Stubbed toe

Electricity and Magnetism Level 1

Electrical signals in our nerves don't travel instantaneously. In fact, the speed of electrical signals in our nervous system ranges from under $1~\mbox{m/s}$ to over $100~\mbox{m/s}$ depending on the size and structure of the myelin layer around the nerve fiber (the more myelin the better). If the distance for a tall person from his toe to his brain is $1.8~\mbox{m}$ and the nerve signal travels at the top speed of $100~\mbox{m/s}$ , how long in seconds after they stub their toe does the person actually receive the pain signal in their brain?

The answer is 0.018.

4 solutions

Michael Tang
Nov 24, 2013

We want the time taken for the signal to arrive. Since time equals distance divided by velocity, the time taken equals $t = \dfrac{1.8 \text{ m}}{100 \text{ m/s}} = \boxed{0.018 \text{ s}}.$

I was thinking though, wouldn't it be 3.6m the distance as it has to go from head to toe and back again. I got it right but I found it confusing.

Sharky Kesa - 7 years, 6 months ago

It wouldn't be, since the problem only wants the time taken to receive the signal in the brain , not the time taken to get back to the toe.

Michael Tang - 7 years, 6 months ago

In the question it was given that the maximum speed was 100m/s but the velocity varied from 1m/s to 100m/s. How could we take 100m/s directly , it should have average...

Harsh Chandak - 7 years, 6 months ago

In the last sentence it says "if .... nerve signals travel at the top speed of 100 m/s ... " so we can let $v = 100 \text{ m/s}.$

Michael Tang - 7 years, 6 months ago

why not (100*1.8)

সমুদ্র মিত্র - 4 years, 7 months ago

Akagami Ng
Nov 28, 2013

In the question above, the distance of the nerves in the tall person from their toe to their brain is 1.8 m, and given that the nerve signal travels at 100 m/s along the nerves, we are required to find the time taken for the nerve signal to travel along the distance of 1.8 m from their toe to their brain. The clue of solving this riddle is by finding out the time ,since we are given the speed (100 m/s), and the distance (1.8 m).

So, by applying the formula speed = distance/time, we will get:

100 m/s = 1.8/ time

time = 1.8/100 =0.018 s.

Edward Jeremy Lo
Nov 30, 2013

Questions like this one is always become difficult if you think out of the concept. The answer is really simple: First, you know the person's tall is 1.8 meter, consider it as d . Second, the speed of the signal is 100m/s, consider it as v . After that, with the calculus v=d/t_ . Because we are looking for the time, t . Therefore, t=d/v . You will get: 1.8/100 = 0.0180000000 .

Kathi Allphin
Nov 25, 2013

1.8 m (the distance)/ 100 (the number of m per second) = 0.018 (the number of seconds)

Stubbed toe

The answer is 0.018.

4 solutions

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