A 85.0 N weight is held in the hand. The upper arm makes an angle of 32.0° with the vertical, and the lower arm is 10.0° above the horizontal. Find the tension in the biceps tendon. See figure below.
To find the tension in the biceps tendon, we need to consider the forces acting on the weight.
Let's break down the weight into its components:
The vertical component of the weight is given by:
F_v = weight * sin(angle with the vertical)
= 85.0 N * sin(32.0°)
= 45.43 N
The horizontal component of the weight is given by:
F_h = weight * cos(angle with the vertical)
= 85.0 N * cos(32.0°)
= 72.17 N
Now, for the lower arm:
The vertical component of the lower arm tension is acting upward and counteracts the vertical component of the weight. So, the vertical component of the lower arm tension is equal to the vertical component of the weight:
T_l * sin(angle of the lower arm) = 45.43 N
Therefore, T_l = 45.43 N / sin(10.0°)
= 264.58 N
For the upper arm,
The horizontal component of the upper arm tension is acting to the left and counteracts the horizontal component of the weight. So, the horizontal component of the upper arm tension is equal to the horizontal component of the weight:
T_u * cos(angle of the upper arm) = 72.17 N
Therefore, T_u = 72.17 N / cos(32.0°)
= 85.99 N
Finally, to find the tension in the biceps tendon:
T_b = √(T_l^2 + T_u^2)
= √(264.58 N^2 + 85.99 N^2)
= √(70250.00 N^2)
= 264.82 N
Therefore, the tension in the biceps tendon is approximately 264.82 N.
To find the tension in the biceps tendon, we can break down the forces acting on the weight.
1. First, let's analyze the weight of 85.0 N. This force can be broken down into two components – vertical and horizontal.
The vertical component can be found using the formula: vertical force = weight * sin(angle with the vertical)
vertical force = 85.0 N * sin(32.0°)
The horizontal component can be found using the formula: horizontal force = weight * cos(angle with the vertical)
horizontal force = 85.0 N * cos(32.0°)
2. Next, let's consider the tension in the biceps tendon. This force can be broken down into two components – vertical and horizontal.
The vertical component can be found using the formula: vertical force = tension * sin(angle with the vertical)
vertical force = tension * sin(10.0°)
The horizontal component can be found using the formula: horizontal force = tension * cos(angle with the vertical)
horizontal force = tension * cos(10.0°)
3. Now, let's consider the equilibrium condition. Since the weight is held in the hand without moving, the vertical and horizontal forces must balance out. Therefore, the vertical force of the weight must equal the vertical force of the biceps tendon, and the horizontal force of the weight must equal the horizontal force of the biceps tendon.
Equating the vertical forces:
85.0 N * sin(32.0°) = tension * sin(10.0°)
Equating the horizontal forces:
85.0 N * cos(32.0°) = tension * cos(10.0°)
4. We now have a system of two equations with two unknowns (tension and sin(10.0°)). We can solve these equations simultaneously to find the tension in the biceps tendon.
Let's solve the equations using algebra or numerical methods to get the final answer for the tension in the biceps tendon.
Note: The figure mentioned in the question is not provided, but you can refer to a figure illustrating the setup to visualize the angle measurements and the forces involved.