Answer:
37.04 %
Explanation:
Young modulus of the disk = stress / strain = F t/ AΔt
where t = thickness in meters = 0.5 cm = 0.5 / 100 = 0.005 m
Δt = the change in the thickness of the disk in meters
F = 95 × 9.8 ( mass × acceleration due to gravity) = 931 N
half of the weight of the man = 931 / 2 = 465.5
young modulus of the disk = 1.0 × 10⁶ N/m²
radius = diameter / 2 = 4 /2 = 2 cm = 2/100 = 0.02 m
Area of the disk = πr² = 3.142 × ( 0.02)²= 0.0012568 m²
1.0 × 10⁶ N/m² = ( 465.5 × 0.005) / ( 0.0012568 × Δt)
0.0012568 Δt = 465.5 × 0.005) / (1.0 × 10⁶) = 2.3275 × 10⁻⁶
Δt = 2.3275 × 10⁻⁶ / 0.0012568 = 0.001852 m
the fraction the disk was compress = 0.001852 / 0.005 × 100 = 37.04 %
