Bonvert 10 newton into dyne using dimensional analysis?

Question: Bonvert 10 newton into dyne using dimensional analysis?

To convert 10 newtons into dyne using dimensional analysis, we can use the following conversion factors:

• 1 newton = 1 kilogram-meter per second squared (N = kg⋅m/s²)
• 1 dyne = 1 gram-centimeter per second squared (dyn = g⋅cm/s²)

We can use these conversion factors to set up a proportion and solve for the number of dynes in 10 newtons:

10 N = x dyn

1 kg⋅m/s² = 1000 g⋅cm/s²

Dividing both sides of the first equation by the second equation, we get:

x dyn / 10 N = 1 kg⋅m/s² / 1000 g⋅cm/s²

x dyn = 10 N * 1000 g⋅cm/s² / 1 kg⋅m/s²

x dyn = 10000 g⋅cm/s²

Therefore, 10 newtons is equal to 10000 dynes.

Dimensional analysis is a method of converting units by using the dimensions of the quantities involved. The dimensions of a quantity are the fundamental physical quantities that are required to define it. For example, the dimensions of force are mass, length, and time (F = MLT^-2).

To convert a quantity from one unit system to another, we can use the following steps:

1. Identify the dimensions of the quantity.
2. Set up a proportion using the conversion factors between the two unit systems.
3. Solve for the quantity in the desired unit system.

Dimensional analysis is a powerful tool for converting units in physics and other sciences.

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