A car rounds a banked curve where the radius of curvature of the road is R, the banking angle is , and the coefficient of static friction is µ.
(a) Determine the range of speeds the car can have without slipping up or down the road. (Use mu for µ, theta for , and R and g as appropriate in your equations.)
minimum speed ----m/s
maximum speed ----m/s
(b) What is the range of speeds possible if R = 150 m, = 10°, and µ = 0.13 (slippery conditions)?
minimum speed ----m/s
maximum speed ---- m/s
2007-10-30 07:57:33 · 1 answers · asked by roxy_799 1 in Science & Mathematics ➔ Physics
Force of friction that holds the car on the road is
f= µN
Normal N=mg/cos(theta)
f=µmg/cos(theta)
N= Fc/sin(theta)
Centripetal force Fc= V^2/R
When parallel to the road component of Fc less parallel component of the weight exceeds the force of friction the car will slide.
f>=Fc cos(theta) - mg sin(theta)
µmg/cos(theta)>=V^2/R - mgsin(theta)
the max speed in then
V=sqrt((mg/R)( µ/cos(theta) + sin(theta))
2007-10-31 08:37:26 · answer #1 · answered by Edward 7 · 0⤊ 0⤋