Chapter 6: Q. 66 (page 157)

A $60 kg$ skater is gliding across frictionless ice at $4.0 m / s$ . Air resistance is not negligible. You can model the skater as a $170 - cm$ -tall, $36 - cm$ -diameter cylinder. What is the skater's speed $2.0 s$ later?

Short Answer

Expert verified

Speed of the skater after $2$ Sec is $3.4 m / s .$

Step by step solution

:Given.

Mass of the skater, $m = 60 kg .$

Speed of the skater, $v = 4 m / s .$

Diameter of the skater, $d = 36 cm .$

Height of the skater, $h = 170 cm .$

Formula used.

The air friction is given by the formula:

$F = \frac{1}{2} ρ \times A \times v^{2}$

Here,

$ρ$ is the density of air.

$A$ is the surface area of the cylinder.

$v$ is the velocity of the skater.

Calculation.

The surface area of the skater is calculated as: $A = π d H$

Plugging the values in the above equation,

$\begin{aligned} A = & π \times 0.36 \times 1.7 \\ = 1.92 m^{2} . \end{aligned}$

Now drag force due to air is calculated as:

$\begin{matrix} F = \frac{1}{2} \times 1.2 \times 1.92 \times 4^{2} \\ = 18.43 N . \end{matrix}$

The deceleration on the skater due to air friction is calculated as:

$\begin{matrix} F = m a \\ 18.43 = 60 \times a \\ a = 0.30 m / s^{2} . \end{matrix}$

The speed of the skater after $2$ sec is calculated as:

role="math" localid="1647774441411" $\begin{matrix} v = u - a t \\ = 4 - 0.3 \times 2 \\ = 3.4 m / s . \end{matrix}$

Conclusion.

Speed of the skater after $2 \sec$ is $3.4 m / s .$

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A $60 kg$ skater is gliding across frictionless ice at $4.0 m / s$ . Air resistance is not negligible. You can model the skater as a $170 - cm$ -tall, $36 - cm$ -diameter cylinder. What is the skater's speed $2.0 s$ later?

Short Answer

Step by step solution

:Given.

Formula used.

Calculation.

Conclusion.

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A 60kgskater is gliding across frictionless ice at 4.0m/s. Air resistance is not negligible. You can model the skater as a 170−cm-tall,36−cm-diameter cylinder. What is the skater's speed2.0s later?

Short Answer

Step by step solution

:Given.

Formula used.

Calculation.

Conclusion.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Physics Textbooks

Waves Physics

Medical Physics

Modern Physics

Measurements

Electric Charge Field and Potential

Further Mechanics and Thermal Physics

Study anywhere. Anytime. Across all devices.

A $60 kg$ skater is gliding across frictionless ice at $4.0 m / s$ . Air resistance is not negligible. You can model the skater as a $170 - cm$ -tall, $36 - cm$ -diameter cylinder. What is the skater's speed $2.0 s$ later?