The SI units for the constant c in the equation F = crv are kilograms per meter per second (kg/(m·s)). This is derived by analyzing the units of force (newtons), radius (meters), and speed (meters per second).
Given the expression for the resistive force F experienced by a spherical ball of radius r moving through air at speed v:
F = c r v
Where F is the force, r is the radius, v is the speed, and c is a constant. We need to find the SI units of the constant c.
Since the equation is F = c r v, we solve for c by re-arranging the formula:
c = F / (r v)
Substitute the SI units into the rearranged formula to find the units of c:
c = newton / (meter * meter/second) = N / (m * m/s)
This simplifies to:
c = N / (m²/s)
The unit of force (newton) is defined as kg·m/s², so:
c = (kg·m/s²) / (m²/s) = kg / (m·s)
Therefore, the SI units of the constant c are kilograms per meter per second (kg / (m·s)).
Your answer is correct. The SI units of the constant c in the equation F = crv are kg/(m·s), derived by isolating c and substituting the known SI units for force, radius, and velocity.
The resistive force F experienced by a spherical ball moving through air is given by the expression F = crv.
Therefore,
[tex]c=\frac{F}{rv}[/tex]
Here, F is the force (in newtons, N),
r is the radius (in meters, m),
v is the speed (in meters per second, m/s),
and c is a constant.
The SI unit of F is newton (N). 1 Newton in terms of mass (kg), length (m), and time (s) is given by:
1 N = 1 kg.m/s²
Substituting the SI units of Force, velocity and radius in above equation, we get
[tex]c=\frac{kg.m/s^{2} }{(m)(m/s)}[/tex]
c = kg/(m·s)
Thus, the SI units of the constant c are kg/(m·s).