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Texas A&M University

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Problem 57

$* * B 10$ Lift with bent legs You injure your back at work lifting a $420-\mathrm{N}$ radiator. To understand how it happened, you model your back as a weightless beam (Figure $\mathrm{P} 7.57 )$ , analogous

a)

b)

to the backbone of a person in a bent position when lifting an object. (a) Determine the tension force that the horizontal cable exerts on the beam (which is analogous to the force the back muscle exerts on the backbone) and the force that the wall exerts on the beam at the hinge (which is analogous

to the force that a disk in the lower back exerts on the backbone). (b) Why do doctors recommend lifting objects with the legs bent?

Answer

1567 $\mathrm{N}$

1622 $\mathrm{N}$

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## Discussion

## Video Transcript

Hello. We're here, too. Find the tension force of Ah horizontal cable and the force that the wall exerts at the pivot point on this being. So let's start with labeling what forces are actually on our being. This would be our attention force. This would be the downward force, too, to the radiator, which we is a known value off Warren 20 Newtons. And here is our force or wall exerts. Call that force of the wall and it's at the pivot point of our being. We will utilize Newton's second law using both the torque portion as well as or horizontal com home it portion. We know since this beam is not living, that all forces both in the X and Y direction are zero as well as all of our net torques. Remembering torque is forced times the perpendicular lever arm. If we use the wall, here is a pivot point. We know we have two forces that are contributing to works in opposite directions, the tension of the wire as well as the weight of the radiator. So for tension of our wire, we know this to be a true statement that these two it works are equal to each other. Now, remember, lever arm is calculated or found. Bye. Finding the perp particular distance to the torque from the pivot point for the tension Force this because this angle is 15 degrees. This would be l signed 15 or radiator here. We know this angle. It's a complimentary to that. So it would be 75. So this would be f G l sign 75 solving here for attention. No, both Els are the same value is there? The forces are acting at the same point on our being attention would be f g sign 75 signed 15 f g is for 20 and solving that we get a value Uh 15. 67. Vince for our attention force now parked. Our next force we were asked to sell for was the force the wall exerts here. We're going to use the horizontal components and know that they are also in equilibrium. So we know that the force attention would be equal to the horizontal component of the wall. That would be because I'm 15 solving for force of the wall that would be forced tension overcoats on 15 and using our value we just calculated something in, We would calculate that the force of the wall is 16 22. It's now Barbie asks an interesting question. It asks why it is that doctors would recommend lifting objects with the legs bent rather than bending over your back in this manner. If you think about it. If our if we lift with our knees bent, what it amounts to is moving this bar more vertical. If it is, that is, in fact, true. That decreases this angle here, increasing this angle, and that would cause this ratio to become more closer to one. And in fact, the tension would be equal to the wait of the radiator. Remember the tension we compared to the bat, the force that the bath muscle would exert on our back? That would decrease that force? And, of course, the tension was decreased. So would the force that the wall is exerting, which is the force that the disc in the lower back exerts on the back. Thank you for learning with me