A spring 20cm long is stretched to 25cm by a load 5N. What will be it's length when stretched by 100N assuming that the elastic limit is not reached?
I remember from my high-school physics classes that the expansion or compression of a spring
is proportional to the force applied to it. That is, it is linears (within obvious restrictions)
A good example of this is a simple fisherman's scale. The "ruler" on it is a linear scale, but trying to weigh a shark with it, would probably not give you a correct reading and would break it.
so ..
Stretch = kN, where N is the force applies in Newtons
When N = 5, Stretch = 5 cm
5 = k(5) ---> k = 1 and
Stretch = N
when N = 100, Stretch = 100 cm
and at rest it is 20cm, so it is 120 cm long.
Look at Sal Khan's simplified video:
https://www.khanacademy.org/science/ap-physics-1/ap-work-and-energy/spring-potential-energy-and-hookes-law-ap/v/intro-to-springs-and-hooke-s-law
Load is now 20x, so stretch will be 20x, or 5cm*20=100cm
length now of spring is 100+20 = 120cm
Answer is 30cm
Use young modulus law
To find the length of the spring when stretched by 100N, we can use Hooke's Law, which states that the extension of a spring is directly proportional to the force applied to it.
Let's first calculate the spring constant (k) of the spring using the data provided.
The initial length (L0) of the spring is 20cm, and it is stretched to 25cm by a load of 5N. The extension (ΔL) of the spring can be calculated as:
ΔL = L - L0
ΔL = 25cm - 20cm
ΔL = 5cm
Hooke's Law can be written as:
F = k * ΔL
Rearranging the equation to solve for k, we have:
k = F / ΔL
k = 5N / 5cm
k = 1 N/cm
Now, we can use this spring constant (k) to calculate the length of the spring when stretched by 100N. Let's call this length L1.
Using Hooke's Law again, we have:
F = k * ΔL
100N = 1 N/cm * ΔL
Rearranging the equation to solve for ΔL, we get:
ΔL = 100N / 1 N/cm
ΔL = 100 cm
Finally, to find L1, we add the extension (ΔL) to the initial length (L0):
L1 = L0 + ΔL
L1 = 20cm + 100cm
L1 = 120cm
Therefore, the length of the spring when stretched by 100N will be 120cm.