Gravity and Motion
Suppose you dropped a baseball and a marble at the same time from the top of a tall building. Which do you think would land on the ground first?
In ancient Greece around 400 BCE, a philosopher named Aristotle thought that the rate at which an object falls depended on the object's mass. If you asked Aristotle whether the baseball or the marble would land first, he would have said the baseball. But Aristotle never tried dropping objects with different masses to test his idea about falling objects.
Gravity and Falling Objects
In the late 1500s, a young Italian scientist named Galileo Galilei questioned Aristotle's idea about falling objects. Galileo argued that the mass of an object does not affect the time the object takes to fall to the ground. According to one story, Galileo proved his argument by dropping two cannonballs of different masses from the top of the Leaning Tower of Pisa in Italy. The people watching from the ground below were amazed to see the two cannonballs land at the same time. Whether or not this story is true, Galileo's work changed people's understanding of gravity and falling objects.
F I G U R E 1
Figure 1 : This stop-action photo shows that a table-tennis ball and a golf ball fall at the
same rate even though they have different masses.
Gravity and Acceleration
Objects fall to the ground at the same rate because the acceleration due to gravity is the same for all objects. Why is this true? Acceleration depends on both force and mass. A heavier object experiences a greater gravitational force than a lighter object does. But a heavier object is also harder to accelerate because it has more mass.
The extra mass of the heavy object exactly balances the additional gravitational force.
Figure 1 shows objects that have different masses falling with the same acceleration.
Acceleration Due to Gravity
Acceleration is the rate at which velocity changes over time. So, the acceleration of an object is the object's change in velocity divided by the amount of time during which the change occurs. All objects accelerate toward Earth at a rate of 9.8 meters per second per second. This rate is written as 9.8 m/s/s, or 9.8 m/s2. So, for every second that an object falls, the object’s downward velocity increases by 9.8 m/s, as shown in Figure 2.
Velocity of Falling Objects
You can calculate the change in velocity (
Δv = g × t
In this equation, g is the acceleration due to gravity on Earth (9.8 m/s2), and t is the time the object takes to fall (in seconds). The change in velocity is the difference between the final velocity and the starting velocity. If the object starts at rest, this equation yields the velocity of the object after a certain time period.
Math Focus
Calculating the Velocity of Falling Objects
- A stone at rest is dropped from a cliff, and the stone hits the ground after a timeof 3 s. What is the stone’s velocity when it hits the ground?
Step 1 : Write the equation for change in velocity.
Δv = g × t
Step 2 : Replace g with its value and t with the time given in the problem, and solve.
To rearrange the equation to find time, divide by the acceleration due to gravity:
t = Δv / g