How much is the spring compressed?jbjohnybaker said:Homework Statement
A child's toy shoots a rubber dart of mass 7.8g, using a compressed spring with a force constant of 3.5 x 10^2 N/m. The spring is initially compressed 4.5cm. All the elastic potential energy is converted into kinetic energy of the dart.
What is the speed of the dart as it leaves the toy?
Homework Equations
Ee = Ek
Ee = 1/2 k x^2
Ek = 1/2 mv^2
The Attempt at a Solution
Ee = Ek
1/2 (3.5 x10^2)(?) = 1/2 (.0078)v^2 ??]
Elastic potential energy is the energy stored in an object when it is stretched or compressed. It is a form of potential energy that can be converted into kinetic energy when the object returns to its original shape.
The formula for calculating elastic potential energy is Ee = 1/2kx^2, where Ee is the elastic potential energy, k is the spring constant, and x is the displacement from the equilibrium position.
Examples of objects with elastic potential energy include springs, rubber bands, trampolines, and bungee cords. These objects can store energy when they are stretched or compressed and release it when they return to their original shape.
Hooke's law states that the force exerted by a spring is directly proportional to the amount it is stretched or compressed. This force is also equal to the negative of the spring constant times the displacement. This relationship is important in calculating elastic potential energy.
Elastic potential energy has many practical applications in everyday life. It is used in the suspension systems of vehicles, in shock absorbers, and in elastic materials used for cushioning. It is also crucial in the design of bridges, buildings, and other structures that need to withstand external forces.