Uniform circular motion on a banked curve

In summary, the conversation discusses finding the speed of a car rounding a banked curve with a mass of 1200 kg and a radius of 130 m, given a frictional force of 3.5 x 10^3 acting down the banked curve. After breaking it down into x and y components, the expression v = sqrt((rFgtanx + Fktanxsinx + Fkcosx)/m) is used to solve for the speed, but a calculation error is made. With the correct distribution of r, the final answer is approximately 29 m/s.
  • #1
Sean1218
86
0

Homework Statement



A car with mass 1200kg rounds a curve banked at 18 degrees. The radius of the curve is 130 m.

Find the speed of the car if the frictional force between the tires and the road is 3.5 x 10^3 down the banked curve.

Homework Equations



ac = v2/r

The Attempt at a Solution



After breaking it up into x and y components, I came up with the following:

v = sqrt((rFgtanx + Fktanxsinx + Fkcosx)/m)

Solving for it, I got about 20 m/s. The answer is 29 m/s. I think I just made some sort of calculating error or missed a negative, but I haven't been able to find it. Any help?
 
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  • #2
That v expression can't be right - the units vary from term to term.
Perhaps all the terms should have an r in them.
I don't see how you get the tans. What is Fk?

I have a diagram with Ff along the ramp, mg down and Fn (road pushing on the car) perpendicular to the ramp. I believe the sum of the horizontal components of these 3 forces is the centripetal force. I get an answer larger than 29 for v.
 
  • #3
im sorry this is irrelevant to the question but I am new and i need to post a question; how do i do that? help I am lost lol
 
  • #4
awertag said:
im sorry this is irrelevant to the question but I am new and i need to post a question; how do i do that? help I am lost lol

New topic button at top of thread listing, left-hand side.
 
  • #5
Ohh, just forgot to distribute r I think, I get approx 29 m/s now, thanks! The tans are from multiplying out terms with sin and cos in them, I was just simplifying.
 
  • #6
thanks very much!
 
  • #7
sorry again but i don't see that "new topic" option
 
  • #8
Click https://www.physicsforums.com/forumdisplay.php?f=153
to go to the introductory physics thread list. On that page, near the top, but below the advertisement and just above the "threads in forum introductory physics" you should see a "NEW TOPIC" button.
 

1. What is uniform circular motion on a banked curve?

Uniform circular motion on a banked curve refers to the motion of an object traveling in a circular path on a banked surface, where the speed of the object remains constant and the surface is angled to allow for the object to maintain its path without slipping or sliding.

2. How is the angle of the banked surface determined for an object in uniform circular motion?

The angle of the banked surface is determined by the velocity of the object, the radius of the circular path, and the force of gravity acting on the object. This can be calculated using the equation tanθ = v2/rg, where θ is the angle, v is the velocity, r is the radius, and g is the acceleration due to gravity.

3. What is the role of centripetal force in uniform circular motion on a banked curve?

Centripetal force is the force that acts towards the center of the circular path, keeping the object in its circular motion. In uniform circular motion on a banked curve, the centripetal force is provided by the horizontal component of the normal force from the banked surface.

4. What factors affect the stability of an object in uniform circular motion on a banked curve?

The stability of an object in uniform circular motion on a banked curve is affected by the angle of the banked surface, the speed of the object, and the coefficient of friction between the object and the surface. A higher angle, lower speed, and higher coefficient of friction will result in a more stable motion.

5. How does changing the mass of an object affect its motion on a banked curve?

The mass of an object does not affect its motion on a banked curve, as long as the other factors (velocity, radius, angle) remain constant. According to Newton's Second Law, the acceleration of an object in uniform circular motion is inversely proportional to its mass, so changing the mass will not affect the object's speed or path.

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