Max Speed Calculation for Tarzan's Vine Swing - AP Physics Problem

[AllAmericanGirl2004]

Hi I'm AllAmericanGirl2004,

I need some serious help in my AP Physics class. This last unit, on forces is nearly killing me. Maybe you guys can help me understand this. Here's a problem I'm stuck on...

Tarzan plans to cross a gorge by swinging in an arc from a hanging vine. If his arms are capable of exerting a force of 1600 N, what is the max speed he can tolerate at the lowest point of his swing? His mass is 80kg and the vine is 6.8 m long.

Now, it seems to me that the net force is 1600 N and since Tarzan's mass is 80kg, wouldn't you just say that using the F=ma equation that 1600=80a? But that seems way too easy...I don't know. HELP!

 

[thermodynamicaldude]

Tarzan is moving in an arc...that means that centripetal acceleration is involved...(since he's moving in a circular direction).

Thusly, there is a centripetal force acting on Tarzan (Fc = mv^2/R) and the graviational force as well (F = mg)...basically...work with that info...and also...try to draw a free body diagram as well.

 

[AllAmericanGirl2004]

Okay thanks...

K, so the Fc is the net force right? and what's the R again? R is the length of the vine? But wait, how do you incorparate both equations at once??

 

[Physics_wiz]

At the bottom, there are two forces acting on him--his weight and the centripetal force. The equation for weight is mg, the equation for centripetal force is (mv^2)/r. r is the radius of the circle that the arc is from. m is the mass, and g is gravity. The total force on him at the bottom of the arc would be (mv^2)/r+mg. Since m, g, and r are all constants, the only variable you're working with is v. See what the maximum velocity is that tarazan can handle (his arms can only handle 1600N).