what is the tension in the biceps tendon if the hand is holding a 10 kg ball while the forearm is held 45 degrees below horizontal
To find the tension in the biceps tendon, we can use the concept of torque. Torque is the rotational force that an object experiences when a force is applied to it at a certain distance from a pivot point.
In this scenario, the forearm acts as the lever and the pivot point is the elbow joint. The weight of the ball creates a torque which is counteracted by the tension in the biceps tendon.
To calculate the tension, we can use the equation:
Torque = Force x Distance
First, we need to calculate the torque created by the weight of the ball. The force acting on the ball is its weight, which can be calculated using the formula:
Force = mass x acceleration due to gravity
Given that the mass of the ball is 10 kg and the acceleration due to gravity is approximately 9.8 m/s^2, we can calculate the force:
Force = 10 kg x 9.8 m/s^2 = 98 N
Now, we need to calculate the lever arm or the distance from the pivot point (elbow joint) to the point where the force is applied (hand). Since the forearm is held 45 degrees below horizontal, we can use basic trigonometry to find the length of the lever arm.
Assuming the length of the forearm from the elbow joint to the hand is L, we can calculate the lever arm:
Lever Arm = L x sin(45 degrees)
Now, using this lever arm and the force calculated earlier, we can find the torque:
Torque = Force x Lever Arm
Finally, the tension in the biceps tendon is equal to the torque, as it exerts an equal and opposite force to prevent the ball from rotating. Hence, the tension in the biceps tendon is equal to the calculated torque.
Remember to measure the length of your forearm and use standard units (such as meters or centimeters) to ensure accurate calculations.
To find the tension in the biceps tendon, we can first calculate the force exerted by the ball due to its weight.
Step 1: Determine the vertical component of the weight of the ball.
The weight of the ball is given as 10 kg. Since the forearm is held 45 degrees below the horizontal, we need to find the vertical component of the weight. To do this, we can use trigonometry.
Vertical component = Weight of the ball * sine(angle)
Vertical component = 10 kg * sin(45 degrees)
Vertical component = 10 kg * 0.7071
Vertical component ≈ 7.071 kg
Step 2: Calculate the tension in the biceps tendon.
The tension in the biceps tendon is equal to the force exerted by the ball due to its weight, which is the same as the vertical component of the weight.
Tension in the biceps tendon ≈ 7.071 kg
Therefore, the tension in the biceps tendon is approximately 7.071 kg.