You and a friend are supporting (with your brute strength) another65 kg person o

Question

You and a friend are supporting (with your brute strength) another65 kg person on top of a 3 kg, 1.2 m long board (assume uniform).The 65 kg person starts out in the middle of the board and you andyour friend are at the ends.
a. Which is easier for you – the 65 kg person moves 0.3 mtowards you, or you move 0.3 m towards the 65 kg person? Supportwith actual numbers.
b. If you can only exert 500 N, what is the maximum weight you andyour friend could support (while standing at the ends) when theweight is 0.7 m away from you. (Assume the board is durable enoughto not break.)

Explanation / Answer

a.let the mass of the two persons supporting the beam be m1and m2 let m1 be on the left end of the long board and m2 on theright end when m1 moves towards the 65 kg person then the net torqueacting on the system is reduced therefore we get net= m2 * g * d2 - m1 * g * d1 = g * (m2 * d2- m1 * d1) g = 9.8 m/s^2,d2 = (1.2/2) = 0.6 m and d1 = (0.6 - 0.3) m =0.3 m b.the net torque acting on the board is F1 * d1 + F2 * d2 = 0 or F2 = -(F1 * d1/d2) F1 = 500 N,d1 = 0.7 m and d2 = (1.2 - 0.7) m = 0.5 m

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