Centripetal acceleration problem

In summary, the conversation discusses a problem involving a train traveling at a constant speed on a curved track and a swinging chandelier suspended from the ceiling. The individual is trying to determine the speed of the train but has encountered difficulty with their calculations. They are advised to analyze the forces acting on the chandelier and apply Newton's 2nd law, focusing on the vertical and horizontal components separately.
  • #1
agentd00nut
6
0
ok i have this problem

A train traveling at a constant speed rounds a curve of radius 375 m. A chandelier suspended from the ceiling swings out to an angle of 18.0° throughout the turn. What is the speed of the train?

so far i have 9.8sin(18)=(v^2)/375
v^2/R being force
and i got V=33.7 but it was wrong and just for kicks i switched from sin to cos and i still got the wrong answer I am not sure where I've gone wrong

thanks for your help,
johnny
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  • #2
Not sure where you got that equation. (And v^2/R is the centripetal acceleration, not force.)

Analyze the forces acting on the chandelier and apply Newton's 2nd law. (Hint: Analyze the vertical and horizontal components separately.)
 
  • #3


Hi Johnny,

It looks like you are on the right track with your calculations. However, there may be an error in your equation. The force causing the chandelier to swing out at an angle is the centripetal force, which is equal to the mass of the chandelier times its centripetal acceleration. In this case, the centripetal acceleration is the tangential velocity squared divided by the radius of the curve (a = v^2/R). So the correct equation should be F = m*a = m*v^2/R.

To solve for the speed of the train, you can rearrange the equation to v = sqrt(F*R/m). Since the mass of the chandelier is not given, you can use the angle of 18.0° to find the tangential component of the force, which is equal to F*cos(18). So the final equation would be v = sqrt((F*cos(18))*R/m).

I hope this helps. Let me know if you have any further questions or if you are still having trouble solving the problem. Good luck!

Best,
 

What is centripetal acceleration?

Centripetal acceleration is the acceleration experienced by an object moving in a circular path. It is always directed towards the center of the circle and its magnitude is given by the formula a = v^2/r, where v is the velocity of the object and r is the radius of the circle.

What is the difference between centripetal and centrifugal acceleration?

Centripetal acceleration is the acceleration towards the center of the circle, while centrifugal acceleration is the apparent outward acceleration experienced by an object in circular motion. Centrifugal acceleration is a result of inertia and is not a true acceleration as it does not change the object's velocity.

What are some real-life examples of centripetal acceleration?

Some common examples of centripetal acceleration include the motion of a satellite in orbit around the Earth, the motion of a car around a curved track, and the motion of a rollercoaster on a loop. Any object moving in a circle or curved path experiences centripetal acceleration.

How does centripetal acceleration relate to gravity?

Centripetal acceleration is often caused by a force, and in the case of circular motion, this force is usually gravity. For example, a satellite in orbit around the Earth experiences centripetal acceleration due to the gravitational force exerted by the Earth.

What are some common misconceptions about centripetal acceleration?

One common misconception is that centripetal acceleration is a separate type of acceleration. In reality, it is simply a component of the object's overall acceleration. Another misconception is that centripetal acceleration always points towards the center of the circle, when in fact it can point in any direction as long as it is perpendicular to the object's velocity.

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