A spring of length 0.1m obeys hookes law when a load of 200N is hung vertically from its free end,the length of the spring become 0.115m.find? (a) calculate its new length when a load of 600N is hung on the spring. (b) name a device whose functioning depends on hookes law.
To solve this problem, we first need to understand Hooke's Law, which states that the force exerted by a spring is directly proportional to the displacement (change in length) of the spring from its equilibrium position. Mathematically, this can be written as F = kx, where F is the force applied, k is the spring constant, and x is the displacement.
Given:
Length of the spring (L₁) = 0.1 m
Load applied (F₁) = 200 N
New length of the spring (L₂) = 0.115 m
(a) To calculate the new length when a load of 600 N is hung on the spring, we can use the same formula F = kx and solve for x:
F₁ = kx₁ (Equation 1)
F₂ = kx₂ (Equation 2)
Divide Equation 2 by Equation 1 to eliminate the spring constant (k):
F₂/F₁ = x₂/x₁
Substituting the given values:
600 N / 200 N = x₂ / 0.1 m
Simplifying the equation:
3 = x₂ / 0.1 m
Cross-multiplying:
x₂ = 3 * 0.1 m
x₂ = 0.3 m
Therefore, the new length of the spring when a load of 600 N is hung on it is 0.3 m.
(b) A device whose functioning depends on Hooke's Law is a spring scale or a dynamometer. It is commonly used to measure the weight or force applied to an object. The displacement of the spring from its equilibrium position is proportional to the force applied, allowing us to measure the force by observing the elongation or compression of the spring.
600 = 3*200
so, it will extend 3*0.015 = 0.045m
anything involving springs, like a spring scale
google can provide you with many more. In fact, I'd bet your text presents several examples.
(a) To calculate the new length of the spring when a load of 600N is hung on it, we can use Hooke's law. Hooke's law states that the force exerted by a spring is directly proportional to its extension or compression.
First, let's calculate the spring constant (k) using the initial length and load applied:
l₁ = 0.1m (initial length)
l₂ = 0.115m (new length)
F₁ = 200N (initial load)
According to Hooke's law:
F = k * Δl
Where:
F is the force applied to the spring
k is the spring constant
Δl is the change in the length of the spring
From the given data, we can calculate the spring constant (k):
k = F₁ / Δl
k = 200N / (0.115m - 0.1m)
k = 200N / 0.015m
k = 13333.33 N/m
Now we can use the spring constant to find the new length (l₃) when the load (F₃) is 600N:
F₃ = 600N
According to Hooke's law:
F₃ = k * Δl₃
Solving for Δl₃:
Δl₃ = F₃ / k
Δl₃ = 600N / 13333.33 N/m
Δl₃ = 0.045m
Finally, we can find the new length (l₃):
l₃ = l₂ + Δl₃
l₃ = 0.115m + 0.045m
l₃ = 0.16m
Therefore, when a load of 600N is hung on the spring, the new length of the spring will be 0.16m.
(b) An example of a device that functions based on Hooke's law is a spring balance or a weighing scale. It measures the weight of an object by utilizing the extension or compression of a spring. The reading on the scale corresponds to the force exerted by the spring, which is directly proportional to the weight of the object.