Circular Motion question. Need direction

[Mike B]

Hey all, I'm new here. I like physics, but I have a hard time with it. It's frustrating because I have a problem of not knowing what all is going on in some problems. The physics tutor at my school is hard to get ahold of so I decided to look online for physics related items. I stumbled across this site and figured it would be a good place to refine my skills.

Well here is my question.

A train traveling at a constant speed rounds a curve of radius 235m. A lamp suspended from the ceiling swings out to an angle of 17.5 throughout the curve. What is the speed of the train?

I see that the speed of of the lamp=speed of the train. Since an angle is involved I initially thought it would be a banking problem, but without a weight to work with I decided that is probably didn't have to do with bankment.

Since the speed is constant does that mean acceleration is also constant in this case?
I know speed and velocity aren't the same in some cases, but I think the speed and velocity are the same in this situation.

I looked at the lamp as being at 270 degree's initially, and 17.5 was a reference angle (or maybe the 197.5 is the reference angle :p. I forget). So I added 17.5 and 180 to get 197.5 degree's if you were looking at it as a circle. I'm uncertain where to go from here.

Any help would be appreciated. Thanks

 

[whozum]

I see that the speed of of the lamp=speed of the train.

This isn't correct. The lamp is suspended, meaning it isn't moving relative to the train. The key point here is that the lamp is being pulled forward by the train and pulled back by the tension in the string. You should notice that the net force on the lamp is 0, that's the most important part here.

I know speed and velocity aren't the same in some cases, but I think the speed and velocity are the same in this situation.

This is a case where speed and velocity are NOT equal. Speed is the MAGNITUDE of the velocity vector. The velocity vector here changes direction as you travel around the curve, but the speed remains the same.


The way to tackle this is to use the angle of the lamp's displacement to find the speed. Draw a force diagram for the lamp, and set up equations for the tension in the string in the vertical and horizontal direction.

You only need to work in two dimensions here, don't confuse yourself and make it a three dimension problem.

 

[quicknote]

for your interest.Hi there, welcome to the physics community! Circular motion problems can definitely be tricky, but with some practice and understanding of the concepts, you'll get the hang of it.

In this problem, we need to use the concept of centripetal force to find the speed of the train. Centripetal force is the force that keeps an object moving in a circular path. In this case, the force is provided by the train's wheels pushing against the track.

To find the speed of the train, we can use the formula for centripetal force: F = mv^2/r, where m is the mass of the object (in this case, the train), v is the speed, and r is the radius of the curve.

We also know that the angle of the lamp (17.5 degrees) is equal to the angle between the horizontal and the string attached to the lamp. This means that the vertical component of the tension in the string is equal to the weight of the lamp. And since the lamp is not accelerating vertically, the vertical component of the tension must also equal the centripetal force.

So, we can set up an equation: mgcos(17.5) = mv^2/r. We know the mass of the lamp (m) and the radius of the curve (r), so we can solve for v.

Once you have the speed of the train, you can also calculate the acceleration using the formula a = v^2/r. And since the speed is constant, the acceleration is also constant.

I hope this helps guide you in the right direction. Remember to always draw a diagram, identify the forces at play, and use the appropriate formulas. Keep practicing and don't hesitate to reach out for help when needed. Good luck!