Maida Wisozk
Dec 21, 2024
A person bending forward to lift a load “with his back” rather than “with his knees”
A person bending forward to lift a load "with his back" rather than "with his knees" is at risk of injury due to the large forces exerted on the muscles and vertebrae. The spine primarily pivots at the fifth lumbar vertebra, with the main supporting force provided by the erector spinae muscle in the back. When lifting a 200-N object, the spine and upper body can be modeled as a uniform horizontal rod weighing 350 N, pivoted at the base of the spine. The erector spinae muscle, which is attached two-thirds of the way up the spine, helps maintain the position of the back. The angle between the spine and this muscle is 12 degrees.
To find the tension in the back muscle and the compressional force in the spine, please show your calculations step-by-step. The expected answers are T = 2.71 kN and Rx = 2.65 kN.
2 Answers
Jan 15, 2025
Sorry, I just imagine the forces and flexural moment diagram on my mind…..
∑τ = 0
(W_object) L + (W_spine) (½ L) – T (⅔ L) sin θ = 0
(200) + (350) (½) – T (⅔) sin 12° = 0
T = 2705.476 N
∑Fx = 0
Rx – T cos θ = 0
Rx – 2705.476 cos 12° = 0
Rx = 2646.355 N
Jan 29, 2025
you need to draw a free body diagram for this guy. Probably didn’t want to hear that. this would be very difficult and lengthy to answer in words. basically what they are getting at is that given the relatively small angle of 12 degrees the components of the force acting perpendicular to the load must be much larger to achieve the required result. All you need to do is draw your force vectors, split them into triangles and do a little SOH CAH TOA and you’ll be golden. If you are unfamiliar or just not practiced with this method go ask a TA, that’s what they are there for. Good luck, we’ve all been there. It ꜱᴜcκs
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