Question

(a) What is the radius of a bobsled turn banked at 75.0° and taken at 30.0 m/s, assuming it is ideally banked? (b) Calculate the centripetal acceleration. (c) Does this acceleration seem large to you?

Answer 1

The radius of the bobsled turn is 24.6 meters and the centripetal acceleration is 36.6 m/s². The acceleration does not seem too large, but bobsledders feel a lot of force on them going through sharply banked turns.

Step-by-step explanation:

To find the radius of a bobsled turn banked at 75.0° and taken at 30.0 m/s, assuming it is ideally banked, we can use the formula:

radius = (speed^2) / (acceleration due to gravity * tangent(angle))

Substituting the given values:

radius = (30.0^2) / (9.8 * tan(75.0°))

radius = 24.6 meters

The centripetal acceleration can be calculated using the formula:

centripetal acceleration = (speed^2) / radius

Substituting the given values:

centripetal acceleration = (30.0^2) / 24.6

centripetal acceleration = 36.6 m/s²

This acceleration does not seem too large, but it is clear that bobsledders feel a lot of force on them going through sharply banked turns.

Answer 2

The radius of the bobsled turn banked at 75.0° and taken at 30.0 m/s, assuming it is ideally banked, is approximately 24.6 meters. The centripetal acceleration of the bobsled in this turn is approximately 36.6 m/s². This acceleration is moderate but not excessively large.

Step-by-step explanation:

(a) What is the radius of a bobsled turn banked at 75.0° and taken at 30.0 m/s, assuming it is ideally banked?

Assuming the turn is ideally banked, we can use the formula:

tan(θ) = (v^2) / (g * r)

where θ is the angle of banking, v is the velocity, g is the acceleration due to gravity, and r is the radius of the turn.

Plugging in the given values, we have:

tan(75°) = (30.0 m/s)^2 / (9.8 m/s² * r)

Solving for r, we get:

r = (30.0 m/s)^2 / (9.8 m/s² * tan(75°)) ≈ 24.6 meters

Therefore, the radius of the bobsled turn is approximately 24.6 meters.

(b) Calculate the centripetal acceleration.

The centripetal acceleration can be calculated using the formula:

a_c = v^2 / r

Substituting in the given values, we have:

a_c = (30.0 m/s)^2 / 24.6 m ≈ 36.6 m/s²

Therefore, the centripetal acceleration is approximately 36.6 m/s².

(c) Does this acceleration seem large to you?

Based on the given values, the centripetal acceleration is 36.6 m/s², which is moderate but not excessively large.