Suppose that 2 J of work is needed to stretch a spring from its natural length of 32 cm to a length of 46 cm. (a) How much work (in J) is needed to stretch the spring from 37 cm to 41 cm

the work required is 0.163 J

Explanation:

Given;

Energy applied to the spring, E = 2 J

initial length of the spring, x₀ = 32 cm

final length of the spring, x₁ = 46 cm

Extension of the spring, Δx = x₁ - x₀ = 46 cm - 32 cm = 14 cm = 0.14 m

The spring constant is calculated as follows;

E = ¹/₂kΔx²

The extension of the spring when it is stretched from 37 cm + 41 cm:

Δx =  41 cm - 37 cm = 4 cm = 0.04 m

The work required:

W = ¹/₂kΔx²

W = ¹/₂ x (204.1) x (0.04)²

W = 0.163 J

Therefore, the work required is 0.163 J

d₁ = displacement of tern from arctic to antarctic = 11000 miles

d₂ = displacement of tern from antarctic to arctic =   - 11000 miles

d = total displacement for the journey

total displacement for the journey is given as

d = d₁ + d₂

d = 11000 + (-11000)

d = 0 miles

t₁ = time of travel from arctic to antarctic = 3 months = 3 x 30 days = 90 days

t₂ = time of travel from antarctic to arctic = 3 months = 3 x 30 days = 90 days

t = total time of travel

total time of travel is given as

t = t₁ + t₂

t = 90 + 90

t = 180 days

average velocity is given as

average velocity = total displacement/ total time

v = d/t

v = 0/180

v = 0 miles/day

the right answer is 0.3 meters per second