Question

A woman rides a carnival Ferris wheel at radius 15 m, completing five turns about its horizontal axis every minute. What are (a) the period of the motion, the (b) magnitude and (c) direction of her centripetal acceleration at the highest point, and the (d) mag- nitude and (e) direction of her centripetal acceleration at the lowest point

Answer 1

Answer:

Explanation:

a ) period of motion = 60 / 5 = 12 s

b ) At the highest level

centripetal acceleration will always be towards the centre so it will be vertically downwards

magnitude

= ω²R

= (2π / T )² R

= (4π² / T² )x R

= (4π² / 12²)x 15

= 4.1 m s⁻²

b ) At the lowest level

centripetal acceleration will always be towards the centre so it will be vertically upwards

Magnitude

Magnitude will be same because woman is moving with uniform speed and radius is also same.

Answer 2

Answer:

Explanation:

Number of turns per minute = 5

Number of turns in 1 second = 5 / 60 = 0.083 Hz

Frequency is defined as the number of turns completed in one second.

So, frequency, f = 0.083 Hz

(a) The time period is defined as the time taken by a body to complete one turn.

Time period is the reciprocal of frequency.

T = 1/ f

T = 1 / 0.083

T = 12 second

(b) The centripetal acceleration is given by

a =  ω² x R

a = ( 2 x π x f )² x R

a = ( 2 x 3.14 x 0.083)² x 15

a = 4.06 m/s²

(c) the direction of acceleration is always towards the centre of the circular path.

At top most point the centripetal acceleration is downwards.

(d) The magnitude of centripetal acceleration is same.

a = 4.08 m/s²

(e) At the bottom most point the centripetal acceleration acts upwards.