(II) If 25 kg is the maximum mass m that a person can hold...

(II) If 25 kg is the maximum mass m that a person can hold in a hand when the arm is positioned with a 105$^{\circ}$ angle at the elbow as shown in Fig. 9-74, what is the maximum force $F_{max}$ that the biceps muscle exerts on the forearm? Assume the forearm and hand have a total mass of 2.0 kg with a $_{CG}$ that is 15 cm from the elbow, and that the biceps muscle attaches 5.0 cm from the elbow. FIGURE 9–74 Problem 37. (Figure can't copy)

Key Concepts

Torque (Moment of Force)

Torque is a measure of the rotational effect of a force applied to a body. It is calculated as the product of the force and the perpendicular distance from the pivot point to the line of action of the force. In problems involving rotation around a joint or pivot, like in lever systems, torque plays a central role in determining equilibrium.

Static Equilibrium

Static equilibrium occurs when an object is at rest and the net force and net torque acting on it are both zero. This principle allows the analysis of forces and moments in a system to ensure that all torques balance, which is essential when solving problems that involve rotational forces.

Lever Systems and Mechanical Advantage

Lever systems consist of a rigid bar rotating around a fixed point (fulcrum), where forces applied at different distances from the pivot provide mechanical advantage. This concept explains how a small force can be amplified to balance or overcome a larger force, depending on the lengths of the lever arms involved.

Transcript

00:01 Chapter 9, problem 37.

00:03 If a 25 kilogram mass is the maximum mass, m that a person can hold in a hand when their arm is positioned with a 105 degree angle at the elbow, as shown in figure 9 -74, what is the maximum force f -max that the biceps muscle exerts on the forearm? assuming the forearm and hand have a total mass of 2 kilograms with a center of gravity that is, 15 centimeters from the elbow and that the bicep muscle attaches 5 centimeters from the elbow.

00:36 All right, so excuse my crude painting of the arm, but this will have to do for now.

00:46 Just focus mainly on the free body diagram or the point mass, the force diagram.

00:54 That's where the important stuff is, but it was just to help me kind of understand the problem a little bit.

01:02 But yeah, we're looking for fmax here, and so we have.

01:06 Just going from left to right, we have fmax pointing in the northwest direction at an angle of 105 degrees.

01:14 So we're looking for this force.

01:17 Next on the line is a little m .g.

01:19 This is just the center of gravity, 15 centimeters away from the elbow.

01:27 And then the big mg, we have the weight at the end of the hand.

01:31 So what can we do with all this to find fmax? well in this chapter we deal a lot with equilibrium and essentially since the hand is not moving the system is in the equilibrium which means there's no angular acceleration there's no linear acceleration and this lets us say that the sum of the forces of the system and some of the torques of the system are zero and with that we can choose a pivot point and then begin to do some calculations and find out some things that we may need to know...

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