Question

The quadriceps muscles pull on the patella simultaneously. Below are the forces from each
muscle. Vastus lateralis: 680N at an angle of 30 degrees to the left of vertical. Rectus femoris:
220N at an angle of 16 degrees to the left of vertical. Vastus intermedius: 600N at an angle
of 15 degrees to the left of vertical. Vastus medialis: 480N at an angle of 35 degrees to the
right of vertical.
1. What is the resultant force due to the quadriceps?
2. What would happen if the vastus medialis was trained and strengthened to contract
with 720N of force?

Answer 1

Based on the calculation of the resultant of vector forces:

1. the resultant force due to the quadriceps is 1795 N
2. the resultant force due to the quadriceps is 1975 N. Training and strengthening the vastus medialis results in a greater force of muscle contraction.

What is the resultant force due to the quadriceps?

The resultant of more than two vector forces is given by:

• F = √Fₓ² + Fₙ²

where:

• Fₓ is the sum of the horizontal components of the forces
• Fₙ is the sum of the vertical components of the forces
• Fx = F₁cosθ + F₂cosθ + F₃cosθ + F₄cosθ
• Fₙ = F₁sinθ + F₂sinθ + F₃sinθ + F₄sinθ
• F₁ = 680N, θ = 90 = 30 = 120°
• F₂ = 220 N, θ = 90 + 16 = 106°
• F₃ = 600 N, θ = 90 + 15 = 105°
• F₄ = 480 N, θ = 90 - 35 = 55°

then:

Fx = 680 * cos 120 + 220 * cos 106 + 600 * cos 105 + 480 * cos 55

Fx = -280.6 N

Fₙ = 680 * sin 120 + 220 * sin 106 + 600 * sin 105 + 480 * sin 55

Fₙ = 1773.1 N

then:

F = √(-280.6)² + ( 1773.1)²

F = 1795.16 N

F ≈ 1795 N

Therefore, the resultant force due to the quadriceps is 1795 N

What would happen if the vastus medialis was trained and strengthened to contract with 720N of force?

From the new information provided:

• F₁ = 680N, θ = 90 = 30 = 120°
• F₂ = 220 N, θ = 90 + 16 = 106°
• F₃ = 600 N, θ = 90 + 15 = 105°
• F₄ = 720 N, θ = 90 - 35 = 55°

then:

Fx = 680 * cos 120 + 220 * cos 106 + 600 * cos 105 + 720 * cos 55

Fx = -142.95 N

Fₙ = 680 * sin 120 + 220 * sin 106 + 600 * sin 105 + 720 * sin 55

Fₙ = 1969.72 N

then:

F = √(-142.95)² + ( 1969.72)²

F = 1974.9 N

F ≈ 1975 N

Therefore, the resultant force due to the quadriceps is 1975 N.

Training and strengthening the vastus medialis results in a greater force of muscle contraction.

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