Question
An elephant has feet with circular bases. Each foot has a radius of 0.2 m, and the total force that the elephant exerts on the ground is 40,000 N. Work out the pressure the elephant exerts when all 4 of its feet are on the ground. Give your answer to 3 s.f.
Answer
4.1
(284 Votes)
Aaron
Elite · Tutor for 8 years
Answer
Substituting the given force and the calculated total area into the pressure calculation formula from step 3, we get:\(\text{Pressure} = \frac{{40,000 N}}{{4 \times \pi \times(0.2m^2)}}\)=
So, the pressure the elephant exerts when all four of its feet are on the ground is
to three significant figures.
Explanation
## Step 1:We are given that the elephant has feet with circular bases, and the radius of each foot is 0.2 m. The total force that the elephant exerts on the ground is 40,000 N. To calculate the pressure, we need to know the total area over which the pressure is being exerted. The elephant is standing on four feet, each foot has a circular base, so total contact area would be the sum of the areas of the circles corresponding to the base of the four feet. ## Step 2:The area of a circle is given by
. Here, 'r' represents the radius of the circle, and in this case it is given as 0.2 m. The total contact area for the elephant we can calculate as \( 4 \times \pi \times (0.2m)^2 \). ### \(\text{Total Area} = 4 \times \pi \times (0.2m)^2\)## Step 3:The pressure exerted by the elephant when all four feet are placed is calculated as the force exerted divided by the total area. ###
## Step 4:Substitute the given values into the formula to compute the desired pressure. And then, we should round the answer (to ensure it has 3 significant figures).