and size of the train, and the age and condition of the track. However, most roller coasters aim to maintain a safe and thrilling speed for riders at the top of the second hill.

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