Leg traction is applied to a patient's leg. If the physician requested a 32N force to be applied to the leg, and the angle is 60 degrees, what mass m must be used for the object hanging from the massless cable?
60 degrees mearsure how?
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leg /_<--angle=60`______
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m
I guess the drawings didn't turn out the way i wanted them...
The angle is between the net force of pulling the leg horizontally and the tension of the string.
To solve this question, we can begin by using trigonometry to resolve the given force into its horizontal and vertical components. Here's how you can calculate the mass:
1. Draw a diagram: Sketch a diagram representing the forces acting on the object in leg traction. Label the given angle (60 degrees) and the force applied to the leg (32N).
2. Resolve the force: The force applied to the leg can be resolved into its horizontal (F_h) and vertical (F_v) components using trigonometry.
F_h = F * cos(angle)
F_v = F * sin(angle)
Substitute the given values:
F_h = 32N * cos(60 degrees)
F_v = 32N * sin(60 degrees)
3. Determine the vertical force: In leg traction, the vertical force is equal to the weight of the hanging mass. So, it can be written as:
F_v = m * g
where m is the mass and g is the acceleration due to gravity (approximately 9.8 m/s^2).
4. Equate the forces: Since the vertical components of both forces are equal, we can equate them:
32N * sin(60 degrees) = m * 9.8 m/s^2
5. Solve for mass (m): Rearrange the equation to solve for m:
m = (32N * sin(60 degrees)) / 9.8 m/s^2
Calculate the value using a calculator:
m ≈ 3.716 kg
Therefore, the mass (m) that must be used for the object hanging from the massless cable is approximately 3.716 kg.