Jessica is riding on a merry-go-round on an outer horse that sits at a distance
of 8.0 m from the center of the ride. Jessica\'s sister, Julie, is on an inner horse
located 6.0 m from the ride\'s center. The merry-go-round turns around once
every 40.0 s. a) Explain which girl is moving with the greater linear speed.
b) What is the centripetal acceleration of Julie and her horse?
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oladayoademosu 1 year ago
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a. Jessica's has a greater linear speed.

b. The centripetal acceleration of Julie and her horse is 0.148 m/s².

a) Explain which girl is moving with the greater linear speed.

Jessica's has a greater linear speed.

To answer the question, we need to know what Linear speed is.

What is linear speed?

This is the tangential speed at which an object in circular motion moves. It is given by v = rω where

  • r = distance of object from center of circle and
  • ω = angular speed.

Now, given that Jessica is riding on a merry-go-round on an outer horse that sits at a distance of 8.0 m from the center of the ride and Jessica's sister, Julie, is on an inner horse located 6.0 m from the ride's center. Also, the merry-go-round is moving at constant angular speed.

Since Linear speed v = rω and ω = constant,

So, v ∝ r.

So, the girl with the greater distance from the center of the merry-go-round would have the greater linear speed.

Since

  • Jessica is at r' = 8.0 m and
  • Julie is at r" = 6.0 m.

Since

  • v ∝ r, and
  • r' = 8.0 m > r" = 6.0 m,

So, Jessica's has a greater linear speed.

b) What is the centripetal acceleration of Julie and her horse?

The centripetal acceleration of Julie and her horse is 0.148 m/s².

Centripetal acceleration a = rω² where

  • r = distance of Julie from center of merry-go-round = 6.0 m and
  • ω = angular speed of merry go round.

Since the merry-go-round turns once every 40.0 s, we have that ω = 2π/40.0 s

= π/20.0 s

= 0.157 rad/s

Since a = rω²

Substituting the values of the variables into the equation, we have

a = rω²

a = 6.0 m × (0.157 rad/s)²

a = 6.0 m × 0.0247 rad²/s²

a = 0.148 m/s²

So, the centripetal acceleration of Julie and her horse is 0.148 m/s².

Learn more about linear speed here:

https://brainacademy.pro/question/25653453

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