Question

Tarzan swings from a vine. When he is at the bottom of his swing, as shown in Figure 5.63, which is larger in magnitude: the force by the Earth on Tarzan, the force by the vine (a tension force) on Tarzan, or neither (same magnitude)? Explain how you know this.

Short answer

The vine's tension force is greater than the gravitational force.

Step-by-step solution

Definition of the tension force

Tension force is the force produced when a load is applied in a directed away from one or more ends of a material, usually to the cross-section of the material. A tension force is also referred to as a "pulling" force.

Representation of the diagram

As the Tarzan swings, the net force acting on him at the bottom of the swing acts in the direction of the rate of change of momentum, which is upward.

Tarzan's veins exert a stronger upward force than their veins exert a downward force.

Tarzan must use this upward force to drive himself upward.

The free body diagram for the given situation is shown in the below figure,

here $mg$is the gravitation force acting on the person, $T$is the tension force offered

by vine, and $F_c$is the centripetal force.

Applying the Newtons second law

Write the net force acting on the Tarzan, according to Newton's second law of motion.

$F_c=T-mg$

Reorganize the above equation to obtain $T$.

$T=F_c+mg$

Thus, the vine's tension force is greater than the gravitational force.