Question on Conservation of Energy

[itsjustwhoiam]

1.

Tarzan and Jane, whose total mass is 115.0 kg, start their swing on a 5.0 m long vine when the vine is at an angle of 30.0° with the horizontal. At the bottom of the arc, Jane, whose mass is 50.0 kg, releases the vine. What is the maximum height at which Tarzan can land on a branch after his swing continues? (Hint: Treat Tarzan's and Jane's energies as separate quantities.)

Relevant equations:
1/2mv^2
mgh
sin, cos

I know that after she jumps, the energy is the same (conserved)
but how do i solve for height? The mass is less and that got me confused since gravity affects the height.

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2.

An 85.0 N box of clothes is pulled 17.0 m up a 30.0° ramp by a force of 115 N that points along the ramp. If the coefficient of kinetic friction between the box and ramp is 0.22, calculate the change in the box's kinetic energy.

KEi + PEi = KEf + PEf + Wfnc
1/mv^2
mgh
sin, cos

I started this pretty well, but here is what happened:

I calculated the components of the incline and got the parallel force and the perpendicular force. So from that i got the Normal force and then i used Fn * u to get Ffr and i multiplied that by 17, to get Wfnc.
but the problem is what i have to do with the net force, since there is 115 N-ffr-parallel force

and would PEi and KEf be zero? are we supposed to assume that?

 

[jscushman]

Tarzan and Jane, whose total mass is 115.0 kg, start their swing on a 5.0 m long vine when the vine is at an angle of 30.0° with the horizontal. At the bottom of the arc, Jane, whose mass is 50.0 kg, releases the vine. What is the maximum height at which Tarzan can land on a branch after his swing continues? (Hint: Treat Tarzan's and Jane's energies as separate quantities.)

All you need is the fact that the initial energy is going to equal the final energy.

The initial energy is the initial potential energies of both Tarzan and Jane. The final energy is the energy that Jane has when she let's go of the vine plus the energy that Tarzan is going to have after he swings alone.

The initial energy is mgh=(115 kg)(9.8 m/s^2)(5 m-5 m sin30˚)=2817.5 J
(1225 J from Jane's 50 kg and 1592.5 J from Tarzan's 65 kg)

When Jane let's go of the vine, all her energy will be kinetic, she will take her 1225 J from the total energy, and Tarzan will have 1592.5 J left for his swing

This will get him 1592.5 J=(65 kg)(9.8 m/s^2)(h)
h=2.5 m

Notice that this is the same as the initial height: Jane adds potential energy and the beginning but takes it away when she releases the vine, meaning for Tarzan, she could have just as well not been there.

 

[itsjustwhoiam]

thank you for explaining it clearly

BUT

what/why is the (5m-5m sin30)?

heres where i got lost:

115 * 9.8 * [sin(30)*5] = 563.5

but you got 2817.5, which is 5x greater?

why the extra 5*?

 

[itsjustwhoiam]

ohhhh
i see know
you did them separate as:

65*9.8*2.5 = 1592.5

and

50*9.8*2.5 = 1225

wow! thank you very much

 

[itsjustwhoiam]

wait am i right? or did you start with the total and how did you do that (why the 5 times)?