A 42.0-kg child takes a ride on a Ferris wheel that rotates four times each minu

Question

A 42.0-kg child takes a ride on a Ferris wheel that rotates four times each minute and has a diameter of 22.0 m.

(a) What is the centripetal acceleration of the child?

magnitude _____ m/s2

direction _____

(b) What force (magnitude and direction) does the seat exert on the child at the lowest point of the ride?

magnitude _____ N

direction ______

(c) What force does the seat exert on the child at the highest point of the ride?

magnitude _____ N

direction _____

(d) What force does the seat exert on the child when the child is halfway between the top and bottom? (Assume the Ferris wheel is rotating clockwise and the child is moving upward.)

magnitude ____ N

direction ______ ° counter-clockwise from the horizontal

Explanation / Answer

here,

mass of the child , m = 42 kg

diameter , d = 22 m

radius , r = 11 m

(a)

angular speed , w = ( 2*pi*4) /(60 )

w = 0.419 rad/s

the centripital accelration , ac = w^2*r

ac = 0.419^2 * 11

ac = 1.93 m/s^2

(b)

the magnitude of the force exerted by seat be N

at the lowest point

N = m*ac + m*g

N = 42 * ( 1.93 + 9.8)

N = 492.71 N

the force seat exert on the child at the lowest point of the ride is 492.71 upwards

(c)

at the highest point

N = m( g - a)

N = 42 * ( 9.8 - 1.93)

N = 330.54 N

the force the seat exert on the child at the highest point of the ride is 330.54 N

(d)

at the half way,

centripital force ,Fc = m*ac = 81.06 N

gravitational force , Fg = m * g= 411.6 N

Fnet = sqrt( Fc^2 + Fg^2)

Fnet = sqrt( 81.06^2 + 411.6^2)

Fnet = 419.51 N

theta = arctan( 411.6/81.06)

theta = 78.86 degree

the magnitude of the force is 419.51 N and the direction is 87.86 degree counter clockwise from the horizontal

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.