Rope, Pulleys. and Lots of Tension

[kazimo]

Rope, Pulleys... and Lots of Tension!

hey,

For the following problem a picture is really needed so I tried drawing one on Paint and uploading a bitmap file ut it said that it was too large...

A 7 kg monkey climbs up a massless rope that runs over a frictionless tree limb and back down to a 20 kg package on the ground.

(a) What is the magnitude of the least acceleration the monkey must have in order to lift the package off the ground?

Assume that after the package has been lifted, the monkey stops its climb and holds onto the rope.
(b) What is the monkey's acceleration?

(c) What is the tension in the rope?
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What I did was use the Equation Force = Mass * acceleration.

Using tension as the force the equation for the monkeys side became

Tension= Mass*(acceleration of gravity + acceleration of monkey)

My answer for (a) was 18.2 m/s^2
(b) was 3.43 m/s^2
(c) I couldn't answer it...

Please help me.... I have spent already 4 hours on this single problem already.

Kazim

 

[Doc Al]

My answer for (a) was 18.2 m/s^2

Correct.

(b) was 3.43 m/s^2

How did you get this?

(c) I couldn't answer it...

If you know the monkey's acceleration, then you should be able to find the tension in the rope that will produce that acceleration.

 

[M98Ranger]

,

Great job on using the correct equation for this problem! Your answers for (a) and (b) are correct. To find the tension in the rope, you can use the equation F=ma again, but this time for the package. The package is not accelerating, so the only force acting on it is gravity, which is equal to its weight, mg. Therefore, the tension in the rope is equal to the weight of the package, which is 20 kg multiplied by the acceleration of gravity, 9.8 m/s^2. This gives a tension of 196 N.

Keep up the good work and don't hesitate to reach out for help if you get stuck on a problem. It's always better to spend a little extra time to fully understand a concept than to rush through and potentially make mistakes. Good luck!