A 0.321-kg mass is attatched to a spring with force constant of 13.3 N/m. If the mass is displaced 0.256 m from the Equalibrium and released, what is its speed when it is 0.128 m from equalibrium?

Question

raspberryjam · Answer

$$  \frac{1}{2}mv^2=\frac{1}{2}kx_{total}^2-\frac{1}{2}kx^2$$ where k is the spring constant and $$ x_{total}$$ is the total displacement from equilibrium. $$x $$ is the distance 0.128 m.

raspberryjam · Answer

Law of conservation of energy yo.
Kinetic energy = (potential energy of spring at total displacement) - (potential energy of spring at whatever point you're trying to find the velocity at)

anonymous · Answer

okay

anonymous · Answer

i thought the potential would be at total displacement like mgh

raspberryjam · Answer

Well you're trying to find the velocity at a specific point so you have to subtract it from the potential energy of when the spring is fully stretched which gives you the amt of potential energy transformed into kinetic energy.

raspberryjam · Answer

Also you can't use mgh in this case because it's a spring-based problem...Hooke's law

anonymous · Answer

do I convert the energy into velocity

anonymous · Answer

I was saying mgh as an example

raspberryjam · Answer

No just solve for v in the equation above

raspberryjam · Answer

You can't just do total displacement because you're trying to find the velocity at a specific point which is when x=0.128 m. You aren't finding the displacement when x=0.256 m.

anonymous · Answer

that worked! I do not quite understan how though.