A spring stretches by 210cm when a 135 N object is attached. What is the weight of a rubber duck that would stretch the spring by 44.9cm?

(44.9cm/210cm) * 135N. =

To find the weight of the rubber duck, we can use the concept of proportionality based on Hooke's Law, which states that the force exerted by a spring is directly proportional to the displacement of the spring.

Here's how you can calculate it:

1. Begin by finding the spring constant (k) of the spring. This constant represents how stiff the spring is and can be determined using the formula:
k = F / x
where k is the spring constant, F is the force applied to the spring, and x is the displacement of the spring.

In this case, the force applied to the spring is 135 N and the displacement is 210 cm (or 2.1 m). Plugging these values into the formula, we have:
k = 135 N / 2.1 m
k ≈ 64.3 N/m

2. Now that we have the spring constant, we can use it to find the force exerted by the spring for the rubber duck. We'll use the same formula as before, but now we need to solve for F:
F = k * x
where F is the force, k is the spring constant, and x is the displacement of the spring.

In this case, we are given that the new displacement of the spring is 44.9 cm (or 0.449 m). Plugging in the values, we have:
F = 64.3 N/m * 0.449 m
F ≈ 28.9 N

3. The force we obtained is the force exerted by the rubber duck. However, the problem asks for the weight of the rubber duck. The weight is the force due to gravity acting on an object. On Earth, the weight of an object can be found using the formula:
weight = mass * gravitational acceleration (g)

If we assume that the gravitational acceleration is approximately 9.8 m/s², then the weight can be calculated as:
weight = F / g
weight ≈ 28.9 N / 9.8 m/s²
weight ≈ 2.95 kg

Therefore, the weight of the rubber duck is approximately 2.95 kg.