please explain and solve The plank (Fig. 11.8a) is a great way to strengthen abd
ID: 1732182 • Letter: P
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please explain and solve
The plank (Fig. 11.8a) is a great way to strengthen abdominal the distance from his toes to the middle of his forearms is 1.53 m. back, and shoulder muscles. You can also use this exercise posi How far from his toes is his center of gravity? tion to locate your center of gravity. Holding plank position with a scale under his toes and another under his forearms, one athlete sOLUTION measured that 66.0% of his weight was supported by his forearms and 34.0% by his toes. (That is, the total normal forces on his forearms and toes were 0.660w and 0.340w, respectively, where w is the athlete's weight.) He is 1.80 m tall, and in plank position IDENTIFY and SET UP: We can use the two conditions for equilib- rium, Es(11.6), for an athlete at rest. So both the net force and net torque on the athlete are zero. Figure 11.8b shows a free-body diagram, including x- and y-axes and our convention that coun- terclockwise torques are positive. of gravity, which is between the two supports (as it must be; see Section 11.2).Our target variable is the distance Legthe lever arm of the weight with respect to the toes T, so it is wise to take torques with respect to T. The torque due to the weight is negative (it tends to cause a clockwise rotation around T), and the torque due to the upward normal force at the forearms F is positive (it tends to cause a counterclockwise rotation around T) The weight w acts at the center 11.8 An athlete in plank position. EXECUTE: The first condition for equilibrium is satisfied (Fig. 11.8b) 2F 0 because there are no x-components and 2F, 0 because 0.340w 0.660w (w)0. We write the torque equation and solve for Lg (b) S eg 1.01 m = 0.340w 1.53 m EVALUATE: The center of gravity is slightly below our athlete's navel (as it is for most people) and closer to his forearms than to his toes, which is why his forearms support most of his weight. You can check our result by writing the torque equation about the forearms F. You'll find that his center of gravity is 0.52 m from his forearms, or53 m) (0.52 .0 m from his toes. C9 CgExplanation / Answer
balancing moment about the center of mass,
Net moment = (Lcg x nT x sin90) - ((1.53 - Lcg)(nF)(sin90)) = 0
0.340w Lcg = (1.53 - Lcg)(0.660w)
0.340 Lcg + 0.660Lcg = 1.53 x 0.660
Lcg = 1.01 m
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