A sprail spring balance 25cm long when 5N hangs on it and 30com, the weigh is 10N. What is the length of the spring if the weigh is 2N. Assume hookie's law is obey
No answer
let L = initial length with no weight
then
extension = ex = x - L
and
F = k * ex = k (x - L)
5 = k * (25-L) = 25 k - kL
10 = k (30-L) = 30 k - kL
-5 = -5 k
k = 1
which you could see by inspection anyway
then
10 = 30 - L
L = 20 = unextended length
2 Newtons = 1 * extension
extension = 2 cm
L = 20
so length with 2 N = 22 cm
F=kx, so you want L when F=2.
(30-25)/(10-5) = (25-L)/(5-2)
L = 22
To solve this problem, we can use Hooke's Law, which states that the force exerted by a spring is directly proportional to the displacement of the spring from its equilibrium position.
Let's assume that the length of the spring when no weight is hung on it (equilibrium position) is L0.
We are given two different scenarios:
Scenario 1:
Length of the spring (L1) = 25 cm (or 0.25 m)
Weight (W1) = 5 N
Scenario 2:
Length of the spring (L2) = 30 cm (or 0.3 m)
Weight (W2) = 10 N
We need to find the length of the spring (L3) when the weight is 2 N.
First, we find the spring constant (k):
Using Scenario 1, we can write Hooke's Law equation as:
W1 = k * (L1 - L0)
5 N = k * (0.25 m - L0)
Using Scenario 2, we can write another equation as:
W2 = k * (L2 - L0)
10 N = k * (0.3 m - L0)
Now, we can solve these two equations to find the value of k:
5 N = k * (0.25 m - L0) --- Equation 1
10 N = k * (0.3 m - L0) --- Equation 2
From Equation 1:
5 N = 0.25 k - kL0
0.25 k = 5 N + kL0
0.25 k = kL0 + 5 N
0.25 k - kL0 = 5 N
From Equation 2:
10 N = 0.3 k - kL0
0.3 k = 10 N + kL0
0.3 k = kL0 + 10 N
0.3 k - kL0 = 10 N
By equating the left sides and the right sides of the two equations:
0.25 k - kL0 = 0.3 k - kL0
0.25 k = 0.3 k
0.3 k - 0.25 k = 0
Simplifying:
0.05 k = 0
k = 0 / 0.05
k = 0
This means that the spring constant (k) cannot be zero since Hooke's Law only applies when the spring is in the linear range. However, in this case, the spring constant evaluates to zero, which indicates that the spring is not behaving as expected or the given information is inconsistent.
Therefore, we cannot determine the length of the spring when the weight is 2 N based on the given information.