Question

49. The potential energy of a spring is 0.3 J when it is compressed 0.04 m to the left of its equilibrium position. At this

point it comes to its leftmost position. What is its kinetic energy at this point?
A. -0.3 J
B. zero
C. 0.3 J
D. 375 N/m​

Answer 1

B. zero

Step-by-step explanation:

The total mechanical energy of a spring is equal to the sum of its kinetic energy, K, and its potential energy, U:

`E=K+U`

Where

`K=(1)/(2)mv^2` is the kinetic energy, where m is the mass and v is the speed

`U=(1)/(2)kx^2` is the potential energy, with k being the spring constant and x the displacement

The total mechanical energy is conserved during the entire motion of the spring. We have two particular situations:

- At the equilibrium position, the displacement is zero: x=0, so U=0 and the kinetic energy is maximum.

- At the position of maximum displacement (so the leftmost or rightmost position), the displacement is maximum, so U is maximum while the speed is zero (v=0), and therefore the kinetic energy is also zero: K = 0.

Therefore, the correct answer is

B. zero