Question

Lab 8: Muscles, Torque and T-Rex 8.1 Purpose: Evolutionary biologists, ecologists, and paleontologists study the development, abundance and diversity of living organisms. One particular creature which has captivated the interest of both scientists and non-scientists is the dinosaurs. Through reconstruction of bones, studying fossils, and other forensic techniques, these animals have undergone numerous studies which have given clues as to their physical and social characteristics. Even with all this research, there remain many unanswered questions In this lab, you will use physics and biomechanical arguments to try to answer one such mystery: What were the front arms of the Tyrannosaunus Rex used for? 8.2: Background The reputation of the Tyrannosaurs Rex is that of a fierce, dominant creature which ruled the land during the Jurassic era. It is one of the largest carnivorous dinosaurs to ever live, standing at 13 feet tall, 40 feet long, and weighting as much as 9 tons. It had the strongest bite of any land animal that ever lived, capable of exerting forces of up to 57,000 N (which is roughly the force you would feel if a medium size elephant sat on you). As ferocious as this creature is, scientists are forced to speculate why it has such diminutive arms. Since the arms of the T- Rex are too short to reach its mouth, what were they used for? There are several hypotheses as to the purpose and function of the small arms of the T-Rex, These include I. In 1970, British paleontologist Bamey Newman suggested that the small arms braced the beast's body as it stood up. 2. Lipkin and Carpenter suggested that they were used to hold onto struggling prey until a final lethal bite is applied. 3. Others, such as G.S. Paul, have suggested that the small limbs are vestigial (degenerated organs that have lost their use). In this lab you will use the knowledge of forces and torques to determine if these options are plausible.

Answer 1

1. As mentioned in 8.3.2. the body will be at rotational equlibrium if and only if the sum of external torques acting on it is zero.

Thus if torque on left arm is $G_{1}$ and that of right arm is $G_{2}$ then equlibrium occurs when

$G_{1}+ G_{2}=0\Rightarrow G_{1}= -G_{2}.$ Tjus they are of equal magnitude but in opposite direction.Option (c)

2.From question No. 1 it is clear that in magnitude $G_{1}= G_{2}.$Now let $G_{1}= G_{2}=G$ . Now if "r" be the distance from pivot we have:

$G=rFsin{90^{\circ}}\Rightarrow F=G/r$ Thus "F" decreases when distance from the pivot increases.Option (c)

5. $a=r\alpha$.Since $\alpha$ is connstant we have $a\propto r$.Thus "a" increases when "r" increases and decreases when "r" decreases.So option (a) is correct.