Question

1. A child rides a bicycle in a circular path with a radius of 3.2 m. The tangential speed of the

bicycle is 2.7 m/s. The combined mass of the bicycle and the child is 54 kg.
What is the magnitude of the bicycle's centripetal acceleration? What is the magnitude of the
centripetal force on the bicycle?

Answer 1

`\huge\boxed{\sf F_c=123.02 \ N}`

`\huge\boxed{\sf a_c=2.28 \ m/s^2}`

Step-by-step explanation:

Given data:

Mass = m = 54 kg

Tangential speed = v = 2.7 m/s

Radius = r = 3.2 m

Required:

Centripetal force =
`F_c` = ?

Centripetal acceleration =
`a_c` = ?

Formula:

`\displaystyle F_c=(mv^2)/(r)`

`\displaystyle a_c=(v^2)/(r)`

Centripetal acceleration:

Put the given data in the above formula.

`\displaystyle a_c=((2.7)^2)/(3.2) \\\\a_c=(7.29)/(3.2) \\\\a_c=2.28 \ m/s^2\\\\`

Centripetal force:

Put the given data in the above formula.

`\displaystyle F_c=((54)(2.7)^2)/(3.2) \\\\F_c=((54)(7.29))/(3.2) \\\\F_c=(393.66)/(3.2) \\\\F_c=123.02 \ N\\\\\rule[225]{225}{2}`

Answer 2

The magnitude of the bicycle's centripetal acceleration can be calculated using the formula:

a = v^2 / r

where v is the tangential speed and r is the radius of the circular path. Plugging in the given values, we get:

a = (2.7 m/s)^2 / 3.2 m

a = 2.27 m/s^2

The magnitude of the centripetal force on the bicycle can be calculated using the formula:

F = m * a

where m is the combined mass of the bicycle and the child. Plugging in the given values, we get:

F = 54 kg * 2.27 m/s^2

F = 122.58 N

Therefore, the magnitude of the bicycle's centripetal acceleration is 2.27 m/s^2, and the magnitude of the centripetal force on the bicycle is 122.58 N.