A metal sphere of radius r is dropped into a tank of water. As it sinks at speed v, it experiences a
drag force F given by F = kr v, where k is a constant.
What are the SI base units of k?
m a = k r v note :m is mass
k = m a/ (rv)
kg m
========== note: m is meters
s^2 m m/s
kg /( m s)
Yes
The SI base units of k can be determined by analyzing the equation F = kr v.
The SI unit of force (F) is the Newton (N), which is defined as kg·m/s^2.
The SI unit of speed (v) is meters per second (m/s).
Thus, the SI unit of the right-hand side of the equation is N.
Substituting the units into the equation, we have:
N = k (kg·m/s) (m/s)
Simplifying, we get:
N = k (kg·m^2/s^2)
Comparing the units on both sides, we can determine the SI base units of k:
kg·m^2/s^2 = k (kg·m^2/s^2)
Therefore, the SI base units of k are kg·m^-1·s^-1.
To determine the SI base units of k, we need to analyze the given equation: F = krv.
The SI base units for force (F) are kilograms (mass) times meters per second squared (acceleration). Therefore, the SI base units for force are kg⋅m/s².
The unit for velocity (v) is meters per second (m/s).
The unit for radius (r) is meters (m).
Since the equation for the drag force F is given as F = krv, we can rearrange it to isolate the constant k: k = F / (rv).
From this expression, we can determine the units of k.
Units of F = kg⋅m/s² (force)
Units of r = m (radius)
Units of v = m/s (velocity)
Plugging these units into the equation for k, we get:
k = (kg⋅m/s²) / (m⋅m/s)
= kg⋅m/s²⋅s/m
= kg/s
Hence, the SI base units of k are kilograms per second (kg/s).