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 due to the ground, we need to first determine the position of the man's center of gravity (CG) and then calculate the force exerted on each hand.
Step 1: Find the distance from the CG to each hand.
Given that the man's hands are 36 cm apart, and the CG is located 85% of the distance from his right hand toward his left, we can calculate the distances from the CG to each hand:
Distance from CG to right hand = 36 cm × 85% = 30.6 cm
Distance from CG to left hand = 36 cm - 30.6 cm = 5.4 cm
Step 2: Calculate the force on each hand due to the ground.
Since the force on each hand is directly proportional to the distance of the hand from the CG, we can use the formula:
Force = (mass of the person) × (distance from CG to each hand) / (total distance between the hands)
Given that the mass of the man is 66 kg, we can substitute the values into the formula:
Force on the right hand = (66 kg) × (30.6 cm) / (36 cm) = 55.5 kg · cm
Force on the left hand = (66 kg) × (5.4 cm) / (36 cm) = 9.9 kg · cm
Therefore, the force on the right hand due to the ground is 55.5 kg · cm, and the force on the left hand is 9.9 kg · cm.