The spring will stretch an additional 157.57 meters when the 800 kg block is added.
Here's how to calculate the additional stretch of the spring:
Step 1: Convert masses to kilograms.
1500 g = 1.5 kg
800 kg (already in kilograms)
Step 2: Calculate the total mass.
Total mass = 1.5 kg + 800 kg = 801.5 kg
Step 3: Calculate the spring constant.
We're given that the spring stretches by 30 mm (0.03 m) for a mass of 1.5 kg.
Using Hooke's Law: F = kx, where F is the force, k is the spring constant, and x is the displacement.
In this case, the force is the weight of the block: F = mg (m is the mass, g is the acceleration due to gravity, 9.81 m/s²).
Therefore, mg = kx.
Substituting known values: (1.5 kg)(9.81 m/s²) = k(0.03 m).
Solving for k: k ≈ 490.5 N/m.
Step 4: Calculate the stretch due to the total mass.
Using the same formula as before: F = kx.
This time, F = (801.5 kg)(9.81 m/s²) and k = 490.5 N/m.
Solving for x: x ≈ 157.6 m.
Step 5: Calculate the additional stretch.
Additional stretch = Total stretch - Initial stretch
Additional stretch = 157.6 m - 0.03 m
Additional stretch ≈ 157.57 m
Therefore, the spring will stretch an additional 157.57 meters when the 800 kg block is added.