Aerodynamic drag force (F_d) acts on vehicles as they move through the air. A group of stu… — ACT

Aerodynamic drag force ( $F_d$ ) acts on vehicles as they move through the air. A group of students measured the drag force, in newtons ( $\text{N}$ ), acting on a scale model of a sports car in a wind tunnel at various wind velocities ( $v$ ), in meters per second ( $\text{m/s}$ ). The data from their trials are recorded in the table below:

Velocity ( $v$ , $\text{m/s}$ )	Drag Force ( $F_d$ , $\text{N}$ )
$10$	$12$
$20$	$48$
$30$	$108$
$40$	$192$

Based on the trend shown in the table, what is the expected aerodynamic drag force, in newtons ( $\text{N}$ ), acting on the scale model when the wind velocity is $50\text{ m/s}$ ?

Answer: 300 N

Answer

The expected aerodynamic drag force is 300 N.

The correct answer is 300 N because the drag force scales quadratically with velocity according to the relation

F_d = 0.12 v^2

. Plugging in

v = 50\text{ m/s}

yields

0.12 \times 2500 = 300\text{ N}

Step-by-Step Solution

Calculate the ratio of drag force to the square of the velocity for the given data points.

For all data points,

F_d / v^2 = 0.12

. This establishes the quadratic trend

F_d = 0.12 v^2

Identifying the mathematical relationship between the variables is necessary to accurately extrapolate beyond the measured data range.

Substitute the target velocity of

50\text{ m/s}

into the identified quadratic formula.

F_d = 0.12 \times (50)^2 = 300\text{ N}

Applying the mathematical trend allows for the calculation of the drag force at the extrapolated velocity.

Key Concept

Extrapolation of a quadratic relationship between velocity and aerodynamic drag force.

Estimated Time:1m 30s

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