A mass is attached to a spring. When is the KE at its maximum?
a) at equlibrium
b) at the highest point
c) at the lowest point
d) after the spring has performed many oscillations and returned to equilibrium
I'm not sure, since none of the choices imply that the spring is moving, which is the only time when there would be kinetic energy...
Thank you!
I think they want a)
That is where the forces add to zero and therefore the potential energy is minimum and the ke is maximum.
As you can see from answer d), their phrasing of the question stinks. Should have said, passing through force equilibrium point.
Thank you!
You are correct in noting that kinetic energy is associated with motion. In the context of a mass attached to a spring, the kinetic energy refers to the energy possessed by the mass as it moves. To find the point at which the kinetic energy is at its maximum, we need to consider the motion of the mass-spring system.
When a mass-spring system is in equilibrium, it means that the restorative force of the spring is equal in magnitude but opposite in direction to the force due to gravity on the mass. At this point, the mass is not moving, and therefore, its kinetic energy is zero. So, choice (a) "at equilibrium" is not correct.
At the highest point of its motion, the mass momentarily comes to rest and changes direction. Since the mass is not moving at this point, its kinetic energy is zero. Therefore, choice (b) "at the highest point" is also not correct.
At the lowest point of its motion, the mass has the highest velocity. The kinetic energy of an object is directly proportional to its velocity squared. Therefore, the mass has the maximum kinetic energy at the lowest point. So, choice (c) "at the lowest point" is correct.
After the spring has performed many oscillations and returned to equilibrium, the mass has zero velocity and no kinetic energy. So, choice (d) "after the spring has performed many oscillations and returned to equilibrium" is not correct.
In summary, the correct answer is (c) at the lowest point.