A spring scale is used to measure the weight of various objects.

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

Hey Lily,

To do this, it seems like you have to assume that this scale is using "ideal" springs that follow Hooke's law. This means that the amount that the spring stretches is proportional to the force applied.

1. With the empty bottle, the force applied = mg = 0.1kg *9.8 m/s². And the spring stretched 1.8 cm.
2. From these 2 numbers, you can find the spring constant, k, by plugging into the Hooke's law formula, F = kx. Here you will get a "k" value in N/cm
3. Now, we can set up the equation again for the 2nd situation, using the k value we just solved, and the x value of 2.7cm.
4. Solving for F will tell us the total force needed to stretch the spring
5. Now, working backwards, we use F =mg to find what the mass must be to supply this force.
6. This total mass = mass of bottle + mass of the water. So you can find the mass of the water.
7. With the mass of the water, you can find the volume, using the density of water. Fortunately, the numbers work out nicely.
8. Good luck!