Question

hookes law states that the distance d that a spring is stretched by a hanging object varies directly as the mass m of the object. if the distance is 58 cm when the mass is 3 kg, what is the distance when the mass is 5 kg?
the distance is □ cm.
(type an integer or a simplified fraction)

Explanation:

Step1: Determine the relationship

Since \(d\) varies directly as \(m\), the equation is \(d = km\) (where \(k\) is the constant of proportionality). When \(d = 58\) cm and \(m=3\) kg, we substitute into the equation: \(58=k\times3\), so \(k=\frac{58}{3}\).

Step2: Find \(d\) when \(m = 5\)

Now use \(k=\frac{58}{3}\) and \(m = 5\) in \(d=km\). Then \(d=\frac{58}{3}\times5=\frac{290}{3}\approx96.67\)

Answer:

\(\frac{290}{3}\)