The standard man in the figure below holds with his left arm vertically a dumbbell of mass M = 5,471 g with the intention to do concentration curls. For the position shown, we consider the following four major forces: the weight of the arm and the tension in the shoulder. This tension is primarily due to the deltoid muscle and several ligaments which run across the interface between the trunk and the arm. The weight of the dumbbell and the force pulling down the fist are equal in magnitude and are directed in the same direction. Calculate the ratio of the tension in the shoulder to the force which pulls down the fist.
You will find the answer in the figure below
5471
To calculate the ratio of the tension in the shoulder to the force that pulls down the fist, we need to analyze the forces acting on the man's arm.
First, let's identify the forces involved:
1. Weight of the arm: This force is acting vertically downward due to the gravitational pull on the arm. It can be calculated as the product of the mass of the arm and the acceleration due to gravity (9.8 m/s²).
2. Tension in the shoulder: This force is exerted by the deltoid muscle and ligaments. It acts upward to maintain the arm in its vertical position and counteracts the weight of the arm.
3. Weight of the dumbbell: This force is acting vertically downward due to the gravitational pull on the dumbbell. It can be calculated similarly to the weight of the arm.
4. Force pulling down the fist: This force is equal in magnitude to the weight of the dumbbell and acts vertically downward.
Since the weight of the dumbbell and the force pulling down the fist are equal in magnitude and direction, we can consider them as a single force.
Now, let's calculate the ratio of the tension in the shoulder to the force pulling down the fist:
Ratio = Tension in the shoulder / Force pulling down the fist
To find this ratio, we need to determine the values of the tension in the shoulder and the force pulling down the fist.
You mentioned that the mass of the dumbbell (M) is given as 5,471 g. To calculate the force pulling down the fist (F), we need to convert the mass from grams to kilograms:
M = 5,471 g = 5.471 kg
The force pulling down the fist can be calculated as:
F = M * g (acceleration due to gravity)
Next, we need more information about the arm and the respective forces to determine the tension in the shoulder. If the values of the mass of the arm, the distances, or any other relevant information is provided, we can use the principles of equilibrium to calculate the tension in the shoulder.
Please provide any additional information so we can proceed with the calculation.