Tarzan, who has a mass of 85.0kg, is going to cross a gorge by swinging in an arc from a 4.0m long hanging vine. If his arms are capable of exerting a force of 1500N on the rope, what is the maximum speed he can tolerate at the tolerate at the lowest point of his swing?
Remember that he has to support his own weight in addition to the centripetal force at the lowest point:
mv²/r + mg = 1500N
Solve for v.
Uhub
To find the maximum speed Tarzan can tolerate at the lowest point of his swing, we need to consider the relationship between centripetal force, gravitational force, and tension in the rope.
The centripetal force is the force required to keep Tarzan moving in a circular path. It is given by the equation:
Fcentripetal = m * v^2 / r
Where:
Fcentripetal is the centripetal force.
m is Tarzan's mass (85.0 kg).
v is the velocity (speed) at the lowest point of the swing.
r is the radius of the swing, which is equal to the length of the hanging vine (4.0 m).
In this case, the tension in the rope is equal to the centripetal force since Tarzan's arms exert a force of 1500 N on the rope.
Tension = Fcentripetal = m * v^2 / r
Now, we can rearrange the equation to solve for v:
v^2 = Tension * r / m
v = √(Tension * r / m)
Plugging in the given values:
Tension = 1500 N
r = 4.0 m
m = 85.0 kg
v = √(1500 N * 4.0 m / 85.0 kg)
Now we can calculate the maximum speed Tarzan can tolerate at the lowest point of his swing.