How Does Tarzan Accelerate Towards the Cliff in a Frictionless Scenario?

[Tensaiga]

Hello, i can't seem to figure this out...i need some help.

Tarzan (mass 100kg) holds one end of an ideal vine (infinitely strong, completely flexible, but having zero mass). The vine runs horizontally to the edge of a cliff, then vertically to where Jane (mass 50kg) is hanging on, above a river. A sudden sleet storm has removed all friction, assuming that Tarzan hangs on, what is his accerleration towards the end of the cliff?

umm, i have no thoughts on this one, how can i solve this without knowing any other variables expect their masses??

Thanks

 

[Doc Al]

Apply Newton's 2nd law to both Tarzan and Jane. You'll get two equations, which you can solve together to find the acceleration.

Hint: Since they are connected by a rope, Tarzan's horizontal acceleration will equal Jane's vertical acceleration.

 

[Tensaiga]

HUH?? sorry, i don't get it...but isn't Jane attached to the cliff? i mean she's hanging on the edge of the cliff? Isn't she at rest?

 

[nrqed]

HUH?? sorry, i don't get it...but isn't Jane attached to the cliff? i mean she's hanging on the edge of the cliff? Isn't she at rest?

I think you misunderstood the question. She is only holding to the vine. And she is accelerating (in fact, the magnitude of her acceleration is the same as the magnitude of the acceleration of Tarzan). Do as Doc Al suggested: set up free body diagrams for Tarzan and Jane and then solve (actually, it's possible here to combine the two in a single equation and do everything in one step but I think it hides a bit the physics.)

So set up a FBD for Tarzan, one for Jane, identify the forces, setp up Newton's second law, see how the acceleration of Tarzan is related to the acceleration of Jane and you will have two eqs for two unknowns (being the tension in the rope and the acceleration).

 

[Tensaiga]

umm, sorry i can't even figure out how to draw the FBD... how are they connected ? Tarzan is holding the vine, and so is Jane? then why did he had to run horizontally? I'm lost...

 

[3trQN]

Think Tug-o-War, Tarzan-----CliffEdge\
                                     |
                                     |
                                     |
                                     |
                                     |
                                   Jane

                            ~~~~River~~~~

 

[Astronuc]

HUH?? sorry, i don't get it...but isn't Jane attached to the cliff? i mean she's hanging on the edge of the cliff? Isn't she at rest?

Gravity is pulling Jane (50 kg) down. The tension in the rope simply couples the force and mass of Jane (50 kg) to Tarzan (100 kg).

So what is the force acting on Jane? Think of weight.

What mass is being accelerated by the force on Jane?

Another way to look at it - Tarzan's mass is resisting the acceleration of Jane. Also since the two are coupled, Jane and Tarzan must be accelerating at the same rate, although Jane is accelerating downward and Tarzan is accelerating horizontally.

 

[Tensaiga]

ohhhh i get it thank you very much with that diagram.
the tensional force is the force pulling down Tarzan, thus the two equations are:

a = T/m and a = (mg-T)/m

plug in the variables:
T/100 = (50*98-T)/50
T = 326.67N

Then acceleration must be 3.26m/s^2

Thank YOU ALL