Question

answer plzzzzzz a monkey is accelerating down a string whose breaking strength is two third of his weight. the minimum acceleration of the monkey should be

Answer 1

The forces on the monkey sum to Fnet in the following 
Fnet = m*a 
Fnet is the sum of the upward tension in the string and the downward force of his weight. His weight is mg, so the max tension in the string is (2/3)*mg. So 
Fnet = (2/3)*mg - mg = -(1/3)*mg 

So, ma = -(1/3)*mg 
Cancel the m, and you have theOK, thatminus sign is a problem. The positive direction could be chosen to be up or down. If I had chosen differently, the acceleration would have come out 1/3 g.

Answer 2

T=w-F
T=mg-ma
T=m(g-a)
To avoid breaking T can be no more than 2/3mg of monkey's weight
T<=2/3mg
Substitute the value of T
m(g-a)=2/3mg
g-a=2/3g
Solve for a
a=1/3g