Downhill Hiking. During vigorous downhill hiking, the force on the knee cartilage (the medial and lateral meniscus) can be up to eight times body weight. Depending on the angle of descent, this force can cause a large shear force on the cartilage and deform it. The cartilage has an area of about 10 cm2 and a shear modulus of 12 MPa. lf the hiker plus his pack have a combined mass of 110 kg (not unreasonable), and if the maximum force at impact is 8 times his body weight (which, of course, includes the weight of his pack) at an angle of 12° with the cartilage (below Fig.), through what angle (in degrees) will his knee cartilage be deformed? (Recall that the bone below the cartilage pushes upward with the same force as the downward force.) Figure:
Solution 33E Step 1 of 4: In the given problem, we need to find the angle of deformation of the cartilage which has the area A=10 cm and shear modulus S = 12 Mpa. The force applied on the cartilage at an angle 12° is eight times of the body weight with mass m=110 kg , that is F=8W=8mg. We need to calculate the deformation angle, using the equation of shear modulus. Given data, Shear modulus S = 12 Mpa= 12× 10 pa6 Area, A=10cm =10 m 3 3 Body mass, m=110 kg Force, F=8 mg Using g=9.8m/s 2 F= 8×110×9.8 F=8624 To find Tangential stress, Ft= Deformation angle, = To calculate the tangential stress, From the given figure, F t Fsin (12° ) F t 8624 sin (12° ) Ft=1793.03 N
