a 20N force is required to stretch a spring by 0.5 m.
a) what is the spring constant?
b)how much energy is stored in the spring ?
a. k = 20N/0.5m = 40 N/m.
b. E = F*d = 40*1 = 40 J.
a) Well, it seems this spring likes to take things seriously and needs a 20N force to stretch by 0.5m. To find the spring constant, we can use Hooke's Law, which states that the force applied is proportional to the amount the spring stretches. So, we have a force of 20N and a stretch of 0.5m. Using the formula F = kx, where F is the force, k is the spring constant, and x is the stretch, we can rearrange it to solve for k. Therefore, k = F/x. Substituting the values, k = 20N / 0.5m. Drumroll, please... the spring constant is 40 N/m. No clowning around here!
b) How much energy is stored in the spring? Well, let me tell you, this spring is quite the energy hoarder! To calculate the energy stored in a spring, we can use the formula for elastic potential energy, which is U = (1/2) kx^2. Let's plug in the values: U = (1/2) (40 N/m) (0.5m)^2. Doing the math, we get U = 5 Joules. So, this spring has stored 5 Joules of energy. It's like a little energy bank, but just don't ask it for a loan! It might not bounce back so easily.
a) To find the spring constant, we can use Hooke's Law, which states that the force required to stretch or compress a spring is directly proportional to the displacement of the spring. Mathematically, it can be expressed as:
F = k * x
where F is the force, k is the spring constant, and x is the displacement.
In this case, the force (F) is 20 N and the displacement (x) is 0.5 m. Plugging these values into the equation, we can solve for the spring constant (k):
20 N = k * 0.5 m
Rearranging the equation to isolate k, we get:
k = 20 N / 0.5 m
k = 40 N/m
Therefore, the spring constant is 40 N/m.
b) The energy stored in a spring can be calculated using the formula:
E = 0.5 * k * x^2
where E is the energy, k is the spring constant, and x is the displacement.
In this case, the spring constant (k) is 40 N/m and the displacement (x) is 0.5 m. Plugging these values into the equation, we can solve for the energy stored in the spring (E):
E = 0.5 * 40 N/m * (0.5 m)^2
E = 0.5 * 40 N/m * 0.25 m^2
E = 5 J
Therefore, the energy stored in the spring is 5 Joules.
a) To find the spring constant (k), we can use Hooke's Law, which states that the force required to stretch or compress a spring is directly proportional to the displacement produced. Mathematically, it can be represented as:
F = k * x
Where:
F is the force applied to the spring (20N)
k is the spring constant (unknown)
x is the displacement from the equilibrium position (0.5m)
Rearranging the equation, we get:
k = F / x
Substituting the given values, we have:
k = 20N / 0.5m
k = 40 N/m
Therefore, the spring constant is 40 N/m.
b) The energy stored in a spring can be calculated using the formula:
E = (1/2) * k * x^2
Where:
E is the energy stored in the spring (unknown)
k is the spring constant (40 N/m)
x is the displacement from the equilibrium position (0.5m)
Substituting the values into the equation, we can calculate the energy stored:
E = (1/2) * 40 N/m * (0.5m)^2
E = 5 J
Therefore, the energy stored in the spring is 5 Joules.