Chapter 13, Problem 115A

To determine

To Find: The maximum weight.

Answer to Problem 115A

  $\text{2}\text{.89}\times {\text{10}}^3\text{N}$

Explanation of Solution

Given:

Power of the motor is - $\text{188}\text{W}$

Speed of the motor is $\text{6}\text{.5}\text{cm/s}$

Formula:

Work done per unit time

  $P=\frac{w}{t}$

Here, $\text{w}$ is the work done and $\text{t}$ is the time taken.

Calculation:

Work done is equal to the product force and displacement

  $W=Fd$.........(2)

Here $\text{F}$ is the force applied and $\text{d}$ is the distance moved.

Substitute $\text{Fd}$ for $\text{W}$ in equation (2)

  $\begin{array}{l}P=\frac{Fd}{t}\\ P=F\left(\frac{d}{t}\right)\\ P=Fv\end{array}$

Here $\text{v}$ is the speed at which the motor lifts the load.

Here the force on the load should equal to its weight

  $\text{P}\text{=}\left(mg\right)v$

Here $mg$ is the weight of the load.

  $mg=\frac{P}{v}$

Substitute $\text{188}\text{W}$ for $P$ and $6.5\text{cm/s}$ for $v$

  $\begin{array}{l}mg=\frac{188}{6.5\text{cm/s}\left(\frac{{\text{10}}^{\text{-2}}\text{m}}{\text{1}\text{cm}}\right)}\\ mg=2.89\times {10}^3\text{N}\end{array}$

Conclusion:

Hence, the maximum weight that can be lifted by the motor is $\text{2}\text{.89}\times {\text{10}}^3\text{N}$ .