PSS 8.1: Static equilibrium problems Learning Goal: To practice Problem-Solving

Question

PSS 8.1: Static equilibrium problems

Learning Goal:

To practice Problem-Solving Strategy 8.1 Static equilibrium problems.

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 1.50kg . If the biceps is connected to the forearm a distance dbiceps = 3.50cmfrom the elbow, how much force Fbiceps must the biceps exert to hold a 750g ball at the end of the forearm at distance dball = 37.0cm from the elbow, with the forearm parallel to the floor? How much force Felbowmust the elbow exert? (Figure 1)

Now use the information you have accumulated to construct mathematical expressions for ?Fy and ?? and use these to derive the solution.

Part G

Write an expression for ?Fy. Take upward to be the positive y direction.

Express your answer in terms of some or all of the variables F biceps, F elbow, m forearm, m ball, and g.

Explanation / Answer

Given that,

mass of the forearm = m = 1.5 kg

dbicep =l = 3.50 cm = 0.035m

Mass of the ball = M = 750 g = 0.75 kg

dball =L= 37 cm = 0.37 m

Lets write an eqn for all the acting forces,

l.F(bicep) -1/2Lmg - LMg = 0

Solving the above eqn for F(bicep), we get

F(bicep) = { (1/2m + M ) Lg } / l = { (1/2x1.5kg + 0.75kg) 0.37 m x 9.8 m/sec2 } / 0.035 m

F(bicep) = 155.4 N

For calculating F(elbow)

L.F(elbow) - l F(bicep) -1/2 Lmg - LMg = 0, we get

F(elbow) = { lF(bicep) + Lg (1/2m + M) } / L = { (0.035 x 155.4 )+ 0.37 x 9.8 (1/2x1.5 + 0.75 ) } / 0.37

F(elbow) = 29.4 N

d(forearm) = 1/2L = 0.185 m

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