Spring #1 has spring constant 61.0 n/m. spring #2 has an unknown spring constant, but when connected in series with spring #1, the connected springs have an effective spring constant of 20.0 n/m. what is the spring constant for spring #2?

29.79 N/m

Explanation:

A spring connected in series behaves like a capacitor connected in series.

Note: Spring and capacitor are alike because they both store energy, While the former store mechanical energy, the later store electrical energy.

From the above, the effective spring connected in series is given by the formula below

1/Kt = 1/K1 + 1/K2 Equation 1

Where Kt = effective spring constant, K1 = spring constant of spring 1, K2 = spring constant of spring 2

Making K2 the subject of the equation,

K2 = KtK1/(K1-Kt) Equation 2

Given: K1 = 61 N/m, Kt = 20 N/m.

Substitute into equation 2

K2 = (61×20)/(61-20)

K2 = 1220/41

K2 = 29.76 N/m.

Hence the spring constant in the second spring = 29.79 N/m

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