Assume L1 = 0.860 m and L2 = 0.437 m. Calculate the normal force exerted by the floor on each hand, assuming that the person holds this position. Assume the force on the left hand is the same as the force on the right hand.

To calculate the normal force exerted by the floor on each hand, we can use the concept of torque equilibrium.

First, let's denote the mass of the person as m and the acceleration due to gravity as g (approximately 9.8 m/s^2).

Since the person holds the position without any vertical acceleration, the sum of torques acting on the person must be zero.

The torques in this case are the weight (mg) acting at the center of mass (which is at the midpoint between the two hands) and the normal forces (N1 and N2) acting at the hands. The torque due to weight is counteracted by the torques due to the normal forces.

The torque due to weight at the center of mass is given by τ = mg * (L1 + L2)/2.

The torque due to the normal forces at each hand is given by τ = N1 * L1 - N2 * L2.

Setting these two torques equal to each other, we have:

mg * (L1 + L2)/2 = N1 * L1 - N2 * L2

Since we're assuming the force on the left hand is the same as the force on the right hand, we have N1 = N2.

Substituting this into the equation, we get:

mg * (L1 + L2)/2 = N1 * L1 - N1 * L2

Dividing both sides by N1, we have:

mg * (L1 + L2)/2N1 = L1 - L2

Simplifying the equation, we get:

2mg * (L1 + L2) = (L1 - L2) * 2N1

Finally, solving for N1, we have:

N1 = mg * (L1 + L2) / (L1 - L2)

Plugging in the given values, we have

N1 = m * 9.8 * (0.860 + 0.437) / (0.860 - 0.437)

Now, you can calculate the normal force N1 by substituting the given values for m, L1, and L2 into the equation.

To calculate the normal force exerted by the floor on each hand, we need to consider the equilibrium of forces.

The person is holding a position where the left and right hands are at different heights. The forces acting on each hand include the weight of the person and the normal force exerted by the floor.

Let's break down the steps to find the normal force exerted by the floor on each hand:

Step 1: Calculate the weight of the person
The weight of the person is given by the formula:
Weight = mass × gravity

Step 2: Divide the weight evenly between the two hands
Since it is assumed that the force on the left hand is the same as the force on the right hand, we divide the weight by 2.

Step 3: Calculate the vertical force exerted by each hand
The vertical force exerted by each hand is equal to the weight of the person divided by 2.

Now, let's apply these steps to the given problem:

Given:
L1 = 0.860 m (height of the left hand)
L2 = 0.437 m (height of the right hand)

Step 1: Calculate the weight of the person
The mass of the person is not given in the problem, so we cannot calculate the weight directly. We would need the mass to find the weight using the formula Weight = mass × gravity. If you have the mass of the person, you can substitute it into the formula.

Step 2: Divide the weight evenly between the two hands
Since we don't have the weight, we can't divide it evenly. So, we cannot proceed further with the calculation.