Tarzan swinging on a rope -- find the acceleration

[isukatphysics69]

Homework Statement

Tarzan swings from a cliff at the end of a 20.0m vine that hangs from a high tree limb. Immediately after Tarzan steps off the cliff, the tension in the vine is 719N and makes an angle of 29.0deg with the vertical. Tarzan's weight is 822N.

What is the magnitude of Tarzan's acceleration immediately after he steps off the cliff?

Homework Equations

netforce = m*a

The Attempt at a Solution

netforce =m*a
netforcex = 719cos71
netforcey = 719sin71-822
netforce= sqrt((719cos71)^2+(719sin71-822)^2))
a = 273.88/822
a=0.3m/s^2not sure what i am doing wrong here! >=[

 

[Orodruin]

a = 273.88/822

Weight is not the same as mass.

In general, always write out and check your units in all steps. It will help you identify mistakes such as, in this case, getting a dimensionless acceleration.

 

[isukatphysics69]

Weight is not the same as mass.

In general, always write out and check your units in all steps. It will help you identify mistakes such as, in this case, getting a dimensionless acceleration.

i see i made a stupid mistake there i meant 273/83.87 now i am getting 3.2 and its still wrong

 

[Orodruin]

netforce= sqrt((719cos71)^2+(719sin71-822)^2))

What is the result of this computation?

 

[isukatphysics69]

What is the result of this computation?

273.8758934

 

[Orodruin]

273.8758934

I suggest you redo that math.

Edit: Also, again, units! The units here should be Newton. Otherwise it is not a force.

 

[isukatphysics69]

I suggest you redo that math.

Edit: Also, again, units! The units here should be Newton. Otherwise it is not a force.

I put it into the calculator and got the same thing, i have the calculator on degree mode do you have yours on radian?

 

[Orodruin]

I put it into the calculator and got the same thing, i have the calculator on degree mode do you have yours on radian?

What is 90-29?

 

[isukatphysics69]

What is 90-29?

omg i am so STUPID! >=[

 

[Orodruin]

So the correct solution is what? There is an easier way of solving this problem, but full solutions are not allowed until the OP shows that they have solved the problem so I cannot tell you until you show your full correct solution.

 

[isukatphysics69]

So the correct solution is what? There is an easier way of solving this problem, but full solutions are not allowed until the OP shows that they have solved the problem so I cannot tell you until you show your full correct solution.

netforce= sqrt((719cos61)^2+(719sin61-822)^2)) = 18.21643467

Edit: this is wrong also, there is something fundamental i am doing wrong here. i think i am supposed to be using v^2/R

 

[Orodruin]

netforce= sqrt((719cos71)^2+(719sin71-822)^2)) = 18.21643467

Edit: this is wrong also, there is something fundamental i am doing wrong here. i think i am supposed to be using v^2/R

First of all, that is still wrong and it still has 71 in it so it is unclear how you changed it. Second, just as he steps off the ledge, his velocity is zero and all acceleration is tangential. The radial acceleration (which is v^2/r) is zero.

 

[isukatphysics69]

First of all, that is still wrong and it still has 71 in it so it is unclear how you changed it. Second, just as he steps off the ledge, his velocity is zero and all acceleration is tangential. The radial acceleration (which is v^2/r) is zero.

Sorry i am so tired i will try again and come back in 10 minutes i am screwing up big time on this problem and in LIFE! BRB

 

[isukatphysics69]

I have no idea what i am doing wrong here whose going to be online tomorrow?? my school is closed again because of the storm and there's no tutoring and my stupid self needs help! >=[ i will get my phd in physics one day tarzan not going to stop me!

 

[Orodruin]

Your original idea is workable. You are just not putting numbers into your calculator correctly. Double check everything.

 

[isukatphysics69]

I FIGURED IT OUT ITS 4.75 M/S^2!

 

[isukatphysics69]

I FIGURED IT OUT ITS 4.75 M/S^2!

 

[isukatphysics69]

Now i am trying to find the angle of acceleration with the vine... i did tan^-1(-193/348) and got -29 degrees but marked wrong what am i doing wrong here

FIGURED IT OUT I WAS DOING ANGLE WITH X AXIS NOT VINE NOW I UNDERSTAND ITS -90 DEGREES I AM SO STUPID

 

[Orodruin]

What is -193 and 348? Consequently, what is the angle that you are computing?

 

[isukatphysics69]

What is -193 and 348? Consequently, what is the angle that you are computing?

I edit post bro see above now I'm working on another problem thank you tho

 

[Orodruin]

So here is the easier way of doing things.

Completely ignore the given forces, they are essentially useless for the solution to the problem. Since the vine has a fixed length, the motion must be along a circle and the vine takes up any force in the radial direction. This means that any force component in the radial direction will be canceled by the tension in the vine. Only the force component in the tangential direction remains and it is equal to the mass multiplied by the projection of the gravitational acceleration on the tangential direction. Since the acceleration is force/mass, the acceleration will just be the projection of the gravitational acceleration onto the tangential direction, i.e., $g\sin(29^\circ) = 4.75~{\rm m/s}^2$.

Since the vine is radial and the motion tangential, the angle between them must be a right angle.