In the above problem, the dumbbell weights 60 lbs. The forearm weighs 15 lbs. Th
ID: 2032852 • Letter: I
Question
In the above problem, the dumbbell weights 60 lbs. The forearm weighs 15 lbs. The biceps is attached to the forearm 2.0 in. from the elbow joint; the center of mass of the forearm is 7.30 in. from the elbow joint. (Note: these units are English rather than metric. Pounds are a unit of force in this system, and the unit of torque for this problem is inch-pounds.) Find the force exerted by the biceps to lift the dumbbell. What is the magnitude of the force exerted by the elbow joint. Show your work and explain your reasoning.
Biceps muscle Elbow joint 2" 7.3 14.5 WDExplanation / Answer
Force exerted by Biceps to lift the dumbbell is, FM = 2176.93 N
Force exerted by the elbow joint is, Fj = 1843.23 N
Answers:
Force exerted by Biceps to lift the dumbbell is, FM = 2176.93 N
Force exerted by the elbow joint is, Fj = 1843.23 N
Explanation:
Given that,
Mdumbbell = 60 Lbs = 27.2155 kg;
Wdumbbell = 27.2155*9.81 = 266.9841 N;
Mforearm = 15 lb = 6.8 kg;
Wforearm = 6.8*9.81 = 66.7 N ;
XM = 2'' = 0.0508 m; Xcg = 0.185 m; L = 14.5'' = 0.368 m
The sum of all the vertical forces should be zero.
Fy = Fm - Fj - Wforearm - Wdumbbell = 0
Fm = Fj + Wforearm + Wdumbbell
Fm = Fj + 66.7 + 266.9841 N
FM = 333.7 + Fj --------------------------------------------------->(1)
Now let us consider the moments about the elbow joints:
Wforearm * Xcg + Wdumbbell * L = Fm * XM
Fm = (Wforearm * Xcg + Wdumbbell * L ) / XM
Fm = (66.7 * 0.185 + 266.9841 * 0.368 ) / 0.0508
FM = 2176.93 N -------------------------------------------------->(2)
Putting value of (2) in (1), we get
2176.93 N = 333.7 + Fj
Fj = 1843.23 N ---------------------------------------------------->(3)
Hence, (2) & (3) are th required values.
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