Up And Down And Up And Down

Classical Mechanics Level 1

A block is attached to a spring so that it oscillates up and down between A and C.

The total potential energy of the system is given by the sum of its gravitational and elastic potential energy. At what point(s) of the block's motion is the total potential energy of the system greatest ?

Details and Assumptions

  • In case A, the mass starts from rest and the spring is fully compressed.
  • In case B, the spring is in motion.
  • In case C, the mass is at rest.
A B C A and C

View wiki
Pranshu Gaba by Pranshu Gaba , 22, India

This section requires Javascript.
You are seeing this because something didn't load right. We suggest you, (a) try refreshing the page, (b) enabling javascript if it is disabled on your browser and, finally, (c) loading the non-javascript version of this page . We're sorry about the hassle.

1 solution

Pranshu Gaba
Sep 11, 2016

Since there are no dissipative forces, the total mechanical energy of the system (sum of the kinetic and the total potential energy) remains conserved.

The block changes direction at A and C, so its instantaneous rest at those points, so the kinetic energy of the block at those points is zero. Kinetic energy is minimum at these points; this implies that the total potential energy is maximum at these points.

Although the gravitational and the elastic potential energies are different at A and C, their sum is equal at both points.

15 Helpful 0 Interesting 0 Brilliant 0 Confused

What about the energy being lost to heat from the motion of the spring itself?

Dellan Zimmerman - 4 years, 8 months ago

Log in to reply

We're assuming there are none.

Clark Kent - 4 years, 8 months ago

Are the distances AB and BC equal to each other while the spring is oscillating?

Puneet Pinku - 4 years, 8 months ago

Log in to reply

They do not not have to be equal, B can be any point between A and C. The potential energy at any point between A and C would be less than the potential energy at A or C.

Pranshu Gaba - 4 years, 8 months ago

I believe that the kinetic energy that starts from point A towards B and C increases as it moves away from A and, on the contrary, its potential energy decreases. When it exceeds C (which is where the weight of the body and the strength of the spring balance) it will even get negative values for the potencial energy. so in a resting state C I think its potential is 0. That would be the same for A.

chris wild - 2 years, 8 months ago

0 pending reports

×

Problem Loading...

Note Loading...

Set Loading...