How to Convert 10,000,000 Ergs to Joules

Instructor: Gerald Lemay

Gerald has taught engineering, math and science and has a doctorate in electrical engineering.

In this lesson we convert 10,000,000 ergs to joules by using the definitions of mass, distance, force and energy in both the MKS and the CGS systems of measurement.

Converting 10,000,000 Ergs to Joules

Energy equals the product of two quantities: the magnitude of a force times a displacement in the same direction as the force. Or, more simply, energy = force x displacement.

In the metric system we use a base unit for each quantity. For example, the quantity ''displacement'' uses ''meter'' as the base unit. Also, in the metric system, prefixes like ''kilo'' refer to powers of 10. The kilo, 1000, is 10 to the third power.

Base units may be combined. These combined units are usually called derived units. For example, when describing energy on a large-scale, we are more likely to use the derived unit, joule, for energy. One joule is the amount of energy expended when using a force of 1 newton over a displacement of 1 meter. The newton is also a derived unit.

The System International (SI) is based on MKS units. ''MKS'' stand for meter, kilogram and second. Thus, in MKS

  • meter is the unit of length
  • kilogram is the unit of mass
  • second is the unit of time
  • newton is the unit of force
  • joule is the unit of energy

A system which predates MKS is CGS. ''CGS'' stands for centimeter, gram and second. This is a popular system for laboratory work where scientists typically deal with smaller quantities. In CGS,

  • centimeter is the unit of length
  • gram is the unit of mass
  • second is the unit of time
  • dyne is the unit of force
  • erg is the unit of energy

The unit of energy in CGS is the erg and is the amount of energy expended when using a force of 1 dyne over a displacement of 1 centimeter. Recall, the joule is the amount of energy expended when using a force of 1 newton over a displacement of 1 meter. We know there are 100 centimeters in 1 meter, but how is a dyne related to a newton?

Remember Newton's second law? The net force, F, equals the product of the mass, m, times the acceleration, a. Written more concisely, F = ma. Acceleration has units of length divided by time squared. Thus,

  • 1 newton = 1 kilogram x 1 meter/sec2 in the MKS system
  • 1 dyne = 1 gram x 1 centimeter/sec2 in the CGS system

Also, we will abbreviate units whenever possible:

  • kg for kilogram
  • m for meter
  • sec for second
  • g for gram
  • cm for centimeter
  • N for newton
  • J for joule

To convert 10,000,000 ergs to joules:

Step 1: Expand 1 erg in CGS units

Using energy equals force times displacement,


From F = ma, 1 dyne is 1 g cm/sec2. Thus,


And cm times cm is cm2:


Step 2: Write 10,000,000 ergs as 107 ergs in CGS

We can make the conversions easier by using ''10 to a power'' instead of writing out a 1 followed by zeros. For example, 1000 g is 103 g. And, 10,000,000 ergs is a ''1'' followed by 7 zeros. Thus, 10,000,000 ergs is 107 ergs.

From 1 erg = 1 g cm2/sec2,


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