Question

a)A car initially traveling at 31.7 m/s undergoes a constant negative acceleration of magnitude 1.60 m/s² after its brakes are applied.

-How many revolutions does each tire make before the car comes to a stop, assuming the car does not skid and the tires have radii of 0.310 m? ______ rev

-What is the angular speed of the wheels when the car has traveled half the total distance? _______ rad/s

b) A 50.0-kg child stands at the rim of a merry-go-round of radius 2.45 m, rotating with an angular speed of 3.80 rad/s.

-what is the child's centripetal acceleration? _______ m/s^2

-what is the minimum force between her feet and the floor of the carousel that is required to keep her in the circular path? _____ N

-what minimum coefficient of static friction is required?

Answer 1

a) given :

u = initial velocity = 31.7 m/s

a = -1.60 m/s²

r = 0.310 m

tangential acceleration =

initial angular velocity =

a) let no of revolutions made = n

therefore, using kinematics of circular motion :

[ theta = angular distance = n x 2 pi]

[answer]

b) let the angular speed be when it travels half distance or n/2 revolutions.

therefore, using kinematics of circular motion :

[answer]

b) i) centripetal acceleration =

(ii) the friction force provides centriptal force.

for minimum force, the friction is acting as fmax.

[answer]

iii)

   [where N = normal force]

[answer]