(II) (a) Calculate the magnitude of the force, FM, required of the "deltoid" muscle to hold up t

step 1 So, once again, welcome to a new problem. This time, we have a forearm that's stretching all the

(II) (a) Calculate the magnitude of the force, FM, required...

Key Concepts

Static Equilibrium

Static equilibrium refers to the state in which a system has no net force or net moment acting on it. In problems involving forces on a body, this means that both the sum of all forces and the sum of all torques (moments) about any point must equal zero. This concept is fundamental in determining unknown forces and moments in a wide range of mechanical and biomechanical applications.

Torque (Moment) Calculation

A torque, or moment, is a measure of the tendency of a force to rotate an object about a pivot or axis. It is calculated as the product of the force and its perpendicular distance (lever arm) from the pivot point. This concept is crucial when analyzing systems in rotational equilibrium, as the sum of the torques must balance out to maintain stability.

Lever Arm

A lever arm is the perpendicular distance from the line of action of a force to the pivot point or axis of rotation. In any torque calculation, identifying the correct lever arm is essential because it directly influences the magnitude of the moment generated by the force. The lever arm concept is widely applicable in mechanics for both simple machines and complex biological systems.

Free Body Diagram

A free body diagram is a simplified representation of an object, isolated from its surroundings, with all external forces and moments acting on it depicted. This tool is fundamental in mechanics as it allows one to systematically apply the principles of static equilibrium, aiding in the identification and resolution of the forces and torques involved in a problem.

Force Decomposition

Force decomposition involves breaking a force vector into components, typically along perpendicular axes (such as horizontal and vertical). This technique is essential in solving problems in statics and dynamics, as it simplifies the analysis of forces acting at angles and allows for the independent application of equilibrium conditions in each direction.

Transcript

00:03 So, once again, welcome to a new problem.

00:07 This time, we have a forearm that's stretching all the way out.

00:16 Okay, we have a forearm.

00:18 Maybe we need to change it a little bit.

00:20 So we have a forearm that's stretching outwards with the fingers out like that.

00:30 And there's a socket.

00:32 There's a bone socket at the shoulder.

00:37 And then there's a joint right there.

00:39 It's not 100 % accurate, but we're just going to go ahead and use this.

00:46 The thing that happens is there is a force that's pulling upwards at an angle of 15 degrees.

00:55 So, you know, there's this force.

00:57 We're going to call it fm at an angle of 15 degrees.

01:01 And then there's another force opposing that motion.

01:05 We're calling that an angle of theta.

01:10 We're calling that force fj.

01:13 The distance between the shoulder socket up until the fm force is 12 centimeters, and then the distance up until where the weight acts, the weight of the arm acts, is an entire distance of 24 centimeters.

01:38 So this is the information that we're given, and we'll see that, in part a, we want to find the, you know, given the total mass of the arm m is 3 .3 kilograms, we want to go ahead and find in part a the force fm.

02:05 So what's the magnitude of the force fm? and then in part b, we want to find the magnitude of the force fm.

02:16 And the angle theta.

02:18 So this is the angle theta right there.

02:20 Those are the two issues we're dealing with.

02:23 In this problem, so the first part, we're going to say that the sum of talks is zero, assuming the talk from the bone socket is our main interest.

02:39 We'll see that fm sign of theta, fm sign of theta obviously is a, component of fm.

02:52 It's a component of fm, so fm, sign of theta times 12 centimeters becomes equal to mg times 24 centimeters.

03:08 That allows us to compute fm as being equivalent to mg 24 centimeters, all of a sign theta.

03:25 12 centimeters.

03:28 But then sine theta is 15.

03:30 So this is mg 24 centimeters all of a sign of 15 times 12 centimeters.

03:42 Next page we start plugging in those numbers to get fm.

03:46 So we see that fm is 3 .3 kilograms times 9 .8 meters per second squared.

03:55 And we don't have to do the conversion to meters even though it helps...