Question

The force required to stretch a spring beyond its natural length is proportional to how far the spring is being stretch.If a force of 8 pounds stretchs a spring 16 centimeters beyond its natural length,what force,in pounds,is need to stretch this spring 42 centimeter beyond its natural length.
RATIO PROBLEM
A) 15 B)21 C)31 D)37 E)42

Answer 1

f = k e
where f = force, k = constant e = extension( difference in length from initial)

8 = k *16
k = 1/2

f = k * 42
f = 1/2 * 42
f = 21pound

Answer 2

explain please

Answer 3

yes sure

Answer 4

a spring always follows a constant extension that, is for each amount of force supplied, the spring extends by a constant amount, say when u give a force of 1 N it extends by 2cm, then if u give a force of 2N it extends by 4 cm and so on, so we can set up a linear equation where force and extension can be used to find the constant

Force = Constant * Extension
(now we know the force as well as the extension, so we can substitute and find the constant)
then we can use that constant to find the force for a given extension)

lets see how it works

8 pounds = constant * 16 cm(extension)
constant = 1/2 ( this is the way it extends )

now use this constant to find force for 42 cm extension

F = 1/2 * 42
F = 21 pounds