Question

1. Bone has a Young’s modulus of about 1.8 × 10^10 Pa. Under compression, it can

withstand a stress of about 1.61 × 10^8 Pa before breaking. Assume that a femur (thigh bone) is 0.47 m long, and calculate the amount of compression
this bone can withstand before breaking.
Answer in units of mm.

2 (Pt 1/2). How much pressure is applied to the ground by a 68 kg man who is standing on square stilts that measure 0.04 m on each edge?
Answer in units of Pa.

3 (Pt 2/2). What is this pressure in pounds per square inch?
Answer in units of lb/in^2.

4 (Pt 1/2). In an 84 s interval, 578 hailstones strike a glass window of area 0.828 m^2 at an angle 32° to the window surface. Each hailstone has a mass of 5 g and speed of 11.7 m/s. If the collisions are elastic, find the average force on the window.
Answer in units of N.

5 (Pt 2/2). Find the pressure on the window.
Answer in units of N/m^2.

6. If a 1-megaton nuclear weapon is exploded at ground level, the peak overpressure (that is, the pressure increase above normal atmospheric pressure) will be 0.2 atm at a distance of 6 km. Atmospheric pressure is 1.013 × 10^5 Pa.
What force due to such an explosion will be exerted on the side of a house with dimensions 2.09 m × 30.9 m?
Answer in units of N.

7. Find the density of seawater at a depth where the pressure is 130 atm if the density at the surface is 1050 kg/m^3. Seawater has a bulk modulus of 2.3 × 109 N/m^2. Bulk modulus is defined to be (look at picture).
Answer in units of kg/m^3.

8. Calculate the depth in the ocean at which the pressure is three times atmospheric pressure. Atmospheric pressure is 1.013 × 10^5 Pa. The acceleration of gravity is 9.81 m/s^2 and the density of sea water is 1025 kg/m^3.
Answer in units of m.

Answer 1

1. Y =
`(P*L)/(Y)` = ((1.61 × 10⁸) × 0.47) ÷ 1.8 × 10¹⁰

Y = 4.20Ε17 mm

2. P = F/A

F = m×g = 68 ×9.8 = 666.4N

A = (2 · (0.04)² = 0.0032²

P = 666.4 ÷ 0.0032 = 208250 Pa

3. Psi = 208250 ÷ 6894.76

Psi = 30.20 lb/in²

4. Δp = 2 × mass × velocity

Δp = 2 × 0.005 × 11.7 × sin32 = 0.0620 kgm/s

Δp = 578 × 0.0620 = 35.83 kgm/s

F = Δp/Δt = 35.83 ÷ 84

F = 0.4266N

5. P = F/A = 0.4266 ÷ 0.828

P = 0.515244 N/m²

**(I'll add the last few later)**