# Falling objects

##### Demonstration

It may seem surprising that the motion of all objects falling freely under gravity is the same.

Click here for a video showing free fall from which you can make measurements (please note this runs only in Internet Explorer 4+).

#### Apparatus and materials

Objects, 2, larger and smaller (e.g. pair of smallish stones, or sets of keys

Vacuum pump

Hoffman clip

#### Health & Safety and Technical notes

Read our standard health & safety guidance

The objects should be dense enough and the length of fall small enough to make the effect of air resistance insignificant.

#### Procedure

Simultaneously release the two objects side by side and watch what happens.

A multiflash photograph could be taken of the falling objects. See the guidance note Multiflash photography.

####

Teaching notes

**1** Your accompanying chat might run like this: *Why doesn’t the heavier object fall faster? I can feel the Earth pulling it with a bigger force.*

The gravitational force acting on each object is found as *F = mg*, where *g* is the gravitational field strength. In other words, the pull of gravity on an object is proportional to its mass.

**2** Ask, *What happens to an object when an unbalanced force acts on it?* Newton’s Second Law will apply and the object’s acceleration will be *a = F/m*. In other words, with a bigger mass, a greater force must be applied to cause the same acceleration.

**3** Putting the two equations together, *a = F/m = mg/m*

As a result, the acceleration of free fall *a = g*, is independent of an object’s mass. All masses fall in the same way. The units of acceleration and gravitational field strength look different but are really the same.

This means that you can measure the strength of the gravity field by finding the acceleration of free fall.

**4** Many students will puzzle over this result because the same symbol *g* is used for both*acceleration of free fall* and *gravitational field strength*. Some students will understand the argument here better if you use a different symbol for the acceleration of free fall, perhaps *a*_{g}.

**5** With more advanced students, you could point out that Newton’s second law refers to inertial mass *m _{i}*, and write

*a = F/m*

_{i}. Likewise, the force of gravity on an object depends on gravitational mass

*m*

_{g}and

*F = m*

_{g}

*g.*

Einstein showed that inertial mass and gravitational mass are the same, i.e.

*m*

_{i}=

*m*

_{g}. So

*a = F/m*

_{i}=

*m*

_{g}

*g/m*

_{i}=

*g*. In other words, mass as measured by accelerations is exactly the same as mass measured by gravitational forces.

*This experiment was safety-checked in May 2005*