The distance a coiled spring stretches varies directly with the amount of weight hanging on the spring. If a spring stretches 2 cm when a 30 gram weight is hung from it, how far will it stretch when a 75 gram weight is hung from the spring?

5 cm

Step-by-step explanation:

The distance a coiled spring stretches varies directly with the amount of weight hanging on the spring.

Distance = D

Weight = W

Hence:

D ∝ W

D = kW

Where k is constant of proportionality

Step 1

We solve for k

If a spring stretches 2 cm when a 30 gram weight is hung from it.

2 = 30k

k = 2/30

k = 1/15

Step 2

how far will it stretch when a 75 gram weight is hung from the spring?

D = kW

We are solving for D

k = 1/15

D = 1/15 × 75

D = 5 cm

The spring would stretch 5cm with a weight of 75 gram.

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