A car is traveling around a horizontal circular track with radius r= 210 m as sh

Question

A car is traveling around a horizontal circular track with radius r= 210 m as shown. It takes the car time T = 51 s to go around the track once. The angle theta_A = 30 degree is above the x-axis, and the angle theta_B = 55 degree is below the x-axis. What Ls the car's speed? What Ls the magnitude of the car's acceleration? What Ls the x component of the car's velocity at point A? What Ls the y component of the car's velocity at point A? What Ls the x component of the car's acceleration at point B? What Ls the y component of the car's acceleration at point B? As the car passes point B. the y component of its velocity is increasing, decreasing, coils taut.

Explanation / Answer

r = 210 m

T = 51 s

A = 30°

B = 55°

a) v = 2r/T =  2*210/51 = 25.9 m/s

b) The magnitude of the car’s acceleration = a = v² / r = 25.9^2/210 = 3.2 m/s^2

c) Vx = v*sinA = 25.9*sin30 = 12.95 m/s
d) Vy = v*cosA = 25.9*cos30 = 22.4 m/s (for counter-clockwise travel)

e) The x component of the car’s acceleration when it is at point B
= -( v²/ r) cos (B) = -3.2*cos(-55) = - 1.84 m / sec²
f) The y component of the car’s acceleration when it is at point B
= - ( v²/ r)sin (B) = - 3.2*sin (-55) = 2.62 m / sec²

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