an elastic wire extended by 1.0cm where a load of 20g hangs from it. what additional load will be required to cause a further extension of 2.0cm
yes.
clearly, k = 20g/cm
so to get an extension of 3cm, you'll need a load of 60g, or another 40g.
(yeah, I know F is weight, not mass, but that pesky g-factor cancels out)
To find the additional load required to cause a further extension of 2.0cm, we need to use Hooke's Law. Hooke's Law states that the extension of an elastic material is directly proportional to the force applied, as long as the elastic limit of the material is not exceeded.
Let's go step by step to solve the problem:
1. Determine the spring constant (k) of the wire:
The spring constant represents the stiffness of the wire and is a measure of how much force is required to extend or compress a spring. We can calculate it using Hooke's Law:
k = F / x
where F is the force applied and x is the extension. In this case, F = weight of the load = mass * acceleration due to gravity, and x = extension.
Given that the load is 20g (0.02 kg) and the extension is 1.0cm (0.01 m), we have:
k = (0.02 kg * 9.8 m/s^2) / 0.01 m
k = 1.96 N/m
2. Calculate the force required for a 2.0cm (0.02 m) extension:
Using Hooke's Law, we can rearrange the formula to solve for force (F):
F = k * x
where k is the spring constant and x is the extension.
Given that the extension is now 0.02 m, we have:
F = 1.96 N/m * 0.02 m
F = 0.0392 N
3. Convert the force into the additional load:
The force required is the same as the weight of the additional load required to cause the extension. This can be calculated using the formula:
force (F) = mass * acceleration due to gravity
Given that the additional load is in equilibrium with the force, we have:
mass * acceleration due to gravity = 0.0392 N
mass = 0.0392 N / 9.8 m/s^2
mass = 0.004 kg
Converting this mass to grams, we have:
additional load = 0.004 kg * 1000 g/kg
additional load = 4.0 g
Therefore, an additional load of 4.0 grams will be required to cause a further extension of 2.0 cm.