Q60E - University Physics with Modern Physics

Question

You are applying a constant horizontal force $\overrightarrow{\mathbf{F}}\mathbf{=}\mathbf{(}\mathbf{-}\mathbf{8}\mathbf{.}\mathbf{0}\mathbf{\hspace{0.33em}}\mathbf{N}\mathbf{)}\mathbf{ }\mathit{i}\mathit{̂}\mathbf{+}\mathbf{(}\mathbf{3}\mathbf{.}\mathbf{0}\mathbf{\hspace{0.33em}}\mathbf{N}\mathbf{)}\mathbf{ }\mathbf{j}\mathbf{ }$  to a crate that is sliding on a factory floor. At the instant that the velocity of the crate is $\stackrel{\mathbf{r}}{\mathbf{v}}\mathbf{=}\mathbf{(}\mathbf{3}\mathbf{.}\mathbf{20}\mathbf{\hspace{0.33em}}\mathbf{m}\mathbf{/}\mathbf{s}\mathbf{ }\mathbf{)}\mathbf{ }\mathbf{i}\mathbf{ }\mathbf{+}\mathbf{(}\mathbf{2}\mathbf{.}\mathbf{20}\mathbf{\hspace{0.33em}}\mathbf{m}\mathbf{/}\mathbf{s}\mathbf{)}\mathbf{ }\mathbf{j}\mathbf{ }$, what is the instantaneous power supplied by this force?

Step-by-Step Solution

Answer

Force applies a total power of $19\hspace{0.33em}\mathrm{W}$ to the crate. 

Step 1: Identification of given data

The given data can be listed below,

• The horizontal force on the crate is, $\mathrm{F} ⃗=(-8.0\hspace{0.33em}\mathrm{N}) \mathrm{i} \mathrm{̂}+(3.0\hspace{0.33em}\mathrm{N}) \mathrm{j} \mathrm{̂}$ 

• The velocity of the crate is, $\mathrm{v} ⃗=(3.20\hspace{0.33em}\mathrm{m}/\mathrm{s} ) \mathrm{i} +(2.20\mathrm{m}/\mathrm{s}) \mathrm{j}$ 

Step 2: Concept/Significance of instantaneous power.

The conceptual definition of instantaneous power is the rate of work or energy transmission with respect to time. Commercial unit of power is kilowatts .

Step 3: Determination of the instantaneous power supplied by force

The instantaneous power of crate supplied by force is given by,

$P=F ⃗\cdot \stackrel{r}{v}$ 

Here, $F ⃗$ is the force applied on crate and $\stackrel{i}{v}$ is the velocity of the crate.

Substitute all the values in the above,

$\begin{array}{l}P=(-80N)i+(3.0N)j).(332m/s)i+(220m/s\left)j\right)\\ =(-800N)(3.2m/s))+(3.0N\left)\right(22m/s)\\ =-19w\end{array}$

Thus, the instantaneous power supplied by force to the crate is 19W.