(a) Find the magnitude of the total force of the traction apparatus applied to the leg, assuming è = 31°, the weight of the leg is 21 N and the weight hanging from the traction apparatus, m, is also 21 N.
1 N
(b) What is the horizontal component of the traction force acting on the leg?
2 N
(c) What is the magnitude of the force exerted on the femur by the lower leg?
3 N
To find the answers to the given questions, we can use trigonometry and the concept of resolving forces into their components.
(a) To find the magnitude of the total force of the traction apparatus applied to the leg, we need to find the vertical component of the traction force. The weight of the leg and the weight hanging from the traction apparatus are both 21 N. Since these weights are balanced by the traction force, the vertical component of the traction force will be equal to their sum, which is 21 N + 21 N = 42 N.
Now, since we are given the angle è = 31°, we can find the magnitude of the total force using trigonometry. The vertical component is the adjacent side, and the total force is the hypotenuse. Therefore, we can use the cosine function to calculate the magnitude of the total force:
cos(31°) = adjacent/hypotenuse
Rearranging the formula to solve for the hypotenuse, we get:
hypotenuse = adjacent/cos(31°) = 42 N / cos(31°) = 48.72 N
So, the magnitude of the total force of the traction apparatus applied to the leg is approximately 48.72 N.
(b) To find the horizontal component of the traction force acting on the leg, we can use the same trigonometric approach. The horizontal component is the opposite side, and the total force is the hypotenuse. Therefore, we can use the sine function to calculate the horizontal component:
sin(31°) = opposite/hypotenuse
Rearranging the formula to solve for the opposite, we get:
opposite = hypotenuse * sin(31°) = 48.72 N * sin(31°) = 24 N
So, the horizontal component of the traction force acting on the leg is 24 N.
(c) To find the magnitude of the force exerted on the femur by the lower leg, we need to find the horizontal component of the traction force acting on the leg. As we calculated in part (b), the horizontal component is 24 N. Since this horizontal component is the force exerted on the femur by the lower leg, the magnitude of this force is 24 N.
In summary, the answers to the given questions are:
(a) The magnitude of the total force of the traction apparatus applied to the leg is approximately 48.72 N.
(b) The horizontal component of the traction force acting on the leg is 24 N.
(c) The magnitude of the force exerted on the femur by the lower leg is 24 N.