2.2.3 Free-Falling Objects

Question 1

Free-Falling Objects

Answer 1

• Objects fall to the ground with uniform acceleration: .
• If air friction is present, it may change the acceleration of a falling object.
• Free-fall acceleration occurs when an object is subject only to the force of gravity.
• The master equations of kinematics with uniform acceleration hold for free-falling objects.
• Be sure to choose a consistent coordinate system when solving free-fall problems.

Question 2

note

Answer 2

• A heavy object and a light object simultaneously dropped tot he ground from the same height will land at exactly the same instant. Both objects experience free-fall acceleration, which is the acceleration due to gravity and is constant near the Earth’s surface:. Galileo Galliei performed the first experiments on the speed of falling objects from the top of the Leaning Tower of Pisa in about 1590.
• Objects that experience a lot of air friction will fall to the ground more slowly than objects that do not experience much air friction. For example, if a feather and a coin are dropped,the coin will land first because it experiences much less air friction than a feather. The acceleration due to gravity is always constant. The air is removed from the tube containing the feather and the coin minimizing the effects of air drag.Now when the two objects are dropped, they fall to the bottom at the same instant.
• Because objects in free fall have constant acceleration, the master equations of kinematics can be used to describe their motion. You should be careful to define a coordinate system before solving free-fall problems. A ball is tossed upwards.How would you calculate its final velocity using the first equation of kinematics? If you choose a coordinate system where up is positive as in the example on the left, the initial velocity would be positive and the free fall acceleration would be . If you choose a coordinate system where down is positive as in the example on the right, vi would be negative and .
• Prof. Pollock and two colleagues find a deep pit. They throw a stone in the pit and it takes 3 s to hit the bottom. How deep is the pit? The stone is in free fall as it drops to the bottom of the pit so you can use the equations of kinematics to determine the distance to the bottom. Choose the third equation since it allows you to solve for xf. Set up a coordinate system that is positive in the downwards direction. The top of the pit (xi) is at 0 m. The stone was at rest before it was dropped so . The time required for the stone to hit the bottom (Dt) is 3 s. Since the coordinate system is positive in the downwards direction, . You can calculate that the pit is about 50 m deep.

Question 3

Acceleration due to gravity, commonly written as agrav  or g, is equal to 9.8 m / s2. Which of the following statements about g is not correct?

Answer 3

With each successive second, the velocity and acceleration of a falling object increase.

Question 4

Suppose you throw an object straight up at an initial velocity of 17 m / s. How long will it take for the object to reach its maximum height?

Answer 4

1.7 s

Question 5

Suppose you throw an object straight up at an initial velocity of 10 m / s. How high will the object go?

Answer 5

5.1 m

Question 6

Air resistance can affect the falling motion of an object. Which of the following statements about air resistance is correct?

Answer 6

• Air resistance is a force (in addition to gravity) that acts on falling objects.
• If an object is subject to air resistance, it does not undergo free fall.
• In the absence of air resistance (or any other force besides gravity), all falling objects have the same acceleration.

Question 7

Which of the following best defines free fall?

Answer 7

Free fall refers to a motion event in which only the object is subject only to the force of gravity.

Question 8

Free-falling objects of different masses dropped from the same height hit the ground at the same time. This demonstrates what basic principle of physics?

Answer 8

Free-falling objects accelerate uniformly

Question 9

Which of the following statements related to free fall is correct?

Answer 9

The value for a is either positive or negative, depending on which direction is chosen as the positive direction.

Question 10

Suppose you throw an object straight up at an initial velocity of 21 m / s. How long will it take for the object to reach its maximum height? What is the object’s maximum height? How long will it take for the object to return to its original position?

Answer 10

time to reach maximum height = 2.1 s
maximum height = 23 m
total time = 4.3 s

Question 11

Compare a ball and a sheet of paper falling. In the first example, the ball hits the ground before the sheet of paper. In the second example, the sheet of paper was crumpled into a ball shape, and the two objects hit the ground at the same time. Which of the following best explains this demonstration?

Answer 11

In the first example, the paper was subject to the forces of gravity as well as the significant force of air drag. In the second example, the force of air drag was minimized by decreasing the surface area of the paper.