Question

A 1000-kg car is slowly picking up speed as it goes around a horizontal curve whose radius is 100 m. The coefficient of static friction between the tires and the road is 0.350. At what speed will the car begin to skid sideways?

Answer 1

Answer:

18.5 m/s

Explanation:

On a horizontal curve, the frictional force provides the centripetal force that keeps the car in circular motion:

$\mu mg = m\frac{v^2}{r}$

where

$\mu$ is the coefficient of static friction between the tires and the road

m is the mass of the car

g is the gravitational acceleration

v is the speed of the car

r is the radius of the curve

Re-arranging the equation,

$v=\sqrt{\mu gr}$

And by substituting the data of the problem, we find the speed at which the car begins to skid:

$v=\sqrt{(0.350)(9.8 m/s^2)(100 m)}=18.5 m/s$

Answer 2

The car will begin to skid sideways at 18.5 m/s

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Further explanation

Centripetal Acceleration can be formulated as follows:

$\large {\boxed {a = \frac{ v^2 } { R } }$

a = Centripetal Acceleration ( m/s² )

v = Tangential Speed of Particle ( m/s )

R = Radius of Circular Motion ( m )

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Centripetal Force can be formulated as follows:

$\large {\boxed {F = m \frac{ v^2 } { R } }$

F = Centripetal Force ( m/s² )

m = mass of Particle ( kg )

v = Tangential Speed of Particle ( m/s )

R = Radius of Circular Motion ( m )

Let us now tackle the problem !

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Given:

mass of car = m = 1000 kg

radius of curve = R = 100 m

coefficient of static friction = μ = 0.350

Asked:

speed of the car = v = ?

Solution:

We will derive the formula to calculate the maximum speed of the car:

$\Sigma F = ma$

$f = m \frac{v^2}{R}$

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

$\mu m g = m \frac{v^2}{R}$

$\mu g = \frac{v^2}{R}$

$v^2 = \mu g R$

$\boxed {v = \sqrt { \mu g R } }$

$v = \sqrt { 0.350 \times 9.8 \times 100 }$

$v = \sqrt { 343 }$

$v = 7 \sqrt{7} \texttt{ m/s}$

$\boxed {v \approx 18.5 \texttt{ m/s}}$

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Learn more

• Impacts of Gravity : brainly.com/question/5330244
• Effect of Earth’s Gravity on Objects : brainly.com/question/8844454
• The Acceleration Due To Gravity : brainly.com/question/4189441

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Answer details

Grade: High School

Subject: Physics

Chapter: Circular Motion