Final answer:
To calculate the stretch of each spring supporting a 2.00 kg box, the weight of the box is divided by two and applied to each spring. Then, using Hooke's Law, the stretch is calculated by dividing the force on each spring by the spring constant, resulting in a stretch of 0.045 m for each spring.
Step-by-step explanation:
To calculate by how much each spring is stretched when supporting a 2.00 kg box, we first need to determine the force of gravity on the box, which is equal to the weight of the box.
The weight of the box (W) can be calculated using the formula W = mg, where m is mass and g is the acceleration due to gravity, which is approximately 9.81 m/s2 on the surface of the Earth.
For a 2.00 kg box, the weight W is 2.00 kg × 9.81 m/s2 = 19.62 N. Since the two springs are identical and support the box side by side, they share the weight of the box equally.
Therefore, each spring supports a force of 19.62 N / 2 = 9.81 N.
To find the stretch (x) in each spring, we use Hooke's Law which states F = kx, where F is the force applied, k is the spring constant, and x is the stretch of the spring. Thus, x = F / k.
Since we have two identical springs with a spring constant k = 220 N/m, the stretch in each spring when supporting half the weight of the box would be:
x = 9.81 N / 220 N/m = 0.0446 m
Expressed to two significant figures, each spring is stretched by 0.045 m when supporting the 2.00 kg box.