i've posted this before, but i really don't get how to do it because we never learned this, so if someone would tell me how or just do the first one or something, i would appreciate it. thanks.
Determine the units of the quantity described by the following combinations of units:
a. kg (m/s)(1/s)
b. (kg/s) (m/s^2)
c. (kg/s)(m/s)^2
d. (kg/s)(m/s)
Just multiply out the dimensions as if you were multiplying fractions and coefficients
a. kg (m/s)(1/s) = kg m/s^2
This is the same as mass x acceleration (force), and has the special name of Newtons.
The same applies to part (d)
c. (kg/s)(m/s)^2 = [kg (m/s)^2]/s = Joules/s
To determine the units of a quantity described by a combination of units, you can use the method of multiplying the dimensions as if you were multiplying fractions and coefficients. Let's go through each combination of units given:
a. kg (m/s)(1/s):
To determine the units, multiply the dimensions:
kg * m/s * 1/s = kg m/s^2
The units of this combination are kg m/s^2, which represents force. In the SI system, this is commonly known as Newtons (N).
b. (kg/s) (m/s^2):
Again, multiply the dimensions:
(kg/s) * (m/s^2) = kg m/s^3
The units of this combination are kg m/s^3, which represents a rate of change of momentum. In the SI system, this is commonly known as Newtons per second (N/s).
c. (kg/s)(m/s)^2:
Multiply the dimensions:
(kg/s) * (m/s)^2 = [kg (m/s)^2] / s = kg m^2/s^2
The units of this combination are kg m^2/s^2, which represents energy. In the SI system, this is commonly known as Joules per second (J/s).
d. (kg/s)(m/s):
Multiply the dimensions:
(kg/s) * (m/s) = kg m/s^2
The units of this combination are kg m/s^2, which represents force. This is the same as part a, Newtons (N).
To summarize:
a. kg (m/s)(1/s) = kg m/s^2 (Newtons)
b. (kg/s) (m/s^2) = kg m/s^3 (Newtons per second)
c. (kg/s)(m/s)^2 = kg m^2/s^2 (Joules per second)
d. (kg/s)(m/s) = kg m/s^2 (Newtons)
By following these steps, you can determine the units of a quantity described by a combination of units.