Drag and air resistance Transitional Reasoning Download PDF

Questions

1. 1.

   An electric test car travels along a straight, horizontal track with negligible rolling friction, experiencing an aerodynamic drag force modeled by $F_d = D v^2$, where $D$ is a positive constant and $v$ is speed. The car cruises at a steady speed $v_1$ when its motor supplies a constant forward traction force $F_1$. To cruise at a higher steady speed of $v_2 = 2v_1$, the motor provides a new constant forward traction force $F_2$. Which statement correctly relates $F_2$ to $F_1$ and identifies the net horizontal force acting on the car while it cruises at speed $v_2$?

   • A) $F_2 = 2F_1$, and the net horizontal force on the car is directed forward.
   • B) $F_2 = 4F_1$, and the net horizontal force on the car is zero.
   • C) $F_2 = 4F_1$, and the net horizontal force on the car is directed forward.
   • D) $F_2 = 2F_1$, and the net horizontal force on the car is zero.
2. 2.

   Two solid, spherical hailstones of uniform density, Hailstone 1 of radius $R$ and Hailstone 2 of radius $2R$, fall vertically through still air and reach their respective terminal speeds. The magnitude of the aerodynamic drag force on each hailstone is given by $F_d = \frac{1}{2} C_D \rho A v^2$, where $C_D$ is the identical drag coefficient, $\rho$ is the air density, and $A$ is the cross-sectional area. Which statement correctly compares the drag force and the terminal speed of Hailstone 2 to those of Hailstone 1 at terminal speed?

   • A) Hailstone 2 experiences 4 times the drag force of Hailstone 1, and its terminal speed is 2 times that of Hailstone 1.
   • B) Hailstone 2 experiences 8 times the drag force of Hailstone 1, and its terminal speed is $\sqrt{2}$ times that of Hailstone 1.
   • C) Hailstone 2 experiences 8 times the drag force of Hailstone 1, and its terminal speed is 4 times that of Hailstone 1.
   • D) Hailstone 2 experiences 4 times the drag force of Hailstone 1, and its terminal speed is $\sqrt{2}$ times that of Hailstone 1.
3. 3.

   An atmospheric research probe is released from rest and falls vertically through calm air, experiencing a drag force modeled by $F_d = kv^2$, where $k$ is a constant and $v$ is its downward speed. As the probe falls, it approaches a steady terminal speed $v_t$. In terms of the acceleration due to gravity $g$, what is the magnitude of the probe's downward acceleration at the instant its speed reaches $0.50v_t$?

   • A) 0.25g
   • B) 0.50g
   • C) 0.75g
   • D) 1.00g
4. 4.

   A skydiver of mass $m$ falls vertically through the atmosphere and has reached a steady terminal speed $v_1$. At a certain altitude, the skydiver deploys a parachute, instantly increasing the upward drag force to a magnitude of $2.5mg$. Taking the upward direction as positive, which statement correctly identifies the skydiver's acceleration immediately after deployment and describes the subsequent change in motion until a new terminal speed is achieved?

   • A) The acceleration is $+1.5g$, which immediately reverses the skydiver's direction of motion and causes an upward ascent.
   • B) The acceleration is $-1.5g$, which increases the downward speed until air resistance completely dissipates.
   • C) The acceleration is $+1.5g$, directed upward, which decreases the downward speed until the drag force reduces back to $mg$.
   • D) The acceleration is $+2.5g$, directed upward, which maintains a constant downward speed while the canopy stabilizes.
5. 5.

   An atmospheric research team releases two identical-geometry sensor pods, P and Q, from rest from an aerial platform at high altitude. Pod Q has four times the mass of Pod P, while both pods have identical shapes, surface textures, and cross-sectional areas. Assuming air density remains constant over the fall and the drag force is proportional to the square of the speed, which statement correctly compares the motion of the two pods?

   • A) Both pods reach the same terminal velocity because aerodynamic drag depends only on cross-sectional area and shape.
   • B) Pod Q reaches a terminal velocity that is four times that of Pod P because terminal velocity is directly proportional to mass.
   • C) At the instant Pod P reaches its terminal velocity, the net force on Pod Q is zero because both pods experience the same gravitational acceleration.
   • D) Pod Q reaches a terminal velocity that is twice that of Pod P, and Pod Q continues to accelerate at the moment Pod P reaches terminal velocity.