Question

The force (F) needed to stretch a spring by a distance x is

given by the equation F = k·x, where k is the spring
constant (measured in Newtons per centimeter, or N/cm).
If a 12 Newton force stretches a certain spring by 10 cm,
calculate each of the following. Round your answers to the
nearest tenth.
a. The spring constant. k =
N/cm
b. The force needed to stretch the spring by 7 cm. F =
N
c. The distance the spring would stretch with a 23 N force. x =
cm

Answer 1

(a) 1.2 N/cm

(b) 8.4 Newtons

(c) 19.2 cm

Step-by-step explanation:

Since the formula is already given as Force=K*x then
`K=\frac {F}{x}` and
`x=\frac {F}{K}`

(a)

Substituting F with 12 N and x with 10cm we obtain

`K=\frac {F}{x}=\frac {12}{10}=1.2 N/cm`

(b)

Using spring constant obtained in part (a) then K=0.12 N/cm and x is given as 7cm then

Force=k*x=1.2 N/cm*7 cm=8.4 Newtons

(c)

`x=\frac {F}{K}` and F is given as 23 N and using same spring constant

`x=\frac {23}{1.2}=19.2 cm`