The diameter of one leg of the stool is missing and it's 2cm.
Answer:
(ΔL/L) = 0.00729%
Explanation:
If the Weight of the man is W, the weight will be distributed equally on the 3 legs and so the reactions for each leg will be W/3 or F/3.
Now, Youngs modulus(Y) of douglas fir wood is about 1.3 x 10^(10) N/m^2. Gotten from youngs modulus of common materials.
Now, weight of man is 70kg.
Now diameter of one leg is 2cm.so radius of one leg = 2/2 = 1cm = 1 x 10^(-2)m
Area for one leg is; π( 1 x 10^(-2)m)^2 = 3.14 x 10^(-4)m
Now as stated earlier, the force on one leg is; F/3.
Now F = mg = 70 x 9.81 = 686.7N
So, force on one leg = 686.7/3 = 228. 9N
Now we know youngs modulus(Y) = Stress/Strain.
Stress = F/A while Strain = ΔL/L
Therefore Y = (F/A) / (ΔL/L)
And therefore, (ΔL/L) = F/(AY)
So (ΔL/L) = 228.9/(3.14 x 10^(-4))x(1.3 x 10^(10)) = 7. 29 x 10^(-5)
When expressed in percentage, it becomes 0.00729%
