a spring that has a spring constant of 1400 n/m is stretched to a length of 2.5 m. if the normal length of…

a spring that has a spring constant of 1400 n/m is stretched to a length of 2.5 m. if the normal length of the spring is 1.0 m, how much elastic potential energy is stored in the spring?\n700 j\n1050 j\n1575 j\n4375 j

a spring that has a spring constant of 1400 n/m is stretched to a length of 2.5 m. if the normal length of the spring is 1.0 m, how much elastic potential energy is stored in the spring?\n700 j\n1050 j\n1575 j\n4375 j

Answer

Explanation:

Step1: Calculate the displacement

The displacement $x$ of the spring is the stretched - length minus the normal length. So $x = 2.5m−1.0m = 1.5m$.

Step2: Use the elastic - potential energy formula

The formula for elastic potential energy of a spring is $U=\frac{1}{2}kx^{2}$, where $k$ is the spring constant and $x$ is the displacement. Given $k = 1400N/m$ and $x = 1.5m$. Substitute the values into the formula: $U=\frac{1}{2}\times1400N/m\times(1.5m)^{2}$. First, calculate $(1.5m)^{2}=2.25m^{2}$. Then $\frac{1}{2}\times1400N/m\times2.25m^{2}=700N/m\times2.25m^{2}=1575J$.

Answer:

1575 J