A car travels at a constant speed around a circular track whose radius is 2.6 km

Question

A car travels at a constant speed around a circular track whose radius is 2.6 km. The car goes once around the track in 360 s. What is the magnitude of the centripetal of the car? At an amusement park there is a ride in which cylindrically shaped chambers spam around a central axis. People sit in seats facing the axis. their backs against the outer wall. At one instant the outer wall moves at a speed of 3.2 m/s, and an 83 kg person feels a 560 N force pressing against his back. What is the radius of a chamber? An automobile with tires of radius 32 cm accelerates from 0 to 45 mph in 9.1 s. Find the angular acceleration of the tires. How many radians do the tires go through during this time?

Explanation / Answer

centripetal accleration is

a = v^2/r = ( 2 pi r/T)^2/ r = 4 pi^2 r/ T^2 = 4 pi ^2(2.6 * 10^3 m)/ ( 360 s)^2 =0.79 m/s^2

(2)

F = mv^2/r

r = mv^2/F = 83 (3.2)^2/560 = 1.51 m

(3)

alpha = wf- wi/ t

=( vf/r)-0/t

= ( 45 mph (0.44704/ mph)/0.32/9.1

=6.9 rad/s^2

(b)

wf^2 - wi^2 = 2 alpha del theta

( 45 mph (0.44704/ mph)^2 - 0 = 2 ( 6.9) del theta

del theta = 29.32 radians

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