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bec2008

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Question:

A mother leans horizontally over the crib to lift her 16.7 kg baby. The moment arm of the baby about the hip joint is b = 0.53 m. Her upper body has a mass of 58.0 kg and a moment arm of t = 0.450 m. The back muscles are equivalent to a single muscle with an angle theta = 11.5° to the horizontal spine giving a moment arm of r = 0.090 m. Calculate the tension in her backbone when she lifts her child. For your own education convert this load into pound weight to appreciate the magnitude of the load on the back muscles and spine. This explains why you should keep the spine upright when lifting.

Attempted Solution:

I chose my system as the upper torso. Then, since it is in static equilibrium, I was able to set the sum of the forces equal to zero. This is the equation I came up with:

Sum Forces = -t*W(upper body) - b*W(baby) + r*T*sin theta = 0

Since they are equal to zero, I changed the equation around:

t*W(upper body) + b*W(baby) = r*T*sin theta

I then solved for T, giving me the following equation:

[t*W(upper body) + b*W(baby)]/r*sin theta = T

I keep coming up with the answer 19089 Newtons, but it is not correct. Any help would be greatly appreciated! (There is a picture, but I'm not sure how to post it. I could use help on that, too!)

A mother leans horizontally over the crib to lift her 16.7 kg baby. The moment arm of the baby about the hip joint is b = 0.53 m. Her upper body has a mass of 58.0 kg and a moment arm of t = 0.450 m. The back muscles are equivalent to a single muscle with an angle theta = 11.5° to the horizontal spine giving a moment arm of r = 0.090 m. Calculate the tension in her backbone when she lifts her child. For your own education convert this load into pound weight to appreciate the magnitude of the load on the back muscles and spine. This explains why you should keep the spine upright when lifting.

Attempted Solution:

I chose my system as the upper torso. Then, since it is in static equilibrium, I was able to set the sum of the forces equal to zero. This is the equation I came up with:

Sum Forces = -t*W(upper body) - b*W(baby) + r*T*sin theta = 0

Since they are equal to zero, I changed the equation around:

t*W(upper body) + b*W(baby) = r*T*sin theta

I then solved for T, giving me the following equation:

[t*W(upper body) + b*W(baby)]/r*sin theta = T

I keep coming up with the answer 19089 Newtons, but it is not correct. Any help would be greatly appreciated! (There is a picture, but I'm not sure how to post it. I could use help on that, too!)

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