A person is sitting with one leg outstretched, so that it makes an angle of = 39.9o with the horizontal. The weight of the leg below the knee is 34.7 N with the center of gravity located below the knee joint. The leg is being held in this position because of the force M applied by the quadriceps muscle, which is attached 0.100 m below the knee joint (see the drawing). Obtain the magnitude of M
To obtain the magnitude of force M, we need to consider the equilibrium of forces acting on the leg. The sum of all the forces acting on the leg should be equal to zero for the leg to remain in its current position.
Let's break down the forces acting on the leg:
1. Weight of the leg (W): The weight of the leg below the knee is given as 34.7 N. This force acts vertically downwards.
2. Force due to the angle (F): The leg is making an angle of 39.9° with the horizontal. Due to this angle, a component of the weight will act horizontally, causing the leg to rotate.
3. Force applied by the quadriceps muscle (M): This force is applied 0.100 m below the knee joint. The direction of this force is unknown, and we need to determine its magnitude.
Since the leg is in equilibrium, the vertical component of the force due to the angle (F) must balance the weight of the leg (W). We can calculate F using trigonometry:
F = W * sin(θ)
F = 34.7 N * sin(39.9°)
F ≈ 21.32 N
Now, let's consider the horizontal forces. We know that the leg is not moving horizontally, so the net horizontal force must be zero. The force applied by the quadriceps muscle (M) must balance the horizontal component of the force due to the angle (F).
M = F
M ≈ 21.32 N
Therefore, the magnitude of the force applied by the quadriceps muscle (M) is approximately 21.32 N.