Question

40. A 3-meter long board weighing 50 N extends out over the edge of a table, with 40% of the

    board’s length off the table. How far beyond the table edge can a 25-N cat walk before the board begins to tilt?

    1. 0.2 m

    2. 0.4 m

    3. 0.6 m

    4. 0.8 m

    5. None of the above.

Answer 1

By torque balance on system about edge of table:

net = 0

Wc*d + Wh*L1 - Wt*L2 = 0

here, Wc = weight of cat = 25 N

Wh = weight of board hanging from rdge = 40% of 50 N = 0.40*50 = 20 N

Wt = weight of boad on the table = 60% of 50 N = 0.60*50 = 30 N

d = distance of cat from edge of table = ??

L1 = center of gravity of portion hanging from edge = 0.40*3/2 = 0.6 m

L2 = center of gravity of portion on the table from edge = 0.60*3/2 = 0.9 m

So,

d = (Wt*L2 - Wh*L1)/(Wc)

d = (30*0.9 - 20*0.6)/25

d = 0.6 m

So, correct option is C.

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