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Physics MCAT Question?

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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:

imageFD=6πηrv

where imageFD is the drag force, imageη is the coefficient of viscosity of the air, imager is the radius of the sphere, and imagev 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, imagevT.

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?

 

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?

 

asked Sep 16, 2015 in PHYSICS by anonymous

2 Answers

0 votes

(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.

image

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.

answered Sep 16, 2015 by Lucy Mentor
edited Sep 16, 2015 by Lucy
0 votes

(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 image.

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

Observe the table:

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

Ratio image 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.

answered Sep 16, 2015 by Lucy Mentor

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