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The upper leg muscle (quadriceps) exerts a force of FQ= 1320 N, which is carried by a tendon over the knee cap. With angles 55 and 75 degrees, find the magnitude in newtons and direction in degrees counter-clockwise from an axis directed to the left of the force exerted by the kneecap on the femur
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Treat the kneecap as a frictionless pulley so the tendon tensions on the two sides are equal to FQ = 1320 N. The two tendon forces are separated by 55° + 75° = 130°, so the resultant magnitude for two equal forces is
R = 2F cos(φ/2) = 2(1320) cos(130°/2) = 2(1320) cos 65°.
Numerically,
R ≈ 2640 × 0.422618 ≈ 1.12 × 10^3 N (≈ 1116 N).
The resultant bisects the angle between the two tendon forces, i.e. it is 65° from either tendon direction. Thus the force exerted by the kneecap on the femur has magnitude ≈ 1116 N and is directed 65° counterclockwise from the axis pointing to the left.
R = 2F cos(φ/2) = 2(1320) cos(130°/2) = 2(1320) cos 65°.
Numerically,
R ≈ 2640 × 0.422618 ≈ 1.12 × 10^3 N (≈ 1116 N).
The resultant bisects the angle between the two tendon forces, i.e. it is 65° from either tendon direction. Thus the force exerted by the kneecap on the femur has magnitude ≈ 1116 N and is directed 65° counterclockwise from the axis pointing to the left.
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