Chapter 15, Problem 1EP

To determine

The input and output distances for a simple machine.

Answer to Problem 1EP

The input distance is greater than the output distancefor the given simple machine.

Explanation of Solution

The device which can alter the direction as well as the amount of an applied force to it for a process, is termed as a simple machine. Therefore, a simple machines are those physical devices used for apply force when the direction or the magnitude of the applied force and its distance is changed.

 The amount of work done by a simple machine is defined as the force applied to the displacement of the object or the parallel distance at which the force is applied. In other words, the work done by the machine is the product of the force applied and the distance to which force is applied.

Write the expression for the work done by the machine.

  $W=Fd$        (I)

Here, $W$ is the work done, $F$ is the force applied and $d$ is the distance at which the force is applied on the machine.

Write the expression for the conservation of energy or work the machine.

  $W_{\mathrm{i}}=W_{\text{o}}$

Here, $W_{\mathrm{i}}$ is the work input and  $W_{\text{o}}$ is the work output of the machine.

Substitute $F_{\text{i}}{d}_{\text{i}}$ for  and $F_{\text{o}}{d}_{\text{o}}$ for  from equation (I) in the above expression.

  $F_{\text{i}}{d}_{\text{i}}=F_{\text{o}}{d}_{\text{o}}$

Here, $F_{\text{i}}$ and $F_{\text{o}}$ are the input and the output forces on the machine and $d_{\text{i}}$ and $d_{\text{o}}$ are the input and the output distances of the machine.

Simplify the above expression as:

  $\frac{F_{\text{o}}}{F_{\text{i}}}=\frac{d_{\text{i}}}{d_{\text{o}}}$

Therefore, it is clear from the above expression that when output force is greater than the input force will make the input distance greater than the output distance for the machine.

Conclusion:

Thus, The input distance is greater than the output distance for the given simple machine.