To calculate the change in length of the upper leg bone (the femur), we can use the formula for the strain in a uniform rod:

strain = (force * length) / (Young's modulus * area)

First, let's calculate the area of the femur using the given radius:

area = π * radius^2

area = 3.14 * (0.02 m)^2

area = 0.001256 m^2

Next, let's calculate the force exerted on the femur by the man's weight:

force = mass * gravity

force = 62.0 kg * 9.8 m/s^2

force = 607.6 N

Now, we can substitute the values into the strain formula:

strain = (607.6 N * 0.40 m) / (9x10^9 N/m^2 * 0.001256 m^2)

strain = 0.193

The strain represents the fractional change in length of the femur. To calculate the change in length, we can multiply the strain by the original length of the femur:

change in length = strain * original length

change in length = 0.193 * 0.40 m

change in length = 0.0772 m

Therefore, the change in length of the upper leg bone (the femur) when a 70.0 kg man supports 62.0 kg of his mass on it is approximately 0.0772 meters.

Question

To calculate the change in length of the upper leg bone (the femur), we can use the formula for the strain in a uniform rod:

strain = (force * length) / (Young's modulus * area)

First, let's calculate the area of the femur using the given radius:

area = π * radius^2

area = 3.14 * (0.02 m)^2

area = 0.001256 m^2

Next, let's calculate the force exerted on the femur by the man's weight:

force = mass * gravity

force = 62.0 kg * 9.8 m/s^2

force = 607.6 N

Now, we can substitute the values into the strain formula:

strain = (607.6 N * 0.40 m) / (9x10^9 N/m^2 * 0.001256 m^2)

strain = 0.193

The strain represents the fractional change in length of the femur. To calculate the change in length, we can multiply the strain by the original length of the femur:

change in length = strain * original length

change in length = 0.193 * 0.40 m

change in length = 0.0772 m

Therefore, the change in length of the upper leg bone (the femur) when a 70.0 kg man supports 62.0 kg of his mass on it is approximately 0.0772 meters.

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