# Given a Force $F$ in newtons, what are the appropriate units for a scalar $Q$ so that $F = Q \times 2.00\rm \:N = 20.0\:N$? [closed]

If: $$\mathrm{force} = Q \times 2.00\rm \:N = 20.0\:N$$ then what does $Q$ equal?

What are the appropriate units for $Q$ so the value of the force comes out with the correct units of newtons?

• Is there some reason $Q=10$ doesn't work? Can you explain your why or why not? – Mike Mar 12 '18 at 17:19
• Q = 10 does work, but what are the units of Q? 10 of what? Newtons? Kilograms? meters/s^2? Is there a unit for the value of Q? – Jack Mar 12 '18 at 17:23
• Alternatively, is Q unit-less? – Jack Mar 12 '18 at 17:24
• Think through it for yourself. If $Q=10\,\mathrm{N}$, then what units does $Q \times 2.00\,\mathrm{N}$ have? How about $Q=10\,\mathrm{kg}$ or $Q=10\,\mathrm{m}/\mathrm{s}^2$? What if $Q$ is dimensionless? We can't do your thinking for you. I assume you're learning about dimensional analysis. What have you learned so far? – Mike Mar 12 '18 at 17:30
• I was using those units for question clarification, as you requested. They are not possible solutions. This was a question put forth on a physics assignment dealing with forces and accelerations. – Jack Mar 12 '18 at 17:44

Well, not the way you posted it but, a Force is a vector quantity. So $10 * \vec 20.0 N$ is a valid "scalar - vector multiplication". So it's totally valid for $Q = 10$, as a scalar, dimentionless.