# Accelerating kilogram masses

##### Demonstration or Class practical

This activity demonstrates that inertia depends on mass and not on any other interpretation of size. Force, mass and acceleration are inter-related quantities.

#### Apparatus and materials

Mass, brass or lead, 1 kg

Mass, aluminium, 1 kg

Dynamics trolleys, 2

Elastic cords for accelerating trolleys, 2

Stopclock

Balance, able to measure or compare two 1kg masses

Long weak spring or rubber thread

Runway, if necessary

#### Health & Safety and Technical notes

A trolley runway requires two persons to carry it and set it up on the bench.

#### Procedure

**a** Use a balance to show that the two (gravitational) masses are equal even though their sizes are not.

**b** Put each mass in turn on a dynamics trolley and accelerate it with a standard force using elastic cord. Show that the time to travel a measured distance is the same in each case.

**c** Repeat this, applying a larger force.

**d** Place two equal trolleys far apart on a level runway. Put one of the masses on each trolley. Stretch a weak spring or long rubber thread between them to accelerate them towards each other.

**e** Repeat all of the previous exercises, but with unequal masses.

####

Teaching notes

**1** You can use the activity to review ideas about inertia, and as an introduction to work on force, mass and acceleration, and their relationship. It shows that the three quantities are interdependent, and provides a basis for further work to determine the nature of the relationship.

Step **b**: This shows that the two inertial masses are the same.

Step **c**: The times are still equal to each other but shorter than before. Force affects acceleration, directly.

Step **d**: When you release the trolleys, they travel equal distances to the point of collision.

Step **e**: The two masses show different degrees of inertia. They experience different accelerations when subject to the same forces. Acceleration is inversely proportional to mass.

**2** At a sophisticated level, there are, in Newtonian physics, two independent definitions of mass - gravitational mass and inertial mass. Steps **a** and **b** in the above procedure relate to this and are suitable for able students only. Gravitational mass determines a body's ability to exert and experience gravitational force. Inertial mass determines a body's resistance to change in its motion (acceleration).

The fact that mass requires two separate definitions is an unsatisfactory aspect of Newtonian physics that is resolved by Einstein's general relativity. According to Newton it is just an incredible coincidence that the two types of mass, gravitational and inertial, are equal in size. According to Einstein, this equivalence is not coincidence but fundamental. These two types of mass become one and the same.

**3** You could use timing techniques, such as use of ticker-timers, for quantitative work. You could then discuss good experimental practice: keeping one variable fixed, varying another, and watching the related changes in the third.

*This experiment was safety-checked in March 2005*