A spring scale… PLEASE HELP! :)

Question

A spring scale is used to measure the weight of various objects. when a 100g empty glass bottle is placed on the scale, the spring stretches down 1.8cm. How much water should be poured into the glass bottle to stretch the spring down by 2.7 cm?

1) 150mL

2)33mL

3)50mL

4)44mL

Answer 1

This is a spring problem that requires using Newton's second law.

First, we must determine the spring constant, k, using the given information.

Apply Newton's second law to the scale at rest when the 100 gram glass bottle is placed on it:

F_net = + F_spring - F_weight = ma = 0

k*Δx = m_bottle*g

Solving for k and substituting given values,

k = ((0.1 kg)*(10 m/s²)) / (0.018 m) = 55.56 N/m

Now, we change the conditions of Newton's second law when Δx = 2.7 cm and solve for m_total:

F_{weight_total} = F_spring

m_total*g = k*Δx

Solving m_total and substituting,

m_total = ((55.56 N/m)*(0.027 m)) / (10 m/s²) = 0.15 kg

Now, we must separate the total mass into its two components and solve for the mass of water:

m_total = m_water + m_bottle

m_water = 150 grams - 100 grams = 50 grams

Finally, use the definition of density to solve for the volume of water:

p = m / V

V = (50 grams) / (1 g/mL) = 50 mL