Tarzan (m = 75 kg) tries to cross a river by swinging from a 10.0 m long vine. His speed at the bottom of the swing, just as he clears the water, is 8.0 m/s. What is the total force Tarzan excerts on the vine?
N
on Tarzan equal to M (g + a), where a is the centripetal acceleration, V^2/R.
Tarzan exerts the same force on the vine, in the opposite direction.
To find the total force Tarzan exerts on the vine, we need to consider the forces acting on him during the swing.
First, let's find the gravitational force acting on Tarzan, which is given by the equation:
F_gravity = m * g
where m is the mass of Tarzan and g is the acceleration due to gravity (approximately 9.8 m/s^2).
F_gravity = 75 kg * 9.8 m/s^2
F_gravity = 735 N (rounded to the nearest whole number)
Next, let's consider the tension in the vine. At the bottom of the swing, just as Tarzan clears the water, the tension force in the vine provides the necessary centripetal force to keep him moving in a circular path.
The centripetal force is given by the equation:
F_centripetal = m * v^2 / r
where m is the mass of Tarzan, v is his speed at the bottom of the swing, and r is the radius of the circular path (which is equal to the length of the vine).
F_centripetal = 75 kg * (8.0 m/s)^2 / 10.0 m
F_centripetal = 480 N
Therefore, the total force Tarzan exerts on the vine is the sum of the gravitational force and the centripetal force:
Total force = F_gravity + F_centripetal
Total force = 735 N + 480 N
Total force = 1215 N
So, Tarzan exerts a total force of 1215 N on the vine.