"Newton's law tells us that Force= Mass x Acceleration. We also know that Energy = Force x Distance and Pressure= Force/Area. Using these relationships and table I-1 [I'll type it out], derive (do math stuff) the dimensions of newtons, joules, and pascals in terms of the fundemental SI quantities."
I-1
Quantity - Unit - Symbol
length - meter - m
mass - kilogram - kg
time - second - s
elec. current - ampere - A
temperature - kelvin - K
lumin. int. - candela - cd
amount - mole - mol
plane angle - radian - rad
solid angle - steradian - sr
I have no clue how to go about deriving the dimensions of newtons, joules, and pascals. Could someone show me how, or at least point me in the right direction?
Please do not double post. I answered your question below. Double posting doesn't get your question answered any faster and it clutters the boards. Thanks.
To derive the dimensions of newtons, joules, and pascals in terms of the fundamental SI quantities, let's start with Newton's second law, which states that Force (F) is equal to Mass (M) times Acceleration (A). The dimensions of force (F) are given by [M L T^-2] (mass length per time squared).
Next, let's consider the relationship between energy (E), force (F), and distance (D): E = F x D. From this equation, we can express energy (E) in terms of the dimensions of force (F) and distance (D). Rearranging the equation, we have F = E / D. The dimensions of energy (E) are given by [M L^2 T^-2] (mass times length squared per time squared). Substituting these dimensions into the equation F = E / D, we get the dimensions of force (F) as [M L T^-2] (mass length per time squared).
Finally, let's consider the relationship between pressure (P), force (F), and area (A): P = F / A. From this equation, we can express pressure (P) in terms of the dimensions of force (F) and area (A). The dimensions of pressure (P) are given by [M L^-1 T^-2] (mass per length per time squared). Substituting the dimensions of force (F) we derived earlier ([M L T^-2]) into the equation P = F / A, we get the dimensions of pressure (P) as [M L^-1 T^-2] (mass per length per time squared).
To summarize:
- The dimensions of newtons (N) are [M L T^-2] (mass length per time squared).
- The dimensions of joules (J) are [M L^2 T^-2] (mass times length squared per time squared).
- The dimensions of pascals (Pa) are [M L^-1 T^-2] (mass per length per time squared).