Little Sally is enjoying her first ride on a merry-go-round. (She is riding a st

Question

Little Sally is enjoying her first ride on a merry-go-round. (She is riding a stationaryhorse rather than one that goes up and down.) A schematic view of the merry goround as seen from above is shown in the drawing below.

A bit after the merry go round has started and is going around uniformly, we start ourclock. Little Sally’s position and velocity at time t = 0 is shown as a dot and arrow.

A. At t = 0, is the net force acting on Sally equal to zero? If it is, give a reasonwhy you think so. If it isn’t, specify the type of force and the objectresponsible for exerting it.

b. For the next 6 parts, specify which of the graphs below could represent theindicated variable for Sally’s motion. If none of the graphs work, say so explicitly.

i. The x component of Sally’s velocity.

ii. The angle Sally’s position makes with the x-axis.

iii. The y-component of the force keeping Sally moving in a circle.

iv. Sally’s angular velocity.v. Sally’s speed.

vi. The x-component of Sally’s position.

Explanation / Answer

A) At t=0 the net force acting on Sally is the centripetal force directed toward the center of the merry-go -round which causes Sally to move on a circular path. This force is exerted by the horse on Sally. B) (i) F - the x-component of velocity is initially zero and follows the pattern of a sine function as Sally moves around the circle (ii) A - this answer is correct assuming the angle is measured counterclockwise from the x-axis and the graph represents one complete revolution of the merry-go-round (iii) B - the y-component of velocity is initially at it's maximum value and follows the pattern of a cosine function (iv) F - Sally's angular velocity is constant (v) B - the x-component of Sally's position starts at it's maximum and follows the pattern of a cosine function

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