Question

Tarzan is running with a horizontal velocity, along level ground. While running, he encounters a 2.21 m vine of negligible mass, the vine was hanging vertically from a tall tree limb and the end of the vine is directly level with his center of mass. Tarzan decides to grab the vine and swing which causes him to experience uniform circular motion. At the maximum height, Tarzan notices that the angle the vine makes with the vertical is 19 degrees. Tarzan mass is 65kg. Ignoring any elastic properties of the vine may have.a) Determine the magnitude of Tarzan's centripetal accelerationb) Determine the magnitude of the tension at the beginning of the swing

Answer 1

a)
`a_c = 1.09m/s^2`

b) T = 720.85N

Step-by-step explanation:

With a balance of energy from the lowest point to its maximum height:

`m*g*L(1-cos\theta)-1/2*m*V_o^2=0`

Solving for
`V_o^2`:

`V_o^2=2*g*L*(1-cos\theta)`

`V_o^2=2.408`

Centripetal acceleration is:

`a_c = V_o^2/L`

`a_c = 2.408/2.21`

`a_c = 1.09m/s^2`

To calculate the tension of the rope, we make a sum of forces:

`T - m*g = m*a_c`

Solving for T:

`T =m*(g+a_c)`

T = 720.85N