Two springs of spring constant 1500n/m and 3000n/m respectively are st...
Explanation of Potential Energy Ratio in Two Springs
Definition of Potential Energy
Potential energy is the stored energy of an object due to its position or configuration. It is the energy that an object possesses because of its position relative to other objects in a system.
Spring Constant
The spring constant is a measure of the stiffness of a spring. It is the amount of force required to stretch or compress a spring by a unit of length. The higher the spring constant, the stiffer the spring.
Calculation of Potential Energy in a Spring
The potential energy stored in a spring can be calculated using the formula:
PE = (1/2)kx^2
where PE is the potential energy, k is the spring constant, and x is the displacement of the spring from its equilibrium position.
Ratio of Potential Energy in Two Springs
When two springs are stretched with the same force, they will have different potential energies because they have different spring constants. The potential energy in a spring is directly proportional to the square of its spring constant.
Therefore, if two springs of spring constant 1500 N/m and 3000 N/m are stretched with the same force, the ratio of their potential energies can be calculated as follows:
PE1/PE2 = (1/2)k1x^2 / (1/2)k2x^2
PE1/PE2 = k1/k2
PE1/PE2 = 1500/3000
PE1/PE2 = 1/2
Therefore, the potential energy ratio in the two springs is 1:2. This means that the spring with the higher spring constant (3000 N/m) will have twice the potential energy of the spring with the lower spring constant (1500 N/m) when stretched with the same force.