Chapter 6: Q27 PE (page 224)

(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?

Short Answer

Expert verified

(a) The radius is $24.6 m$ .

(b) $36.6 m/s$ is centripetal acceleration.

Step by step solution

Definition of Centripetal acceleration

The rate of change of transverse velocity is known as centripetal acceleration.

Calculating radius of bobsled turn

(a) The ideal velocity for a banked road is,

$v = \sqrt{R g \tan θ}$

Here, R is the radius of the turn, g is the acceleration due to gravity, and $θ$ is the ideal angle of banking.

Rearranging the above equation in order to get an expression for the radius of the turn,

$R = \frac{v^{2}}{g \tan θ}$

Substitute $30.0 m/s$ for v, ${9.8 m/s}^{2}$ for g, and $75 . 0^{0}$ for $θ$ ,

$R = \frac{{(30.0 m / s)}^{2}}{(9.8 m / s^{2}) \times \tan (75 . 0^{0})} = 24.6 m$

Here, the radius of the bobsled turn is $= 24.6 m$

Calculating centripetal acceleration

(a) The centripetal acceleration is,

$a_{c} = \frac{v^{2}}{r}$

Substitute $30.0 m/s$ for v , and $24.6 m$ for r,

$a_{c} = \frac{{(30 m/s)}^{2}}{(24.6 m)} {= 36.6 m/s}^{2}$

Hence, the centripetal acceleration is $36.6 m/s$ .

Determining is acceleration seem larger

The proportion of centripetal to gravitational acceleration is,

$\frac{a_{c}}{g} = \frac{{36.6 m/s}^{2}}{{9.8 m/s}^{2}} = 3.7 = 3.7g$

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(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?

Short Answer

Step by step solution

Definition of Centripetal acceleration

Calculating radius of bobsled turn

Calculating centripetal acceleration

Determining is acceleration seem larger

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

Short Answer

Step by step solution

Definition of Centripetal acceleration

Calculating radius of bobsled turn

Calculating centripetal acceleration

Determining is acceleration seem larger

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Physics Textbooks

Classical Mechanics

Fundamentals of Physics

Fluids

Radiation

Force

Energy Physics

Study anywhere. Anytime. Across all devices.

(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?