Acceleration from Gravity

What is gravity?

Gravity is a force of attraction between all masses. The largest mass near us, the planet Earth, pulls on all masses near its surface. This pulling force can cause these masses to accelerate towards the earth - to fall down.

Near the surface of the earth, all masses accelerate at the same rate, known as the acceleration of gravity, g.

g = 9.8 m/s²

This fact, that all objects fall at the same rate, has been known for hundreds of years, since Galileo's famous experiment at the Leaning Tower of Pisa where he supposedly let fall two different masses from the top of the tower. Both hit the ground at the same time. The experiment is repeated in the video below.

Sign Convention

Gravity accelerates masses downwards. It is common to call the downward direction the negative direction, in which case, gravity would have the value g = −9.8 m/s². It is within your power to call down positive, but before doing this, remember that up is then negative, and this may need to be considered when doing the math.

Example 1 - off the tower

• Question
• Answer

A 2.5kg ball is dropped from the top of a 55m tower.
A) How long does it take for the ball the reach the sidewalk below?
B) How fast is the ball moving when it hits the ground?

A 2.5kg ball is dropped from the top of a 55m tower.
A) How long does it take for the ball the reach the sidewalk below?
B) How fast is the ball moving when it hits the ground?

Symmetry Up and Down

For an object that is thrown up and then falls back down, if it comes back to the same height, then the trip up and the trip down are symmetrical.

• time up = time down
• initial speed up = final speed down (directions opposite)
• net displacement is zero
• speed at top is zero
• the object slows on the way up and speeds up on the way down, but the acceleration for the entire trip is downwards g = −9.8 m/s².

Example 2 - pop fly

• Question
• Answer

Moustapha Jones hits a pop fly that goes straight up over home plate. The TV cameras record the ball being caught by the catcher exactly 4.65 seconds after it was hit.
A) How fast is it going when it strikes the catcher's mitt?
B) How high up did the ball go?

Moustapha Jones hits a pop fly that goes straight up over home plate. The TV cameras record the ball being caught by the catcher exactly 4.65 seconds after it was hit.
A) How fast is it going when it strikes the catcher's mitt?
B) How high up did the ball go?

Example 3 - penny down a well

• Question
• Answer

Moustapha Jones drops a penny down a well to wish for good grades on his upcoming physics test. He times the penny's drop and he hears the splash exactly 2.65s after the release. If sound travels at 332m/s, how deep is the well?

Moustapha Jones drops a penny down a well to wish for good grades on his upcoming physics test. He times the penny's drop and he hears the splash exactly 2.65s after the release. If sound travels at 332m/s, how deep is the well?

Graphing motion of objects in free fall

If air resistance is ignored, then acceleration is constant during free fall, both during the trip up and the trip down. Velocity will change at a constant rate. The position-time graph will be curved.

Play with the applet below to see how to graph objects in free fall.