A 76-kg person is rappelling off a rock cliff and at one point in time has a velocity of -4.7 m/s and an acceleration of -0.89 m/s².What is the tension in the rope? A)360 N B)680 N C)740 N D)810 N

Question

Quizplus · Accepted Answer

We can use Newton's second law (F=ma) to solve for the tension in the rope. In this case, the person is in equilibrium (not moving up or down), so the weight force and the tension force must balance each other out. Thus, the tension force is equal to the person's weight force which is (76 kg)(9.81 m/s^2)=746.56 N. 
Next, we can use the given velocity and acceleration to solve for another force acting on the person, which is the force due to air resistance. This force is given by:
F = ma (for the vertical direction)
F = (76 kg)(-0.89 m/s^2) = -67.64 N
We can then use the formula for net force to find the tension:
Net force = tension force - force due to air resistance
- 67.64 N = T - 746.56 N
T = 746.56 N - (-67.64 N) = 814.2 N
Rounding to the nearest 10 N, the tension in the rope is 680 N (choice B).

A 76-Kg Person Is Rappelling Off a Rock Cliff and at One