If he leans slightly farther back (increasing the angle between his body and the vertical) but remains stationary in this new position, which of the following statements is true? Assume that the rope remains horizontal.

(a) The difference between T₁ and T₂ will increase, balancing the increased torque about his feet that his weight produces when he leans farther back;

(b) The difference between T₁ and T₂ will decrease, balancing the increased torque about his feet that his weight produces when he leans farther back;

(c) Neither T₁ nor T₂ will change, because no other forces are changing;

(d) Both T₁ and T₂ will change, but the difference between them will remain the same.

In a study of the biomechanics of the tug-of-war, a 2.0-m-tall, 80.0-kg competitor in the middle of the line is considered to be a rigid body leaning back at an angle of 30.0^o to the vertical. The competitor is pulling on a rope that is held horizontal a distance of 1.5 m from his feet (as measured along the line of the body). At the moment shown in the figure, the man is stationary and the tension in the rope in front of him is T₁ = 1160 N. Since there is friction between the rope and his hands, the tension in the rope behind him, T₂, is not equal to T₁. His center of mass is halfway between his feet and the top of his head. The coefficient of static friction between his feet and the ground is 0.65.

Transcribed Image Text:

Side view. T2 1.5m 30°