The drag force acting on a car travelling at a speed v is given by the equation F=kAv^2
Where A is the area of the front of the car.
Show that a suitable unit for the quantity k is kgm-3.
Mark scheme answer:
F= kgms-2
or
A=m2
V=ms-1
Which is K=kgm-3
I am confused could someone show the working out clearly involving all steps and equations used.
Please help.
To find a suitable unit for the quantity "k" in the equation F = kAv^2, we can start by looking at the units of each variable in the equation.
F represents force, and its standard unit is Newton (N), which is equivalent to kg·m/s^2.
A represents the area of the front of the car, and its standard unit is square meters (m^2).
V represents the velocity or speed of the car, and its standard unit is meters per second (m/s).
Now, let's substitute the units into the equation:
F = kAv^2
(N) = k(m^2)(m/s)^2
To make the equation mathematically correct, we need to verify if the units on both sides of the equation are equivalent.
On the left-hand side, we have N (Newtons), which is equal to kg·m/s^2.
On the right-hand side, we have k(m^2)(m/s)^2. Expanding this further, we get:
k(m^2)(m/s)^2 = k(m^2)(m^2/s^2)
Now, in order for the equation to balance, the units on both sides must be equal. Therefore:
kg·m/s^2 = k(m^2)(m^2/s^2)
To simplify the right side of the equation, we can cancel out the terms:
kg·m/s^2 = k(m^2)⋅(m^2/s^2)
kg·m/s^2 = k(m^4/s^2)
The only way the equation balances is if:
k = kg/m^3
Therefore, a suitable unit for the quantity "k" is kg/m^3.