Bones and muscles. A patient in therapy has a forearm that weighs 20.5 N and lifts a 112.0 N wei

step 1 Okay, so now we're going to be doing chapter one, problem 65. So this one's kind of complicated.

Bones and muscles. A patient in therapy has a forearm that...

Bones and muscles. A patient in therapy has a forearm that weighs 20.5 $\mathrm{N}$ and lifts a 112.0 $\mathrm{N}$ weight. The only other significant forces on his forearm come from the biceps muscle (which acts perpendicularly to the forearm) and the force at the elbow. If the biceps produce a pull of 232 $\mathrm{N}$ when the forearm is raised $43^{\circ}$ above the horizontal, find the magnitude and direction of the force that the elbow exerts on the forearm. (Hint: The elbow force and the biceps force together must balance the weight of the arm and the weight it is carrying, so their vector sum must be 132.5 $\mathrm{N}$ upward.)

Bones and muscles. A patient in therapy has a forearm that weighs 20.5 $\mathrm{N}$ and lifts a 112.0 $\mathrm{N}$ weight. The only other significant forces on his forearm come from the biceps muscle
(which acts perpendicularly to the forearm) and the force at the elbow. If the biceps produce a pull of 232 $\mathrm{N}$ when the forearm is raised $43^{\circ}$ above the horizontal, find the magnitude and
direction of the force that the elbow exerts on the forearm. (Hint: The elbow force and the biceps force together must balance the weight of the arm and the weight it is carrying, so their vector sum must be 132.5 $\mathrm{N}$ upward.)

Key Concepts

Static Equilibrium

Static equilibrium is the condition in which a system experiences no net force or moment, resulting in no motion. In biomechanics, this principle is applied to ensure that all the forces and torques acting on a body part, such as the forearm, balance out. This allows one to determine unknown forces by setting up equations where the sum of the forces and the sum of the torques are equal to zero.

Force Vector Decomposition

Force vector decomposition involves breaking a force into its horizontal and vertical components, especially when the force is applied at an angle. This technique is crucial in solving equilibrium problems because it allows each component to be balanced separately, providing a systematic way to handle forces acting in multiple dimensions.

Torque and Lever Arm Analysis

Torque, or moment, is the rotational effect of a force, calculated as the product of the force and its perpendicular distance (lever arm) from the pivot point. This concept is essential in determining how different forces, including muscle pulls and weights, produce rotational effects that must counterbalance each other in scenarios such as lifting a weight with the forearm.

Moment Balance

Moment balance is the application of the principle that in rotational equilibrium, the sum of all torques about any pivot point must equal zero. This is fundamental in biomechanics for solving for unknown muscle and joint forces by taking moments about strategic points to simplify the problem.

Vector Summation

Vector summation is the process of combining multiple force vectors into a single resultant vector by adding their respective components. In the context of biomechanics, summing the forces from muscles and external loads provides the net force required to maintain equilibrium, which is then used to determine the magnitude and direction of unknown forces.

Transcript

00:01 Okay, so now we're going to be doing chapter one, problem 65.

00:05 So this one's kind of complicated.

00:06 We're talking about a patient in therapy, and they have a forearm that weighs 20 .5 mutons, but they can lift 112 newtons with it.

00:18 The only other significant forces on the arm come from the biceps muscle, which acts perpendicularly to the forearm and the force at the elbow.

00:29 If the biceps produce a pole of 232, so magnitude of the bicep force is 232 newtons, it's like that known, when the forearm is raised at 43 degrees, okay, above the horizontal.

00:46 And then we want to find the magnitude direction of the elbow force.

00:50 So we know that elbow plus bicep is going to equal this resultant force.

00:59 So now let's draw this to figure out where we're talking about.

01:03 So draw our xy plane.

01:07 Our resultant force needs to be just straight up.

01:10 We know that.

01:12 And this is the bicep force.

01:16 And this is at an angle of 43 degrees.

01:21 Okay, cool.

01:22 So we can rearrange this equation here to write in terms of e, we know this is r minus b.

01:30 Okay? so in components we can write ex equals rx minus bx, which equals 0 minus 232 times the sign of 43 to get the x component.

01:48 So it's 158 newton's in the x...