Solving Speed of Train on Curve of Radius 235m

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In summary, a train traveling at a constant speed rounds a curve of radius 235 m, causing a chandelier suspended from the ceiling to swing out to an angle of 17.5° throughout the turn. To find the speed of the train, the equations a=v^2/r and v=2πr/T can be used, along with the use of cosine and sine. A free body diagram can also be drawn to consider the forces on the chandelier, including tension and gravity. However, the unit of time must be accounted for in the calculations.
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sugarntwiligh
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Homework Statement



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

Homework Equations



a=v^2/r
use of cosine and sine

v=2x3.14xr/T

The Attempt at a Solution



Not sure what 17.5 degrees tells me about the problem, except its continuing along straight while the train turns. I tried to draw but it really doesn't make much sense to me. Also, even if I did compute using cosine and sine, what would that tell me about the problem except distance? And, I can't find acceleration, velocity, or period without time.
Any thoughts?
 
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  • #2
Consider the forces on the chandelier (draw a free body diagram). You will have the tension of the string, and gravity.
 
  • #3
I did that and I guess I can derive T from the triangle, but since T is a unit of time, I would have to cancel the time from both sides. Where is the unit of time in my free body diagram?
 
  • #4
Somebody please help I have to get this done by a deadline!
 
  • #5
slkdfjklsdkfjjjj!
 

1. What is the formula for calculating the speed of a train on a curve with a radius of 235m?

The formula for calculating the speed of a train on a curve is v = √(r*g*tan(θ)), where v is the speed, r is the radius of the curve, g is the acceleration due to gravity, and θ is the angle of the curve.

2. How do you determine the angle of a curve with a given radius of 235m?

The angle of a curve can be determined using the formula θ = arctan (v² / (r*g)). This formula can be rearranged to solve for θ, given the speed and radius of the curve.

3. Can the speed of a train on a curve with a radius of 235m be greater than its speed on a straight track?

Yes, the speed of a train on a curve can be greater than its speed on a straight track. This is because the curve provides a centripetal force that allows the train to maintain its path and speed, whereas on a straight track, the train may experience friction or resistance that slows it down.

4. Is the speed of a train on a curve with a radius of 235m affected by the weight or length of the train?

Yes, the speed of a train on a curve can be affected by the weight and length of the train. A heavier or longer train may require a greater centripetal force to maintain its speed on a curve, and thus may have a lower speed compared to a lighter or shorter train.

5. Can the speed of a train on a curve with a radius of 235m be calculated using only the radius and angle of the curve?

No, the speed of a train on a curve cannot be calculated using only the radius and angle of the curve. The speed also depends on other factors such as the acceleration due to gravity and the weight and length of the train. These factors must be taken into account to accurately calculate the speed on a curve.

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