A 85.0 N weight is held in the hand. The upper arm makes an angle of 29.0° with the vertical, and the lower arm is 13.0° above the horizontal. Find the tension in the biceps tendon.
To find the tension in the biceps tendon, we can break down the forces acting on the weight and use the equations of static equilibrium.
First, let's resolve the weight vector into vertical and horizontal components:
Vertical component = weight * sin(angle with the vertical)
Horizontal component = weight * cos(angle with the vertical)
Since the angle between the lower arm and the horizontal is given, we need to find the horizontal component of the weight component acting on the lower arm. We can do this by multiplying the horizontal component of the weight (found above) by cos(angle with the horizontal).
Horizontal component of weight on the lower arm = Horizontal component * cos(angle with the horizontal)
Once we have the horizontal component of the weight on the lower arm, we can find the tension in the biceps tendon by equating it to the horizontal force exerted by the biceps tendon.
Tension in the biceps tendon = Horizontal component of weight on the lower arm
Let's plug in the given values and solve the problem step-by-step:
Weight = 85.0 N
Angle between upper arm and vertical = 29.0°
Angle between lower arm and horizontal = 13.0°
Vertical component = 85.0 N * sin(29.0°)
Horizontal component = 85.0 N * cos(29.0°)
Horizontal component of weight on the lower arm = Horizontal component * cos(13.0°)
Finally, we can calculate the tension in the biceps tendon:
Tension in the biceps tendon = Horizontal component of weight on the lower arm
Now, substitute the values and solve the equation to find the tension in the biceps tendon.
To find the tension in the biceps tendon, we need to break down the weight into its vertical and horizontal components.
First, we need to find the vertical component. The weight is acting vertically downward, so we can use trigonometry to find the vertical component of the weight:
Vertical Component = Weight * cos(angle)
= 85.0 N * cos(29.0°)
Next, we need to find the horizontal component. The weight is acting horizontally, so we can use trigonometry to find the horizontal component of the weight:
Horizontal Component = Weight * sin(angle)
= 85.0 N * sin(29.0°)
The tension in the biceps tendon is equal to the upward force required to balance the vertical component of the weight. Since the weight is acting vertically downward, the upward force must be equal to the vertical component. Therefore, the tension in the biceps tendon is:
Tension in the biceps tendon = Vertical Component
= 85.0 N * cos(29.0°)
Now we can calculate the tension in the biceps tendon using the given values:
Tension in the biceps tendon = 85.0 N * cos(29.0°)
≈ 75.21 N
Therefore, the tension in the biceps tendon is approximately 75.21 N.