Algebra word problem

Question

When we say y is directly proportional to x , we write y = kx where k is some constant. Suppose we have a spring and we stretch it a distance of x beyond its natural length. Hooke's law says that the force required to hold the spring x units beyond its natural length is directly proportional to x

 

(a) A force of 40N is required to hold a spring that has been stretched from its natural length of 10cm to 15cm . Denote the force by y. Find an equation for y.

 

(b) Find the force needed to hold a spring from its natural length to 18cm.

Answer 1

(a)

 

y = kx ⇒

 

k = y/x

 

x = (15 - 10) cm = 5 cm

 

k = (40 N)/(5 cm) = (40 N)/(0.05 m) = 800 N/m

 

y = (800 N/m) x, with x in meters

 

(b)

 

y = kx = (800 N/m)(18 cm) = (800 N/m)(0.18 m) = 144 N