Question

A 600-kg car is going around a banked curve with a radius of 110 m at a speed of 27.5 m/s. What is the appropriate banking angle so that the car stays on its path without the assistance of friction?

Answer 1

the appropriate banking angle would be 33.8°

Answer 2

The appropriate banking angle so that the car stays on its path without the assistance of friction is about 35.1°

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Further explanation

Centripetal Acceleration of circular motion could be calculated using following formula:

$\large {\boxed {a_s = v^2 / R} }$

a = centripetal acceleration ( m/s² )

v = velocity ( m/s )

R = radius of circle ( m )

Let us now tackle the problem!

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Given:

mass of car = m = 600 kg

radius of banked curve = R = 110 m

speed of car = v = 27.5 m/s

Asked:

banking angle = θ = ?

Solution:

Firstly , we will draw free body diagram of the car as shown in the attachment. Next , we could use Newton's Law of Motion and Centripetal Force to solve the problem as follows:

$\Sigma F_y = ma_y$

$N\cos \theta - mg = m(0)$

$N\cos \theta = mg$

$\boxed {N = mg \div \cos \theta}$ → Equation 1

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$\Sigma F_x = ma_x$

$N \sin \theta = m \frac{v^2}{R}$

$( mg \div \cos \theta ) \sin \theta = m \frac{v^2}{R}$  ← Equation 1

$mg \tan \theta = m \frac{v^2}{R}$

$g \tan \theta = \frac{v^2}{R}$

$\tan \theta = \frac{v^2}{gR}$

$\theta = \tan^{-1} ( \frac{v^2}{gR} )$

$\theta = \tan^{-1} ( \frac{27.5^2}{ 9.8 \times 110 } )$

$\boxed {\theta \approx 35.1^o}$

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Learn more

• Velocity of Runner : https://brainly.com/question/3813437

• Kinetic Energy : https://brainly.com/question/692781

• Acceleration : https://brainly.com/question/2283922

• The Speed of Car : https://brainly.com/question/568302
• Uniform Circular Motion : https://brainly.com/question/2562955
• Trajectory Motion : https://brainly.com/question/8656387

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Answer details

Grade: High School

Subject: Physics

Chapter: Circular Motion