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A spherical ball of radius r experiences a resistive force F due to the air as it moves through the air at speed v. The resistive force F is given by the expression: F=crv Where c is a constant. Find the SI units of c.
(I found them to be kg/ms but I'm not sure if it's right.)​

Verified Answer :

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.

  1. The SI unit of force, F, is the newton (N).
  2. The SI unit for radius, r, is meters (m).
  3. The SI unit for speed, v, is meters per second (m/s).

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,

\(c=\frac{F}{rv}\)                                                                

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

\(c=\frac{kg.m/s^{2} }{(m)(m/s)}\)

c = kg/(m·s)

Thus, the SI units of the constant c are kg/(m·s).

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