Question

At how many revolutions per minute will the riders be subjected to a centripetal acceleration 1.50 times that due to gravity if the horizontal circular path has an 8.00 m radius?

a) 15.6 rpm
b) 18.9 rpm
c) 22.3 rpm
d) 26.8 rpm

Answer 1

The riders will be subjected to a centripetal acceleration 1.50 times that due to gravity at approximately 33.0 rpm.

Step-by-step explanation:

To find the revolutions per minute (rpm) at which the riders will be subjected to a centripetal acceleration 1.50 times that due to gravity, we can use the formula for centripetal acceleration:

ac = Rω²

where ac is the centripetal acceleration, R is the radius of the circular path, and ω is the angular velocity.

Given that the riders will experience an acceleration 1.50 times that due to gravity, we can write:

ac = 1.50g

Substituting the values we have, we get:

1.50g = Rω²

ω² = (1.50g) / R

ω = √((1.50g) / R)

Now we can calculate the angular velocity:

ω = √((1.50 * 9.8 m/s²) / 8.00 m)

ω ≈ 3.47 rad/s

To convert the angular velocity to revolutions per minute, we can use the conversion factor:

1 rev = 2π rad

1 min = 60 s

So, the angular velocity in rpm is:

ω(rpm) = (3.47 rad/s) * (1 rev / (2π rad)) * (60 s / 1 min)

ω(rpm) ≈ 33.0 rpm

Therefore, the riders will be subjected to a centripetal acceleration 1.50 times that due to gravity at approximately 33.0 rpm.