If two springs have their spring constants as k1 and k2 (k1>k2 . When they are stretched by same force what will be the relation between their elongations
k = f / e
k1 e1 = k2 e2
e2 / e1 = k1 / k2
When two springs with different spring constants, k1 and k2, are stretched by the same force, the relationship between their elongations can be determined using Hooke's Law.
Hooke's Law states that the elongation (x) of a spring is directly proportional to the applied force (F) and inversely proportional to the spring constant (k):
F = k * x
Since the force applied to both springs is the same, we can equate the forces:
k1 * x1 = k2 * x2
Rearranging the equation, we get:
x1 / x2 = k2 / k1
Since k1 > k2 (as given in the question), the ratio of their elongations will be:
x1 / x2 < 1
In other words, the elongation of the spring with the larger spring constant will be less than the elongation of the spring with the smaller spring constant, when both are stretched by the same force.
To determine the relation between the elongations of two springs with different spring constants, we can use Hooke's Law. Hooke's Law states that the force exerted by a spring is directly proportional to its elongation.
Mathematically, Hooke's Law is expressed as:
F = kx
where F is the force applied to the spring, k is the spring constant, and x is the elongation of the spring.
In this case, we have two springs with spring constants k1 and k2, where k1 > k2. Let's assume that both springs are stretched by the same force, denoted as F.
The elongation of a spring can be calculated using Hooke's Law as:
x = F / k
Using this formula, let's calculate the elongation of each spring separately.
For the first spring with spring constant k1:
x1 = F / k1
For the second spring with spring constant k2:
x2 = F / k2
To determine the relation between their elongations, we can compare the values of x1 and x2.
Since k1 > k2, we can conclude that the elongation of the spring with the larger spring constant will be smaller. Therefore, the relation between their elongations can be expressed as:
x1 < x2
In other words, the elongation of the spring with the smaller spring constant will be greater when both springs are stretched by the same force.