When you lift an object by moving only your forearm, the main lifting muscle in
ID: 1462358 • Letter: W
Question
When you lift an object by moving only your forearm, the main lifting muscle in your arm is the biceps. Suppose the mass of a forearm is 1.10 kg . If the biceps is connected to the forearm a distance dbiceps = 3.50 cmfrom the elbow, how much force Fbiceps must the biceps exert to hold a 1000 g ball at the end of the forearm at distance dball = 34.0 cm from the elbow, with the forearm parallel to the floor? How much force Felbowmust the elbow exert? What is the horizontal distance dforearmbetween the elbow and the point where the weight of the forearm acts?
Explanation / Answer
Given that :
mass of the ball, mball = 1000 g = 1 kg
mass of the forearm, marm = 1.1 kg
(a) Force exerted by the biceps which is given as :
To Sum the moments about the elbow :
dball x Fball + dball x Farm = dbiceps x Fbiceps { eq.1 }
inserting the values in above eq.
(34 cm) [(1 kg) (9.8 m/s2)] + (34 cm) [(1.1 kg) (9.8 m/s2)] = (3.5 cm) Fbiceps
(333.2 N.cm) + (366.5 N.cm) = (3.5 cm) Fbiceps
Fbiceps = (699.7 N.cm) / (3.5 cm)
Fbiceps = 199.9 N
(b) Force exerted by the elbow which is given as :
To Sum the vertical forces :
(mball + marm) g + Felbow = Fbiceps { eq.2 }
inserting the values in eq.2,
[(1 kg) + (1.1 kg)] (9.8 m/s2) + Felbow = (199.9 N)
(20.58 N) + Felbow = (199.9 N)
Felbow = (199.9 N) - (20.58 N)
Felbow = 179.3 N
(c) The horizontal distance between the elbow and the point where the weight of the forearm acts which is given as :
dforearm = L / 2 { eq.3 }
where, L = 34 cm
inserting the value of 'L' in eq.3,
dforearm = (34 m) / 2
dforearm = 17 cm
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