Question

High-impact activities such as jogging can cause considerable damage to the cartilage at the knee joints. Peak loads on each knee can be eight times body weight during jogging. The bones at the knee are separated by cartilage called the medial and lateral meniscus. Although it varies considerably, the force at impact acts over approximately 11.0cm^2 of this cartilage. Human cartilage has a Young's modulus of about 24.0MPa (although that also varies). a) By what percent does the peak load impact of jogging compress the knee cartilage of a 76.0kg person? b)What would be the percentage for a lower-impact activity, such as power walking, for which the peak load is about four times body weight?

Answer 1

Answer:

a. ε = 0.225 , % = 22.56 %

b. ε = 0.1128 , % = 11.28 %

Explanation:

E = 24.0 Mpa

m = 76.0 kg

d = 11.0 cm ² * = 1.1 x 10⁻³ m

a.

Use the equation ti determine the force and stress replacing and solve to  ε'

E = σ / ε    ⇒     ε =  σ / E  

σ is the relation between the force in determine area and know the force is mass by gravity

F/A / E    ⇒   mg / EA

ε = [ 8 * 76.0kg * 9.8m/s² ] / (24.0x 10⁶ Pa * 1.1 x 10 ⁻³ m²)

ε = 0.225

Now the

% 0.205 * 100 = 22.57 %

b.

ε = [ 4 * 76.0kg * 9.8m/s² ] / (24.0x 10⁶ Pa * 1.1 x 10 ⁻³ m²)

ε = 0.1128

% 0.1128 * 100 = 11.28 %

Notice is the half of the porcent