Question

Tarzan swings from a vine that is 15m long and has a tensile strength of 1 x 10^2 m. He grabbed it while running at 7m/s and he weighs 80kg. Will the vine break when he swings on it?

Answer 1

Answer on Question #48380, Physics, Mechanics | Kinematics | Dynamics

Tarzan swings from a vine that is 15m long and has a tensile strength of $1 \times 10^{\wedge}2$ N. He grabbed it while running at 7m/s and he weighs 80kg. Will the vine break when he swings on it?

Solution:

Tarzan, represented by a blue ball, is swinging from a 15 meter vine.

We also show Tarzan's weight $W$ , the force exerted on him by the tension of the vine $T$ , and the sum of these two forces $S$ .

$$\vec {S} = \vec {T} + \vec {W}$$ $$m a = T - m g$$

where $a$ is the centripetal acceleration, $a = \frac{v^2}{L}$ .

$$m (a + g) = m \left(\frac {v ^ {2}}{L} + g\right) = T$$

Thus,

$$T = 8 0 * \left(\frac {7 ^ {2}}{1 5} + 9. 8\right) = 1 0 4 5. 3 \mathrm {N}$$ $$T > 1 \cdot 1 0 ^ {2} \mathrm {N}$$

Thus, the vine will break when he swings on it.

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