Homework Question (Newton's Laws)

[sheri1987]

Homework Statement

A 12.0 kg monkey starts to climb a long rope to reach a banana located at a height of 7.00 m. The rope will snap if the tension exceeds 132 N. Calculate the least amount of time the monkey could take to reach the banana without breaking the rope.

Homework Equations

F =ma
x = Vot +1/2at2

The Attempt at a Solution

I know I need to use an equation to solve for t. I tried the two above first solving for the acceleration, then plugging that into solve for the time. What am I doing wrong? Thanks!

 

[Dick]

Hard to tell what you doing wrong since you didn't give us any details of what you did. If the monkey is heading up the rope with acceleration 'a', what's the tension in the rope? What's the biggest 'a' can be before the rope snaps?

 

[rootX]

according to the free body diagram, that acceleration is due to two forces,
ones if weight of the money(gravity) and other one due to the force app. by money (you need to find this a )..

 

[Dick]

The forces acting on the monkey are his weight downwards and the tension in the rope upwards. The monkey can't directly exert a force on him/herself. The resulting sum is the F in F=ma.

 

[sheri1987]

I plugged 132 N as the force and 12.0 kg in as the mass and solved for the acceleration..I got 11 m/s2. Then I plugged the 11 m/s2 into the x=Vot +1/2at2 and the 7.00 m as x, 0 for the inital velocity and solved for t. The answer isn't working out though?

 

[Dick]

You forgot the mg force downward didn't you? T-mg is the total force.