your answer must match the given answer plz :) As illustrated in Fig. 3.32, cons

Question

your answer must match the given answer plz :)

As illustrated in Fig. 3.32, consider an athlete performing lower leg exercises from a seated position to strengthen hamstring muscles by using a special training system. The training system provides a set resistance to the leg through a cylindrical pad attached to the load while leg flexing. Point O represents the knee joint, point A is the center of gravity of the lower leg, W is the weight of the lower leg, theta defines an angle that the long axis of the lower leg makes with the horizontal, and M_O is the net moment about point O by forces applied to the leg. If a = 0.23 m, b = 0.45 m, theta = 45^degree, W = 65 N, and M_O = 86.14 Nm, determine the magnitude of the set resistance (F). Considering the same position of the lower leg, calculate the net moment about point O when the set resistance is increased by 10 N. (a) F = 215 N; (b) M_O = 90.64 Nm

Explanation / Answer

part a:

moment=force*perpendicular distance

for force F, perpendicular distance is b.

for force W, component of W, perpendicular to the distance

=W*sin(90-theta)=W*cos(theta)

W*cos(theta) is in clockwise direction while F*b is in anticlockwise direction

net moment is in anticlockwise direction

so F*b-W*cos(theta)*a=M0

using the values provided,

F=(M0+W*cos(theta)*a)/b

=214.9138 N

which is approximately 215 N

part b:

when new value of F=215+10=225 N

then M0=F*b-W*cos(theta)*a

=90.678 N.m

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