1. A 455 g mass, hanging at rest on a spring, stretches the spring 22.4 cm beyond its relaxed position. What is the spring constant of that spring?

19.9 N/m

Explanation:

From the question,

Applying Hook's law

F = Ke Equation 1

Where F = Force on the spring, k = spring constant, e = extension

But the force on the spring is the weight of the mass

Therefore,

mg = ke Equation 2

Where m = mass. g = acceleration due to gravity

make e the subject of the equation

e = mg/e Equation 3

Given: m = 455 g = 0.455 kg, e = 22.4 cm = 0.224 m,

Constant: g = 9.8 m/s²

Substitute these values into equation 3

e = (0.455×9.8)/0.224

e = 19.9 N/m

emily ruth's annual premium is $1058.50

step-by-step explanation:

emily ruth is a female of 27 years age purchasing 20 year endowment insurance with face value $25000.

from the given table,

for females, the age of a male 3 years younger should be used.

so, we have to check for 24 year male for 20 year endowment.

it is 42.34 for every $1000 face value.

for a face value of $25000,

it is 25 * 42.34 = $1058.50

∴ emily ruth's annual premium is $1058.50