Answer:
108.8N
Step-by-step explanation:
We can use Hooke's Law to solve for the force required to stretch the spring. Hooke's Law states that the force (F) applied to a spring is directly proportional to the amount it is stretched or compressed (x), as long as the spring does not exceed its limit of proportionality. Mathematically, this can be expressed as:
F = kx
where k is the spring constant, which depends on the properties of the spring and is measured in units of N/m (newtons per meter).
To solve for the force required to stretch the spring by 13 cm, we first need to find the spring constant. We can use the information given in the problem to do this. When the load of 46 N was attached to the spring and it was stretched 5.5 cm, we can write:
46 N = k (5.5 cm) (1)
To convert the units of length to meters, we divide both sides by 100:
46 N = k (0.055 m)
Solving for k, we find:
k = 46 N ÷ 0.055 m = 836.36 N/m
Now we can use Hooke's Law again to solve for the force required to stretch the spring by 13 cm. Since the spring is now horizontal, we need to convert the displacement from vertical to horizontal. We can assume that the spring is stretched in a straight line, so the displacement is the same for both orientations. Therefore, we can write:
F = kx
F = (836.36 N/m) (0.13 m)
F ≈ 108.8 N
Therefore, the force required to stretch the spring by 13 cm is approximately 108.8 N.