A spring stretches by 6cm when supporting a load of 15w.by how much would it stretch when supporting a load of 5kg
To solve this problem, we can assume that the spring obeys Hooke's Law, which states that the force applied to a spring is directly proportional to the displacement of the spring from its equilibrium position.
Given that the spring stretches by 6 cm (or 0.06 m) when supporting a load of 15 N, we can use this information to find the spring constant.
Hooke's Law can be written as:
F = k * x,
where F is the force applied to the spring, k is the spring constant, and x is the displacement of the spring.
Plugging in the values, we have:
15 N = k * 0.06 m.
Solving for k, we get:
k = 15 N / 0.06 m
k = 250 N/m.
Now, we can use this spring constant to determine the displacement of the spring when supporting a load of 5 kg (or 49 N).
Using Hooke's Law again, we have:
F = k * x.
49 N = 250 N/m * x.
Solving for x, we get:
x = 49 N / 250 N/m
x = 0.196 m or 19.6 cm.
Therefore, the spring would stretch by 19.6 cm when supporting a load of 5 kg.
To calculate the spring's extension when supporting a load of 5 kg, we can use Hooke's Law, which states that the extension of a spring is directly proportional to the force applied.
First, let's convert the weight of the load from kilograms to newtons. The gravitational force acting on an object is given by:
Weight = mass * acceleration due to gravity
The acceleration due to gravity is approximately 9.8 m/s². So, the weight of the load is:
Weight = 5 kg * 9.8 m/s² = 49 N
Now we can set up a proportional relationship using Hooke's Law:
extension_1 / force_1 = extension_2 / force_2
Given:
extension_1 = 6 cm = 0.06 m
force_1 = 15 W (unknown)
force_2 = 49 N (the weight of the 5 kg load)
extension_2 (the unknown we want to find)
Plugging in the values into the equation, we get:
0.06 m / 15 W = extension_2 / 49 N
To solve for extension_2, we can cross-multiply and solve for extension_2:
extension_2 = (0.06 m / 15 W) * 49 N
extension_2 ≈ 0.196 m or 19.6 cm
Therefore, the spring would stretch by approximately 19.6 cm when supporting a load of 5 kg.