Question

A spring balance used to weigh candy is built with a spring. The spring stretches 3.00 cm when a 15 N weight is placed in the pan. When the weight is replaced with 3kg of candy what distance will the spring stretch?

7.0cm
4.5cm
3.8cm
5.9cm

Answer 1

5.9 cm

Step-by-step explanation:

We'll begin by calculating the spring constant (K) of the spring. This can be obtained as follow:

Force (F) = 15 N

Extention (e) = 3 cm

Spring constant (K) =.?

F = Ke

15 = K × 3

Divide both side by 3

K = 15 / 3

K = 5 N/cm

Therefore, the spring constant (K) is 5 N/cm.

Now, we shall determine how far the spring will stretch when a 3 kg candy is placed on the spring balance.

This can be obtained as follow:

First, we shall determine the weight of the object.

Mass of object = 3 Kg

Acceleration due to gravity (g) = 9.8 m/s²

Weight (W) =?

W = mg

W = 3 × 9.8

W = 29.4 N

Finally, we shall determine how far the spring will stretch as follow:

Weight (W) = Force (F) = 29.4 N

Spring constant (K) = 5 N/cm

Extention (e) =?

F = ke

29.4 = 5 × e

Divide both side by 5

e = 29.4 / 5

e = 5.88 ≈ 5.9 cm

Therefore, the spring will stretch 5.9 cm when a 3 kg candy is placed on the spring balance.