Question

While unrealistic, we will examine the forces on a leg when one falls from a height by approximating the leg as a uniform cylinder of bone with a diameter of 2.3 cm and ignoring any shear forces. Human bone can be compressed with approximately 1.7 × 108 N/m2 before breaking. A man with a mass of 80 kgfalls from a height of 6 m. Assume his acceleration once he hits the ground is constant. For these calculations, g = 10 m/s2.

What is his speed just before he hits the ground?
What is his speed just before he hits the ground?
a. 880 m/s
b. 11 m/s
c.120 m/s
d.7.7 m/s

Answer 1

The correct answer is b 11 m/s

Step-by-step explanation:

To solve this problem we can use mechanical energy. Let's write the energy at two points: initial at the highest point and end at the lowest point

Initial

Em₀ = U

Em₀ = m g y.

Final

`Em_(f)` = K

`Em_(f)` = ½ mv2

How mechanical energy is conserved because there is no friction

Em₀ =
`Em_(f)`

m g y = ½ m v²

v = √ 2 g y

Let's calculate

v = √( 2 10 6)

v = 11 m / s

The correct answer is b 11 m/s