Fish are hung on a spring scale to determine their mass. (a) What is the force constant of the spring in such a scale if it stretches 8.20 cm for a 18.3 kg load? N/m (b) What is the mass of a fish that stretches the spring 5.50 cm? kg (c) How far apart are the half-kilogram marks on the scale? mm

Fish are hung on a spring scale to determine their mass.

(a) What is the force constant of the spring in such a scale if it stretches 8.20 cm for a 18.3 kg load?
N/m

(b) What is the mass of a fish that stretches the spring 5.50 cm?
kg

(c) How far apart are the half-kilogram marks on the scale?
mm

(a) What is the force constant of the spring in such a scale if it stretches 8.20 cm for an 18.3 kg load?

In this question, we are given the stretching distance of the spring (8.20 cm) and the weight of the load (18.3 kg). We need to find the force constant of the spring.

The force constant of a spring, denoted as k, is a measure of how stiff or resistant the spring is to stretching. It is determined by the formula:

k = F / e

Where F is the force applied to the spring and e is the change in length of the spring.

In this case, the force applied to the spring is the weight of the load, which is given by the equation F = mg, where m is the mass of the load and g is the acceleration due to gravity (approximately 9.8 m/s^2).

Substituting the values into the equation, we get:

k = (m * g) / e

= (18.3 kg * 9.8 m/s^2) / 0.082 m

≈ 1225 N/m

Therefore, the force constant of the spring is approximately 1225 N/m.

(b) What is the mass of a fish that stretches the spring 5.50 cm?

In this part, we are given the stretching distance of the spring (5.50 cm) and we need to find the mass of the fish.

Using the same formula as before (F = ke), we can rearrange it to solve for the mass:

m = ke / g

Substituting the given values into the equation, we get:

m = (k * e) / g

= (1225 N/m * 0.055 m) / 9.8 m/s^2

≈ 6.875 kg

Therefore, the mass of the fish is approximately 6.875 kg.

(c) How far apart are the half-kilogram marks on the scale?

In this part, we are asked to determine the distance between the half-kilogram marks on the scale. To solve this, we need to use the equation e = mg / k, where e is the change in length of the spring.

Given that the mass is 0.5 kg, the force constant is 1225 N/m, and the acceleration due to gravity is 9.8 m/s^2, we can substitute these values into the equation:

e = (m * g) / k

= (0.5 kg * 9.8 m/s^2) / 1225 N/m

≈ 0.004 m

To convert this to centimeters, we multiply by 100:

e = 0.004 m * 100 cm/m

= 0.4 cm

Therefore, the half-kilogram marks on the scale are approximately 0.4 cm apart.