Tarzan tries to cross a river by swinging from one bank to the other on a vine that is 11.6 m long. His speed at the bottom of the swing is 7.4 m/s. Tarzan does not know that the vine has a breaking strength of 1.0 ✕ 103 N. What is the largest mass that Tarzan can have and still make it safely across the river?
Never mind I got it!
To find the largest mass that Tarzan can have and still make it safely across the river, we need to consider the tension in the vine during the swing. When Tarzan is at the bottom of the swing, the tension in the vine should be equal to the breaking strength of the vine.
First, we need to find the tension in the vine at the bottom of the swing. The centripetal force experienced by Tarzan is equal to the tension in the vine:
Fc = Tension
The centripetal force can be given by:
Fc = (m * v^2) / r
Where:
m is the mass of Tarzan
v is the velocity of Tarzan at the bottom of the swing
r is the length of the vine
Rearranging the equation, we can solve for the mass m:
m = (Fc * r) / v^2
Now we can substitute the given values into the equation to find the largest mass:
Fc = 1.0 * 10^3 N (breaking strength of the vine)
r = 11.6 m (length of the vine)
v = 7.4 m/s (velocity at the bottom of the swing)
m = (1.0 * 10^3 N * 11.6 m) / (7.4 m/s)^2
Now we can calculate the final answer:
m = (11600 N * 11.6 m) / (54.76 m^2/s^2)
m = 2453 kg
Therefore, the largest mass that Tarzan can have and still make it safely across the river is 2453 kg.