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A fish of weight 108 N is attached to the end of a dangling spring, stretching the spring by 14.0 cm. What is the mass of a fish that would stretch the spring by 23.0 cm?

a. 2.5 kg
b. 3.0 kg
c. 3.5 kg
d. 4.0 kg

User Jeff Nyak
by
8.5k points

1 Answer

3 votes

Final answer:

To find the mass of a fish that would stretch the spring by 23.0 cm, we can use Hooke's Law. The mass is approximately 18.41 kg.

Step-by-step explanation:

To find the mass of a fish that would stretch the spring by 23.0 cm, we can use Hooke's Law, which states that the force exerted by a spring is proportional to the displacement of the spring from its equilibrium position.

The formula for Hooke's Law is F = kx, where F is the force, k is the spring constant, and x is the displacement.

Given that the weight of the fish is 108 N and it stretches the spring by 14.0 cm, we can determine the spring constant by dividing the weight by the displacement: k = F / x.

So, the spring constant is 108 N / 14.0 cm = 7.71 N/cm.

To find the mass of a fish that would stretch the spring by 23.0 cm, we can rearrange the formula and solve for the mass:

F = kx = mg

m = F / g

Using the given equation and substituting the values, we get:

m = (7.71 N/cm)(23.0 cm) / 9.8 m/s^2 = 18.41 kg

Therefore, the mass of a fish that would stretch the spring by 23.0 cm is approximately 18.41 kg.

User Suneel
by
8.0k points
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