If it takes 4.00 J of work to stretch a Hooke's Law spring 10.0 cm from its unstressed length, determine the extra work required to stretch it an additional 10.0 cm
so the question asks to determine the extra work to stretch the string from 10 to 20 cm, so it's obvious that the extra amount of work is greater than the first work done, so we can do cross product when w1=4, x1=0.1m and when w2-4(which is w2-w1), x=0.2 so we'll get x2-4=(4*0.2)/ 0.1, we'll get 8, and then we'll get -4 to the other side wich will give us 8+4=12 and that's your ansewr.
That's my method and i'm not sure if it could work in other examples, hope it makes sense
To determine the extra work required to stretch the Hooke's Law spring an additional 10.0 cm, we need to understand the relationship between the force applied to the spring and its displacement.
According to Hooke's Law, the force required to stretch or compress a spring is directly proportional to the displacement from its unstressed length. Mathematically, this can be expressed as:
F = k * x
Where:
F is the force applied to the spring,
k is the spring constant (a measure of the stiffness of the spring),
x is the displacement from the unstressed length.
In this case, we are given that it takes 4.00 J of work (W) to stretch the spring 10.0 cm (0.10 m) from its unstressed length. The work done on the spring can be calculated using the formula:
W = 0.5 * k * x^2
Solving for k:
k = 2 * W / x^2
k = 2 * 4.00 J / (0.10 m)^2
k = 2 * 4.00 J / 0.01 m^2
k = 800 J/m^2
Now, we want to determine the extra work required to stretch the spring an additional 10.0 cm (0.10 m) from its already stretched position.
For the additional displacement, the force required can be calculated using Hooke's Law:
F = k * x
F = 800 J/m^2 * 0.10 m
F = 80 N
The extra work done on the spring can be calculated using the formula:
W = 0.5 * k * x^2
W = 0.5 * 800 J/m^2 * (0.10 m)^2
W = 0.5 * 800 J/m^2 * 0.01 m^2
W = 4.00 J
Therefore, the extra work required to stretch the Hooke's Law spring an additional 10.0 cm from its already stretched position is 4.00 J.