The 66 kg man's hands in Figure 9-56 are 36 cm apart. His CG is located 85% of the distance from his right hand toward his left. Find the force on each hand due to the ground.
To find the force on each hand, we first need to determine the position of the man's center of gravity (CG).
Given that the 66 kg man's hands are 36 cm apart, we can split the distance in half to find the position of his CG with respect to his hands. So, the distance from the right hand to the CG is 36 cm / 2 = 18 cm.
Next, we need to find the distance from the CG to the left hand. Since the CG is located 85% (or 0.85) of the total distance from the right hand to the left hand, we can calculate it as follows:
Distance from the right hand to the left hand = 36 cm
Distance from the right hand to the CG = 18 cm
Distance from the CG to the left hand = (36 cm - 18 cm) * 0.85 = 18 cm * 0.85 = 15.3 cm
Now that we know the distances, we can calculate the force on each hand due to the ground using the principle of equilibrium. The total force on the man's body must be zero, so the forces on his hands must balance out.
Let's denote the force on the right hand as FR and the force on the left hand as FL. Considering the torques around the CG, we can set up the following equation:
FR * 18 cm = FL * 15.3 cm
Since we need to solve for FR and FL separately, we can rearrange the equation to isolate FR:
FR = FL * (15.3 cm / 18 cm) = FL * 0.85
Given that the man's weight is 66 kg, the force exerted by his weight is given by:
Weight of the man = mass * gravity
Weight of the man = 66 kg * 9.8 m/s^2 = 646.8 N
Since the man's weight is distributed equally between his two hands, we can divide it by 2 to get the force exerted on each hand:
Force on each hand due to the weight of the man = 646.8 N / 2 = 323.4 N
Now, we can substitute this value into the equation for FR:
FR = 323.4 N * 0.85 = 275.49 N
Finally, we can find FL by rearranging the equation:
FL = FR / 0.85 = 275.49 N / 0.85 = 324.11 N
Therefore, the force on the right hand due to the ground is approximately 275.49 N, and the force on the left hand is approximately 324.11 N.