How Does Banking Angle Affect Centripetal Force on a Curve?

In summary, the net centripetal force needed to keep the car from skidding sideways is 30476.19 N. Without friction, the normal force would be the only force contributing to centripetal force, and it is equal to 32718.5452 N. However, there may have been other errors in the previous calculations.
  • #1
lzh
111
0
QUESTION:A car travels at a speed of 16 m/s around a
curve of radius 21 m.
The acceleration of gravity is 9.8 m/s^2 :
http://img262.imageshack.us/img262/3067/bankedcurvera4.jpg
What is the net centripetal force needed to
keep the car from skidding sideways? Answer
in units of N.
if there was no friction, what centripedtal force could be provided just by the banking of the road?
ANSWER:
http://img523.imageshack.us/img523/4331/bankrz7.jpg
i used 2 eqns for this by dividing all the forces into separate components.
y-direct:
mg+fcos72=ncos18
x-direct:
mv^2/r=nsin18+fsin72
i used those and found
n=32718.5452
f=21413.6627
coeff of frict=.65448
net centripetal=30476.19
i found all of the above for the other parts of the question, and they are all correct. But the question i presented above confused me. If no friction is present, the only force contributing to centripetal force would be the normal force. so that'd be nsin18, but it wasn't right.

what am i thinking wrong here?
 
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  • #2
mg+fcos18=ncos18

Redo this part.
 
  • #3
oh srry about that, i wrote the eqn down wrong, but i did it the right way on paper. its been changed
 
  • #4
lzh said:
If no friction is present, the only force contributing to centripetal force would be the normal force. so that'd be nsin18, but it wasn't right.

Yep, that's correct. Maybe there are some other errors in your previous results.
 
  • #5
but i know for a fact that my normal force is correct...
 
  • #6
lzh said:
but i know for a fact that my normal force is correct...
Recalculate the normal force without the friction.
 
  • #7
ok, ty, i got it
 

1. What is a banked curve?

A banked curve is a curved section of a road or track that is angled or tilted towards the center of the curve. This design allows vehicles to travel at higher speeds without losing control.

2. How does a banked curve work?

A banked curve works by using the force of friction to keep a vehicle on the intended path. The banking angle of the curve is designed to counteract the centrifugal force that pushes the vehicle outwards, allowing it to maintain a constant speed and direction.

3. What factors affect the banking angle of a curve?

The banking angle of a curve is affected by several factors, including the speed of the vehicle, the radius of the curve, and the coefficient of friction between the tires and the road surface.

4. Why are banked curves important in racing?

Banked curves are important in racing because they allow vehicles to maintain higher speeds while turning, resulting in faster lap times. They also reduce the risk of accidents by providing a safer and more stable path for vehicles to follow.

5. How does the banking angle affect the speed of a vehicle?

The banking angle of a curve affects the speed of a vehicle by providing a force that helps to keep the vehicle on the intended path. The greater the banking angle, the higher the speed the vehicle can maintain without losing control.

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