How much force must be produced by the biceps brachia at a perpendicular
distance of 3 cm from the axis of rotation at the elbow to support a weight of
200 N at a perpendicular distance of 25 cm from the elbow?
25*200N=3*Force
To calculate the force required to support the weight at the given distances, we can use the principle of torque. Torque is defined as the product of force and the perpendicular distance from the axis of rotation.
The torque equation is given by:
Torque = Force × Distance
In this case, the torque produced by the weight must be equal to the torque produced by the biceps brachii muscle.
The torque produced by the weight is:
Weight Torque = Weight × Weight Distance = 200 N × 25 cm
The torque produced by the biceps brachii muscle is:
Muscle Torque = Muscle Force × Muscle Distance
Since the muscle and weight are in equilibrium, the muscle torque must equal the weight torque.
Thus,
200 N × 25 cm = Muscle Force × 3 cm
To find the force produced by the biceps brachii muscle, we rearrange the equation to solve for Muscle Force:
Muscle Force = (200 N × 25 cm) / 3 cm
Muscle Force = 1666.67 N
Therefore, the force required to be produced by the biceps brachii muscle to support the weight is approximately 1666.67 N.
To find the force required to support the weight at a certain distance from the elbow, we can use the principle of torque.
Torque is the product of force and the perpendicular distance from the axis of rotation. In this case, the axis of rotation is at the elbow.
The equation for torque is: Torque = force x distance
First, let's find the torque exerted by the weight at a distance of 25 cm from the elbow. We can calculate this by multiplying the weight by the distance:
Torque = 200 N x 0.25 m (converting 25 cm to meters) = 50 Nm
Next, we need to find the perpendicular distance from the axis of rotation to the biceps brachii muscle, which is 3 cm or 0.03 m.
Now, we can rearrange the torque equation to solve for force:
Force = Torque / Distance
Force = 50 Nm / 0.03 m = 1666.67 N
Therefore, the biceps brachii muscle must produce a force of approximately 1666.67 Newtons to support the weight at a perpendicular distance of 3 cm from the axis of rotation at the elbow.