Physics

posted by .

In the Daytona 500 car race in Daytona, FL, a curve in the oval track has a radius of 316 m (near
the top of the curve) and is banked at 31.0
O
.
a) What speed would be necessary to make this turn if there was no friction on the road?
b) If the coefficient of static friction between the tires and the road is 0.70, what are the minimum
and maximum speeds that a car could take this turn and not slide?

• Physics -

(a)
x: ma=N•sinα
y: 0=N•cosα –mg, => N=mg/cosα
a=v²/R
m• v²/R = N•sinα= mg•sinα/cosα= mg•tanα
v=sqrt(R• g•tanα)
(b)
x: ma=N•sinα+F(fr) •cosα
y: mg= N•cosα –mg-F(fr) •sinα

Since F(fr)=μ•N,
ma=N(sinα+μ•cosα)
mg= N(cosα - μ• sinα)
ma/mg = (sinα+μ•cosα)/ (cosα - μ• sinα)
a=v² /R
v² /Rg= (sinα+μ•cosα)/ (cosα - μ• sinα)
v=sqrt[Rg (sinα+μ•cosα)/ (cosα - μ• sinα)]

Similar Questions

1. Physics

A car, having a mass of 1.2 x 10^3kg rounds a curve which is banked at an angle of 18 degrees to the horizontal. The radius of the curve is 130m. Find the speed of the car if the frictional force between the tires and the road is 3.5 …
2. physics

Two banked curves have the same radius. Curve A is banked at 11.0 °, and curve B is banked at an angle of 17.4 °. A car can travel around curve A without relying on friction at a speed of 15.3 m/s. At what speed can this car travel …
3. physics

Two banked curves have the same radius. Curve A is banked at 11.0 °, and curve B is banked at an angle of 17.4 °. A car can travel around curve A without relying on friction at a speed of 15.3 m/s. At what speed can this car travel …
4. College Physics

The Daytona 500 stock car race is held on a circular track that is approximately 2.25 miles long, and the turns are banked at an angle of 32.5°. It is currently possible for cars to travel through the turns at a speed of about 189 …
5. Physics

A car can be driven around a 120 m radius curve at constant speed without sliding if the maximum centripetal acceleration is 0.130g. (a) What is the maximum speed that the car can travel around the curve without sliding?
6. physics

If a car takes a banked curve at less than the ideal speed, friction is needed to keep it from sliding toward the inside of the curve (a real problem on icy mountain roads). (a) Calculate the ideal speed to take a 105-m radius curve …
7. physics

highway curve in northern Minnesota has a radius of 230 m. The curve is banked so that a car traveling at 21 m/s and will not skid sideways, even if the curve is coated with a frictionless glaze of ice. At what angle to the horizontal …
8. physics

If a car takes a banked curve at less than the ideal speed, friction is needed to keep it from sliding toward the inside of the curve (a real problem on icy mountain roads). (a) Calculate the ideal speed to take a 95 m radius curve …
9. physics

Curve A is banked at 11.2 °, and curve B is banked at an angle of 15.2 °. A car can travel around curve A without relying on friction at a speed of 14.5 m/s. At what speed can this car travel around curve B without relying on friction?
10. Physics

A 410 kg race car is rounding a curve in the road which is banked at an angle of 23.4 degrees from the horizontal. Assume that there has just been a massive snowfall and the road’s surface is frictionless. What must the radius of …

More Similar Questions