Physics MCAT Qusetion

Question

When an object is falling through air, it experiences a drag force due to the frictional effects of the air. The drag force is always directed opposite the direction of motion of the object. For a spherical object, the drag force can be calculated using Stokes' law:

FD=6πηrv

where FD is the drag force, η is the coefficient of viscosity of the air, r is the radius of the sphere, and v is the velocity of the sphere.

Since the drag force is related to the velocity of the sphere, as the sphere's velocity increases, so does the drag force. After a certain time, the drag force will be large enough that the net force acting on the sphere is zero. At this point, the sphere falls with a constant velocity, known as the terminal velocity, vT.

A student experiments with different spherical objects falling on Earth in order to test Stokes' law. The experiment involves dropping a variety of spheres from the balcony of a building. The relative mass and radius for each sphere are listed in Table I.

Object	Mass	Radius
Beach Ball	m	20r
Bowling Ball	20m	10r
Golf Ball	m	r
Ping Pong Ball	0.25m	r

Table I: Mass and Radius of spheres.

How does the drag force on the beach ball compare to the drag force on the bowling ball when the velocities of the two balls are the same?

The drag force on the beach ball is 2 times the drag force on the bowling ball.

The drag force on the beach ball is  the drag force on the bowling ball.

The drag force on the beach ball is  the drag force on the bowling ball.

The drag force on the beach ball is 20 times the drag force on the bowling ball.

 

Which ball has the greatest terminal velocity?

Golf Ball

Ping Pong Ball

Bowling Ball

Beach ball

 

Answer 1

(1)

Drag force can be calculated using the Stoke's law: .

Where  is the coefficient of viscosity of the air,  is the radius of the sphere and  is the velocity of the sphere.

For beach ball:  and bowling ball: .

Drag force on beach ball is .

Drag force on bowling ball is .

Thus, the drag force on beach ball is 2 times the drag force on the bowling ball.

Option (a) is correct.

Answer 2

(2)

Object reaches the terminal velocity when the net force on the object is to be zero.

Thus, .

Therefore, the force due to gravity and the drag forces are equal.

Drag force is .

Force due to gravity is .

When the object reaches the terminal velocity, .

Observe the expression:

 depends on  value.

Since the bowling ball has the maximum ratio , it will have largest terminal velocity.

Option (c) is correct.