How Much Force Does a Lift Chain Apply to a Roller Coaster?

So the lift chain is pulling the roller coaster up the hill at an angle of 66 degrees. In summary, to calculate the force applied by the lift chain, we can use the formula F=ma, where m is the mass of the roller coaster (4140 kg) and a is the acceleration due to gravity (9.8 m/s^2). This gives us a force of 40572 N. However, since the lift chain is pulling the coaster at an angle, we need to use the cosine function to find the component of the force in the vertical direction. This gives us a final force of 16502 N. The 120 meters mentioned in the problem is not needed for this calculation.
  • #1
smoothmar
1
0

Homework Statement



THe length that the train is pulled up the lift hill is 120 meters. How much force did the lift chain apply to the coaster to pull it up the hill. Mass of the roller coaster = 4140 kg θ = 66°

Homework Equations





The Attempt at a Solution


I Tried F=ma to get (4140kg)(9.8m/s) = 40572N then (40572N)cos(66° to get 16502. i do not know if that is correct. Help is needed please
 
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  • #2
force times distance = work = ? (hint: has to do with the 120m and the 66 deg.)
 
  • #3
THe length that the train is pulled up the lift hill is 120 meters. How much force did the lift chain apply to the coaster to pull it up the hill. Mass of the roller coaster = 4140 kg θ = 66°

Draw the diagram.

Check where the angle 66 degrees is measured. eg is it cos(66) or sin(66) you need.

The 120m doesn't need to feature in the calculation. That's probably for another part of the question.
 
  • #4
CWatters said:
Draw the diagram.

Check where the angle 66 degrees is measured. eg is it cos(66) or sin(66) you need.

The 120m doesn't need to feature in the calculation. That's probably for another part of the question.

Oh, right.
 
  • #5


Your approach is correct. To calculate the force applied by the lift chain, you need to use the formula F=ma, where m is the mass of the roller coaster and a is the acceleration due to gravity (9.8m/s^2).
However, since the roller coaster is being pulled up at an angle of 66°, you need to use the component of the force in the direction of motion, which is given by Fcosθ.
Therefore, the force applied by the lift chain would be (4140kg)(9.8m/s^2)cos(66°) = 16502N. This is the amount of force needed to overcome the force of gravity and pull the roller coaster up the lift hill.
 

Related to How Much Force Does a Lift Chain Apply to a Roller Coaster?

1. What is the science behind roller coasters?

The science behind roller coasters is primarily based on the principles of physics, particularly Newton's laws of motion. Roller coasters use potential and kinetic energy to propel the train along the track, and the forces of gravity, inertia, and friction help to create the thrilling experience.

2. How do roller coasters stay on the track?

Roller coasters stay on the track through a combination of design elements such as wheels, tracks, and the forces of gravity and inertia. The wheels on the train are designed to fit snugly onto the track, and the shape of the track helps to keep the train on its path as it moves through the ride.

3. Why do roller coasters have loops and corkscrews?

Roller coasters have loops and corkscrews to add extra excitement and thrill to the ride. These elements also utilize the principles of physics, specifically centripetal force, to keep the train moving in a circular motion and allowing riders to experience the feeling of weightlessness.

4. How do engineers design roller coasters?

Engineers use a combination of math, physics, and computer simulations to design roller coasters. They must consider factors such as speed, height, and g-forces to create a safe and enjoyable ride for riders. Computer simulations allow them to test different designs and make adjustments before physically building the ride.

5. Are roller coasters safe?

Yes, roller coasters are designed with safety as the top priority. Engineers follow strict safety regulations and conduct thorough inspections to ensure that the ride is safe for riders. However, it is important for riders to follow all safety instructions and guidelines while on the ride.

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