if the unit of power is the watt (W), and P = Fd/t, show using the result of question (2) and the fact that distance (d) uses units of meters and time has units of seconds.
*** question 2. If m represents mass in kg, v represents speed in m/s, and r represents radius in m, show that the force F in the question F = mv^2/r can be expressed in the unit kgm/s^2.
F=mv^2/r -----> kg(m/s)^2/m ---> kgm^2s^2/m = kgms^2
To show that the unit of power can be expressed as the watt (W) using the result from question 2 and the fact that distance (d) is measured in meters and time is measured in seconds, we need to substitute the expression for force (F) from question 2 into the power equation P = Fd/t.
From question 2, we have F = mv^2/r where F is expressed in kgm/s^2.
Substituting this expression for F into the power equation, we get:
P = (mv^2/r)d/t
Now let's analyze the units:
Since distance (d) is measured in meters (m) and time (t) is measured in seconds (s), we need to show that the resulting unit of power, P, is in watts (W), which are defined as joules per second (J/s).
First, let's simplify the expression (mv^2/r)d/t:
(mv^2/r)d/t = (kgm/s^2)(m)(m)/(s)
Simplifying further:
(kgm^2/s^2)(m)/(s) = kgm^3/s^3
The resulting unit is kgm^3/s^3, which does not match the unit of a watt (W).
Therefore, using the given formula for force (F) as F = mv^2/r and the fact that distance (d) is measured in meters and time (t) is measured in seconds, we cannot directly relate it to the unit of power (Watt) using the given equation P = Fd/t.
To show that the unit of power can be expressed in watts using the formula P = Fd/t, we need to substitute the units for force (F), distance (d), and time (t) into the formula.
From question (2), we found that the force F can be expressed in kgms^2.
Substituting this into the power formula, we have:
P = (F * d) / t
Substituting the units:
P = (kgms^2 * m) / s
Simplifying:
P = (kgm^2s^2) / s
Since the denominator s cancels out, we are left with:
P = kgm^2s^2
Therefore, the unit of power can be expressed in kgm^2s^2, which is equivalent to a watt (W).