a man weighs 162 pounds, and is 69 inches tall. his forearm is parallel to the ground. he holds an 8 pound weight in his hand. the biceps has an angle of insertion of 85 degrees with a distance of 1.4 inches at insertion. the system is equilibrium. what force is the biceps brachii producing?
To determine the force that the biceps brachii is producing, we need to use the concept of torques. A torque is the rotational force produced by a force acting at a distance from a pivot point. In this case, the pivot point is the biceps brachii insertion point on the forearm.
First, let's calculate the torque produced by the weight in the man's hand. Torque is given by the formula:
Torque = Force × Distance
The weight in the man's hand is 8 pounds, which is equivalent to 8 pounds of force. The distance from the insertion point of the biceps brachii to the weight is the full length of the forearm, as the forearm is parallel to the ground. So, we need to convert the 69 inches to feet: 69 inches ÷ 12 inches/foot = 5.75 feet.
Torque from the weight = 8 pounds × 5.75 feet = 46 pounds-feet
Now, to maintain equilibrium, the torque produced by the biceps brachii must be equal and opposite to the torque from the weight. The torque produced by the biceps brachii can be calculated as:
Torque from the biceps brachii = Force × Distance
We need to find the force produced by the biceps brachii. To do this, we can use the fact that the system is in equilibrium. This means that the sum of all torques in the system must equal zero.
Therefore, Torque from the biceps brachii = Torque from the weight
Force × Distance = 46 pounds-feet
The distance at insertion is given as 1.4 inches. To convert it to feet, we divide by 12: 1.4 inches ÷ 12 inches/foot = 0.117 feet.
Substituting the values into the equation:
Force × 0.117 feet = 46 pounds-feet
Now, we can solve for the force:
Force = 46 pounds-feet ÷ 0.117 feet
Force ≈ 393.16 pounds
Therefore, the biceps brachii is producing a force of approximately 393.16 pounds.