Q82PP - University Physics with Modern Physics

Question

The experiment is designed so that the seeds move no more than 0.20 mm between photographic frames. What minimum frame rate for the high-speed camera is needed to achieve this? 

(a) 250 frames/s; 

(b) 2500 frames/s; 

(c) 25,000 frames/s; 

(d) 250,000 frames/s.

Step-by-Step Solution

Answer

The minimum frame rate required is 23000 frames/s which is close to option (c) 25000 frames/s.

Step 1: Approach

We are given a maximum distance of 0.2 mm, which can travel between frames, and the maximum velocity, which is 4.6 m/s, for which we can determine the minimum frame rate required. A small interval of time dt is considered for which the small instantaneous velocity can be assumed to be constant.

Step 2: Calculation

The minimum frame rate can be found as follows:

$\begin{array}{rcl}d\mathrm{v}& =& \frac{d\mathrm{x}}{d\mathrm{t}}\\ \frac{1}{\mathrm{dt}}& =& \frac{\mathrm{dv}}{\mathrm{dx}}\\ & =& \frac{4.6 \mathrm{m}/\mathrm{s}}{0.20\times {10}^{-3} \mathrm{m}}\\ & =& 23000 \mathrm{frames}/\mathrm{s}\end{array}$

The answer is close to option (c) 25000 frames/s.