(I) Approximately what magnitude force, FM, must the extensor muscle in the upper arm exert on t

step 1 Once again, welcome to a new problem. This time we have an arm that's holding on to a short put.

(I) Approximately what magnitude force, FM, must the...

Key Concepts

Static Equilibrium

Static equilibrium occurs when a system is at rest and the sum of forces and torques acting on it is zero. In problems involving the human arm holding a weight, static equilibrium means that all torques about the joint must cancel out. This principle allows one to set up equations to solve for unknown forces, such as the muscle force required to support an external load.

Muscle Force in Biomechanics

Analyzing muscle force in biomechanics involves understanding how muscles generate force to counteract external loads through lever systems. In problems like holding a weight, the muscle force must produce a torque that balances the torques produced by the weight of the load and the mass of the limb. This concept is pivotal for understanding bodily mechanics, injury prevention, and designing biomechanical aids.

Torque

Torque is the measure of a force’s tendency to produce rotation about a pivot point. In biomechanics and physics, torque is calculated by multiplying the force magnitude by the perpendicular distance from the pivot to the line of action of the force. Understanding torque is essential when analyzing the forces acting on the arm when balancing weights, as it must be opposed by muscle-generated torques for equilibrium.

Lever Arm

The lever arm, or moment arm, is the perpendicular distance from the pivot point to the line of action of the force. It determines how effectively a force can produce torque about that pivot. In the context of the arm, muscle attachment points and the distance from the joint are critical factors in how the applied force translates into rotational motion or balance.

Transcript

00:01 Once again, welcome to a new problem.

00:04 This time we have an arm that's holding on to a short put.

00:15 So these are like the fingers right here.

00:19 You know, just having an arm like that.

00:23 And it's holding on to a short put.

00:29 The arm itself, the short put itself is right here.

00:34 So the mass of the short foot happens to be given us 7 .3 kilograms.

00:51 So that's the mass of the short foot, and then there are the piece of information that we're given is that there is a specific distance.

01:06 This one right here, the distance between the elbow and the extensor and that distance, we're going to call it d equals to small d equals to 2 .5 centimeters.

01:27 Also, we're supposed to find, so this is the information we've given.

01:34 We are also given that the entire distance from this point, up until the center of the short put is 30 centimeters the distances are in centimeters and we do see that the lower arm this lower arm right here i'm gonna call it ml mass lower has a mass of 2 .3 kilograms with the center of gravity so this distance right here, that's the center of gravity.

02:20 And up until there, that's 12 centimeters.

02:25 This one too is 12 centimeters.

02:28 So that's the information that's given.

02:33 That's from the elbow.

02:34 So we're saying from the elbow right here, it's 12 centimeters.

02:38 That's the distance.

02:40 Our purpose is to find this force, fm, that's the distance.

02:47 That holds on to the ball itself such that the ball doesn't get, doesn't fall off.

02:55 It's holding not the ball but the short put.

02:59 That's what's going on with this problem.

03:02 So we're supposed to find, we want to find the force fm...