The distance a spring stretches varies directly as the amount of weight that is hanging on it. A weight of 2.5 pounds stretches a spring 18 inches. Find the stretch of the spring when a weight of 6.4 pounds is hanging on it.
we use the equation y = kx
y = 18, x = 2.5
18 = k2.5
k = 7.2
x = 6.4
y = 7.2*6.4
y = 46.08
hope this help
Answer:
The stretch of the spring is 46.08 inches.
Explanation:
Given that,
Weight = 2.5 pounds
Stretches a spring = 18 inches
new weight = 6.4
We need to calculate the stretch of the spring
let stretch of the spring is x .
Using formula of restoring force
\(F=-kx\)
For first weight,
\(2.5=k\times18\)....(I)
For another weight,
\(6.4=k\times x\)....(II)
Ratio of equation (I) and (II)
\(\dfrac{2.5}{6.4}=\dfrac{18}{x}\)
\(x=\dfrac{18\times6.4}{2.5}\)
\(x = 46.08\ inches\)
Hence, The stretch of the spring is 46.08 inches.