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salantis [7]
3 years ago
13

If a car takes a banked curve at less than the ideal speed, friction is needed to keep it from sliding toward the inside of the

curve (a real problem on icy mountain roads). (a) Calculate the ideal speed in (m/s) to take a 100 m radius curve banked at 15°. m/s (b) What is the minimum coefficient of friction needed for a frightened driver to take the same curve at 15.0 km/h?
Physics
1 answer:
PolarNik [594]3 years ago
3 0

Answer:

a. v₁ = 16.2 m/s

b. μ = 0.251

Explanation:

Given:

θ = 15 ° , r = 100 m , v₂ = 15.0 km / h

a.

To determine v₁ to take a 100 m radius curve banked at 15 °

tan θ  = v₁² / r * g

v₁ = √ r * g * tan θ

v₁ = √ 100 m * 9.8 m/s² * tan 15° = 16.2 m/s

b.

To determine μ friction needed for a frightened

v₂ = 15.0 km / h * 1000 m / 1 km * 1h / 60 minute * 1 minute / 60 seg

v₂ = 4.2 m/s

fk = μ * m * g

a₁ = v₁² / r = 16.2 ² / 100 m = 2.63 m/s²

a₂ = v₂² / r = 4.2 ² / 100 m = 0.18 m/s²

F₁ = m * a₁  ,  F₂ = m * a₂

fk = F₁ - F₂   ⇒  μ * m * g = m * ( a₁ - a₂)

μ * g = a₁ - a₂   ⇒  μ = a₁ - a₂ / g

μ = [ 2.63 m/s² - 0.18 m/s² ] / (9.8 m/s²)

μ = 0.251

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The volume of the rod is 1.26×10⁻⁵ m³, and the linear charge density of the rod is 3.64 C/m

<h3>What is volume?:</h3>

This is the product of the height of a solid object and its crossectional area.

The Volume of the rod is can be calculated using the formula below.

Note: A rod has the shape of a cylinder.

Formula:

  • V = πr²h............... Equation 1

Where:

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From the question,

Given:

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Substitute these values into equation 1

  • V = 3.14(0.004²)(0.25)
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<h3>What is linear charge density:</h3>

This is the ratio of the charge on an object to the length of the object.

The linear charge density of the rod can be calculated using the formula below.

  • D = Q/h.................... Equation 2

Where:

  • D = Linear charge density of the rod
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From the question

Given:

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Substitute these values into equation 2

  • D = 0.91/0.25
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Hence, The volume of the rod is 1.26×10⁻⁵ m³, and the linear charge density of the rod is 3.64 C/m

Learn more about charge density here: brainly.com/question/14568868

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