no 12 and g. Check t limiting cases you can check as well. he units of your expr

Question

no 12

and g. Check t limiting cases you can check as well. he units of your expression, and try to determine if there are any 12. Fiona's Finger Foils the Falling Flap In the figure below is a table with an extension flap that swings out on a hinge. The length of the flap is ( and the mass of the flap is M. A mass m hangs a distance d from the left end of the flap from a massless cord, and Fiona supports the flap with a single finger placed a distance D from the left end. a. For each of the following special cases where certain of the variables take on certain specific values, determine the force F Fiona must exert upward to prevent the flap from falling. In each case, any variable for which no special value is specified 7

Explanation / Answer

length of flap = l, mass of flap = M

hanging mass = m, distance from left enfd of flap = d

dikstance from the left end of the finger = D

let the force from the finger to keep the flap from falling be F

then from moment balance about the pivot

mg(l - d) + Mgl/2 = F*(l - D)

a. m = 0, D = 0

Ml/2 = Fl

F = Mg/2

b. m = 0, D = l/2

Mgl/2 = Fl/2

F = Mg

c. m = 0, D = l

Mgl/2 = 0

hence no amount of force F will keep the system balanced

d. m = M, d = l/2, D = 0

Mgl/2 + Mgl/2 = Fl

F = Mg

e. m = M, d = l/2, D = l/2

Mgl/2 + Mgl/2 = Fl/2

F = 2Mg

f. m = M, d = l/2, D = l

no amount of force can stabilise the flap

g. d = l/2, D = 0

mgl/2 + Mgl/2 = F*l

F = (m + M)gl/2

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