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The deltoid muscle. The deltoid muscle is the main muscle that allows you to raise your arm or even hold it out. It is connected to the humerus of the upper arm. (See part (a) of Figure $10.67 .$ ) The person shown is holding his arm out horizontally with a 2.50 kg weight in his hand. This weight is 60.0 $\mathrm{cm}$ from the shoulder joint. His forearm (including his hand) has a mass of 2.44 $\mathrm{kg}$ and is 34.0 $\mathrm{cm}$ long; its center of mass is 43 $\mathrm{cm}$ from the shoulder joint, measured along the arm. His upper arm is 26.0 $\mathrm{cm}$ long and has a mass of 2.63 $\mathrm{kg}$ ; its center of mass is 13.0 $\mathrm{cm}$ from the shoulder joint. The del-toid muscle is attached to the humerus 15.0 $\mathrm{cm}$ from the shoulder joint and makes a $14.0^{\circ}$ angle with the humerus. (See part (b) of the figure.) (a) Make a free-body diagram of the arm. (b) What is the tension in the deltoid muscle?

a) see drawingb) 781 $\mathrm{N}$

Physics 101 Mechanics

Chapter 10

Dynamics of Rotational Motion

Newton's Laws of Motion

Rotation of Rigid Bodies

Equilibrium and Elasticity

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Hope College

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So let's make a free body diagram of the arm for party. Well, we can just draw simple line. And at the end of the the weight here, it would be the weight of the forearm. Here would be the weight of the upper arm. Here would be the tension of the deltoid muscle. And we have going in the white direction a T sign of data and the extraction, of course, T co sign if they where this angle here is to find the data. And here we have the ex component of the shoulder joint, and then here would be the white component of the shoulder joint. We're going to say that counterclockwise is positive and we can say that from the weight of it. If we say that this is the pivot, uh, the weights of the upper arm from the pivot is 13 centimeters. And then from the pivot to the tension of the deltoid muscle, this is 15 centimeters. The pivot to the weight of the forearm is going to be 43.0 centimeters and then the distance from the pivot to the wait would be, of course, six t's such meters. So this would be the complete thiss would be the full free by diagram for the arm. And then we want to find the attention and deltoid muscles weaken suit for Part B, some of forces of some of the torque. There's going to be equal to zero because again, this is not rotating. This will be quick to t sign of theta times 15 minus double the use of you times 13 minus W SUB F times 43 minus W times 60 Again If all of these and if all of these are in centimeters, we don't really have to convert into meters because they're all going to counsel out at the end anyway, So essentially for tea is going to be equal to 9.8 the exploration due to gravity times the mass of each of these respective waits. So it will be 2.63 times 13 plus 2.44 times 43 plus 2.5 times 60. And then this is going to be divided by 15 sign of 14 degrees. And we find that the tension and the deltoid muscle is 781 Newtons. This would be our final answer. That is the end of the solution. Thank you for watching

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