Two Formula racing cars are negotiating a circular turn, and they have the same
ID: 1396410 • Letter: T
Question
Two Formula racing cars are negotiating a circular turn, and they have the same centripetal acceleration. However, the path of car a has a radius of 48 m, while that of Car B is 36 m. (a) determine the ratio of angular speed of car a to the angular speed of car B. (b) the coefficient of static friction between the tires and the pavement is 0.9. Find the maximum linear speeds at which car a and B, respectively, can make the turn along the paths described in part a.
(Please thoroughly explain how the answers are provided)
Explanation / Answer
a) we know, cetripetal(radial) acceleration, a_rad = r*w^2 (here r is radius and w is angular speed)
given,
a_radA = a_radB
r_A*w_A^2 = r_B*w_B^2
==> w_A/w_B = sqrt(r_B/r_A)
= sqrt(36/48)
= 0.866
b) static firctional force provides ncessary centripetal froce on car.
static friction = centripetal force
for car A,
mue_s*m*g = m*Vmax^2/r_A
==> Vmax = sqrt(mue_s*g*r_A)
= sqrt(0.9*9.8*48)
= 20.6 m/s
for car B, mue_s*m*g = m*Vmax^2/r_B
==> Vmax = sqrt(mue_s*g*r_B)
= sqrt(0.9*9.8*36)
= 17.8 m/s
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