Drag and air resistance Knowledge-Based Download PDF

Questions

1. 1.

   A ball is thrown vertically upward in the presence of air resistance and eventually returns to its launch position. How does the time of ascent to its maximum height, $t_{\text{up}}$, compare to the time of descent back to the launch position, $t_{\text{down}}$?

   • A) The time of ascent is always greater than the time of descent ($t_{\text{up}} > t_{\text{down}}$).
   • B) The time of ascent is always less than the time of descent ($t_{\text{up}} < t_{\text{down}}$).
   • C) The time of ascent is always equal to the time of descent ($t_{\text{up}} = t_{\text{down}}$).
   • D) The time of ascent is greater than the time of descent only for large initial speeds.
2. 2.

   A ball is thrown vertically upward into the air, where it experiences air resistance that depends on its speed. At the instant the ball reaches its maximum height, what is the magnitude of its acceleration in terms of the acceleration due to gravity, $g$?

   • A) 0
   • B) $g$
   • C) Greater than $g$
   • D) Between 0 and $g$
3. 3.

   Two objects of identical mass and aerodynamic shape fall vertically through air where the drag force is modeled as $D = C A v^2$, with $C$ being a constant and $A$ representing cross-sectional area. If object 1 has a cross-sectional area four times that of object 2, what is the ratio of the terminal speed of object 2 to that of object 1, $v_2 / v_1$?

   • A) 1/4
   • B) 1/2
   • C) $\sqrt{2}$
   • D) 2
4. 4.

   A projectile travels through the air under the influence of gravity and air resistance. At the highest point of its trajectory, where its velocity is directed horizontally to the right, what is the direction of the net force acting on the projectile?

   • A) Straight downward
   • B) Downward and to the left
   • C) Horizontally to the left
   • D) Upward and to the left
5. 5.

   An object of mass $m$ falls vertically through the air where the drag force is modeled as $D = kv^2$, with $k$ being a positive constant. Which of the following expressions represents the terminal speed $v_t$ of the object?

   • A) $v_t = \frac{mg}{k}$
   • B) $v_t = \sqrt{\frac{k}{mg}}$
   • C) $v_t = \frac{k}{mg}$
   • D) $v_t = \sqrt{\frac{mg}{k}}$
6. 6.

   An object is projected vertically downward with an initial speed greater than its terminal speed. What is the direction of the net force acting on the object immediately after release, and how does its speed subsequently change?

   • A) The net force is upward, and the speed decreases toward the terminal speed.
   • B) The net force is downward, and the speed decreases toward the terminal speed.
   • C) The net force is upward, and the speed increases further beyond the terminal speed.
   • D) The net force is zero, and the speed remains constant at the initial value.
7. 7.

   Two solid spheres of identical size and shape, with masses $m_1$ and $m_2$ such that $m_1 = 4m_2$, fall through the air where the drag force is proportional to the square of the speed. What is the ratio of the terminal speed of the first sphere to that of the second sphere, $v_1 / v_2$?

   • A) 4
   • B) 2
   • C) 1
   • D) 1/2
8. 8.

   An object is released from rest in air and accelerates downward under the influence of gravity and air resistance. As the downward speed of the object increases toward terminal velocity, how do the magnitude of the drag force and the magnitude of its acceleration change?

   • A) The magnitude of the drag force decreases, and the magnitude of the acceleration increases.
   • B) The magnitude of the drag force remains constant, and the magnitude of the acceleration decreases.
   • C) The magnitude of the drag force increases, and the magnitude of the acceleration decreases.
   • D) The magnitude of the drag force increases, and the magnitude of the acceleration increases.