3) Three children are trying to balance on a seesaw, which consists of a fulcrum

Question

3) Three children are trying to balance on a seesaw, which consists of a fulcrum rock, acting as a pivot at the center, and a very light board L = 3.78 m long, Two boys are already on either end. One has a mass of m1 = 48.0 kg, and the other a mass of m2 = 32.6 kg. How far from the center should the third boy, whose mass is m3 = 24.2 kg, place himself so as to balance the seesaw?

4) Calculate the mass m needed in order to suspend the leg Assume the leg (with cast) has a mass of 14.2 kg, and its CG is 34.2 cm from the hip joint; the sling is 72.0 cm from the hip joint

5) A rigid uniform horizontal plank of mass m1 = 91 kg and length L = 7.9 m is supported by two vertical strings as shown above. String A is attached at a distance of d = 1.6 m from the left end of the bar and is connected to the ceiling. String B is attached to the left end of the bar and is connected to the floor.An object of mass m2 = 1610 kg is supported by the crane at a distance x = 6.1 m from the left end of the bar.

Calculate the tension in string A. Calculate the tension in string B.

6) how far out on the diving board would a 59.4 kg diver have to be to exert a torque of 1480 m*N on the board, relative to the left support post?

Explanation / Answer

3)
Let the other mass be placed at a distance x from the pivot towards the lighter mass i.e. m2 ..

for balancing moment about the pivot... the moment due weight of m2 and m3 should balance the momnet due to weight m1

so... m1 * g*(3.78 /2 ) = m2 * g * ( 3.78 /2 ) + m3 * g * ( x )

48 * g * 1.89 = 32.6 * g * 1.89   + 24.2 * g * x

so... x = 1.20273

so m3 should be placed at a distance of 1.20273 m from the pivot towards m2 ..


4)
Hey for this quesition... it would have been good if you could include a figure as it is not clear.. still I am solving it based on some intution...

m_leg * distance from hip = m_required * distance from hip

so.. 14.2 * 34.2 = m * 72

so m_required = m = 6.745 kg


5) Let the tension in string B be T ..
The weight of the plank acts at the center i.e. at 7.9/2 = 3.95 m from B

so taking moment of all the forces about the point of th erod where A is connected..
the moment due to T should balance the moment due to the weight of 1610 kg and weight of mass of plank

so...
T * distance of B from A = 1610 * g * distance of point of hanging og mass from A
                                                + 91 * g * distacne of center from A

T * 1.6 = (1610 * 9.8 * ( 6.1 - 1.6 ) )+( 91 * 9.8 * ( 3.95 - 1.6) )

so tension in string B = T =45685.45625 N


6)
torque = weight * distance

so... 1480 = 59.4 * 9.8 * distanc
so distance = 2.54243 m

so the diver should be placed 2.54243 meter fotm the left of the post

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