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2 years ago

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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 f

riction between the tires and the road is 0.350. At what speed will the car begin to skid sideways?

2 answers:

Snezhnost [94]2 years ago

7 0

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:

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

adell [148]2 years ago

5 0

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

$\texttt{ }$

<h3>Further explanation</h3>

Centripetal Acceleration can be formulated as follows:

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

<em>a = Centripetal Acceleration ( m/s² )</em>

<em>v = Tangential Speed of Particle ( m/s )</em>

<em>R = Radius of Circular Motion ( m )</em>

$\texttt{ }$

Centripetal Force can be formulated as follows:

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

<em>F = Centripetal Force ( m/s² )</em>

<em>m = mass of Particle ( kg )</em>

<em>v = Tangential Speed of Particle ( m/s )</em>

<em>R = Radius of Circular Motion ( m )</em>

Let us now tackle the problem !

$\texttt{ }$

<u>Given:</u>

mass of car = m = 1000 kg

radius of curve = R = 100 m

coefficient of static friction = μ = 0.350

<u>Asked:</u>

speed of the car = v = ?

<u>Solution:</u>

<em>We will derive the formula to calculate the maximum speed of the car:</em>

$\Sigma F = ma$

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

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

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

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

$v^2 = \mu g R$

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

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

$v = \sqrt { 343 }$

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

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

$\texttt{ }$

<h3>Learn more</h3>

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

$\texttt{ }$

<h3>Answer details</h3>

Grade: High School

Subject: Physics

Chapter: Circular Motion

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