A car travels around a circle with a diameter of 500 m at a constant speed of 25 m/s. The static friction coefficient is 0.3 and the kinetic friction coefficient is 0.2. Will the car skid?
Use the static coefficien, mus, to determine if it will skid. The centripetal force needed to keep from skidding is
M V^2/R. The maximum friction force available is
M*g*mus
Compare V^2/R to g*mus
V^2/R = 25^2/250 = 2.5 m/s^2
g*mus = 9.8*0.3 = 2.94 m/s^2
So it won't skid.
Thank you very much!
no the car will not skid.
To determine if the car will skid while traveling around the circle, we need to compare the centripetal force acting on the car with the maximum frictional force available.
Centripetal force is given by the formula:
F = (m * v^2) / r,
where:
F is the centripetal force,
m is the mass of the car,
v is the velocity of the car,
and r is the radius of the circle (which is half the diameter).
First, we need to calculate the radius:
r = d / 2,
where:
d is the diameter of the circle.
Plugging in the values:
d = 500 m,
r = 500 m / 2 = 250 m.
Now, we can calculate the centripetal force:
F = (m * v^2) / r.
Next, we need to calculate the maximum frictional force:
Ffriction_max = µ * N.
The normal force (N) acting on the car can be calculated as:
N = m * g,
where:
m is the mass of the car,
and g is the acceleration due to gravity.
The maximum frictional force can then be determined using the static friction coefficient (µ):
Ffriction_max = µ * N.
If the centripetal force is greater than the maximum frictional force, the car will skid.
Let's calculate and compare the values to find out if the car will skid.