# Work and Energy for a mass sliding down a curved ramp (why does the ramp move?)

• MatinSAR
In summary: Perhaps sometimes three components are better than two!Perhaps sometimes three components are better than two!
jbriggs444 said:
Not if the surface exerting the normal force ##N## is moving.
Can you explain how is it negative ?

MatinSAR said:
Can you explain how is it negative ?
The component of the surface's motion in the direction of the normal force is negative. It is moving away from the force it exerts. So the force pair does positive work on the surface and negative work on the ball.

MatinSAR
MatinSAR said:
Can you explain how is it negative ?
For a small time interval, you will need to imagine the displacement of the ball. Does this displacement have a component parallel or antiparallel to the normal force acting on the ball?

MatinSAR
TSny said:
Does this displacement have a component parallel or antiparallel to the normal force acting on the ball?
N is neither perpendicular nor parallel to displacement.
As the object descends and the surface moves to the left, the object tilts slightly downward and does not move parallel to the surface.

Am I wrong?!

MatinSAR said:
N is neither perpendicular nor parallel to displacement.
As the object descends and the surface moves to the left, the object tilts slightly downward.
But does the displacement of the ball have a component parallel (or antiparallel) with N?

The picture below shows a small interval of time with initial time in black and final time in brown for the case of an inclined plane for the ramp.

If the ball were to move only parallel to the plane, then it would end up at the position shown by the open circle. But the ball must end up on the brown ramp. The overall displacement of the ball is from the intial black position of the ball to the final brown position of the ball.

Lnewqban and MatinSAR
TSny said:
But does the displacement of the ball have a component parallel (or antiparallel) with N?
antiparallel ??

Yes. Good. So, do you see how N does negative work on the ball?

MatinSAR
TSny said:
Yes. Good. So, do you see how N does negative work on the ball?
N and one of the displacement components are in the opposite direction, so the work is negative.
Is it true ??

MatinSAR said:
N and one of the displacement components are in the opposite direction, so the work is negative.
Is it true ??
Yes.

MatinSAR
TSny said:
Yes.
Your answer was one of the best I have ever received, even better than my professors at university. Thank you for your valuable time.

Lnewqban
Thank you for the kind comment.

MatinSAR
kuruman said:
Right. If there is potential energy to consider, then the conserved quantity is mechanical energy which is the sum of kinetic and potential energy of the two-mass system. In other words, the sum of the kinetic energies of the masses plus the potential energy when the mass is at some point on the ramp does not change as the mass descends and the ramp moves to the left.
Thanks a lot.
jbriggs444 said:
The component of the surface's motion in the direction of the normal force is negative. It is moving away from the force it exerts. So the force pair does positive work on the surface and negative work on the ball.

Lnewqban

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