Uniform circular motion on a banked curve

[Sean1218]

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

a_c = v²/r

The Attempt at a Solution

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

v = sqrt((rF_gtanx + F_ktanxsinx + F_kcosx)/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?

 

[Delphi51]

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.

 

[awertag]

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

 

[physicsman2]

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.

 

[Sean1218]

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.

 

[awertag]

thanks very much!

 

[awertag]

sorry again but i don't see that "new topic" option

 

[Delphi51]

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.