An elastic extended by 20cm when a load of 40gm hangs from it.what adition of load will be required to cause a futher extention of 4.0cm?
k = 40 g/20 cm
Mass in grams = (40/20) * x in cm
Mass = (40/20)(24) = 48 grams total
= 8 grams additional
To calculate the additional load required to cause a further extension of 4.0 cm, we will need to use Hooke's Law, which states that the extension of an elastic material is directly proportional to the force applied to it.
Hooke's Law can be expressed as:
F = kx
Where:
F is the force applied
k is the spring constant
x is the extension
First, we need to calculate the spring constant (k) for the given elastic material. The spring constant represents the stiffness of the material and can be calculated using the formula:
k = F / x
Given that the extension is 20 cm (or 0.2 m) when a load of 40 g (or 0.04 kg) hangs from it, we can substitute these values into the formula:
k = 0.04 kg / 0.2 m
k = 0.2 N/m
Now that we have the spring constant, we can calculate the additional load required to cause a further extension of 4.0 cm (or 0.04 m). Rearranging Hooke's Law to solve for force, we have:
F = kx
F = 0.2 N/m * 0.04 m
F = 0.008 N
Therefore, an additional load of 0.008 N will be required to cause a further extension of 4.0 cm.