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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 anddirection 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.)

$-13.2^{\circ}$

Physics 101 Mechanics

Chapter 1

Models, Measurements, and Vectors

Physics Basics

Rutgers, The State University of New Jersey

University of Washington

Hope College

University of Winnipeg

Lectures

04:16

In mathematics, a proof is a sequence of statements given to explain how a conclusion is derived from premises known or assumed to be true. The proof attempts to demonstrate that the conclusion is a logical consequence of the premises, and is one of the most important goals of mathematics.

09:56

In mathematics, algebra is one of the broad parts of mathematics, together with number theory, geometry and analysis. In its most general form, algebra is the study of mathematical symbols and the rules for manipulating these symbols; it is a unifying thread of almost all of mathematics.

04:20

Bones and Muscles. A patie…

10:31

A physical therapy patient…

05:09

07:32

The bones of the forearm (…

04:17

00:45

07:09

02:01

The arm in Figure P8.17 we…

01:59

The arm in Figure $\mathrm…

03:39

The arm in Figure Pl2.41 w…

17:48

02:12

Find the force exerted by …

03:11

Find the force that the bi…

01:33

(I) Approximately what mag…

11:44

03:44

The forearm shown below is…

00:47

To determine the force a p…

03:48

A man holds a 178-N ball i…

over. Okay, so now we're going to be doing Chapter one problems. 65 2 This one is kind of complicated. We're talking about a patient in therapy, and they have a forearm that weighs 24 5 News, but and lit that can lift 112 thie. Only other significant forces on the harm come from the biceps muscle, which acts perpendicular, perpendicular early, 24 on and a force at the elbow. If the bicep spirits of pole of 232 7 magnitude of the bicep forces 232 years of that, when the forum is raised at 43 degrees, okay, above the horizontal, and then we want to find the magnitude direction of the mobile force. So we know that elbow plus bicep is going to equal this resulting. So now lets you do all this to figure out where we're talking about. So char X y plain our resultant force needs to be just straight up. We know that, and this is the bicycle force, and this is at a angle of 43 degrees. Okay, Cool. So we can rearrange this equation here toe right? In terms of you know this is our minus B. Okay, so in components we can write, he acts are exploiters the X, which equals zero minus 2 32 Time's a sign of for these three to get the X component. So it's 158 Newton's and the ex So sue the same with the why here This becomes 130 2.5 because that is the total weight from the forum, plus the wait. So this is the week er that resulted vector magnitude, and we can subtract B y. So this is 132.5 minus 2 32 Times Co signed a 43 so that comes out to be native. 37. Newton's Okay, clear. So now that we have that, we could find the magnitude of the elbow force. This is a square root of 37 squared plus 1 58 square. I could put that on a calculator. He's our elbow, has a magnitude force of 162 Newtons. So let's draw this and our ex wife trying to figure out what direction the elbow is, right? So if it's 158 Newton's not degrees on the wire, about that 158 newbies north her up in the X direction right such this way 1 50 feet in the negative, 37 down here. So the elbow wasn't doing this kind of force. So for wanting to find this angle here, we can take data equals arc Tangent of negative 37 over 1 58 and we see that this becomes 13 degrees south of horizontal, which is also the same as negative 15 degrees. Cool, then we have the magnitude and the direction of our resulted vector our elbow after not a result of awesome.

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