Physics MCAT Question?

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.

Ignoring air resistance, which ball will hit the ground first?

The beach ball, since it has the largest radius.

The bowling ball, since it has the largest mass.

all the balls will hit at the same time.

The golf ball; it has the smallest radius, & more mass than a ping pong ball.

 

Considering Air resistance, which ball will take the longest time to reach the ground when dropped, assuming none of the balls reaches its terminal velocity?

Golf Ball

Beach Ball

Ping Pong Ball

Bowling Ball

 

Answer 1

(1)

Experiment of throwing different spherical balls from certain height:

Ignore the air resistance, hence the drag force due to air is not considered.

For a freely falling body, the net force acting on the body is equal to the force due to gravity.

Hence each and every ball moves with same acceleration, that is, acceleration due to the gravity.

Since the balls are dropped from same height and move with the same acceleration, they hit the ground at the same time.

Hence all the balls will hit at the same time.

Option (c) is correct choice.

Answer 2

(2)

Experiment of throwing different spherical balls from certian height:

The drag force due to air is considered.

The net force acting on the body:

Hence the acceleration depends on the ratio .

Larger the ratio , larger amount will be subtracted from g. Hence the ball will move with less acceleration.

Therefore the object which moves with less acceleration will take the longest time.

Compare the ratio  of Beach Ball, Bowling Ball, Golf Ball and Ping Pong Ball.

Observe the table:

Ratio  of Beach ball, Bowling ball, Golf ball and Ping Pong ball are  and .

Ratio  is large for Beach ball.

Hence acceleration of beach ball is less and it takes long time to reach the ground.

Option (b) is correct choice.