Physics 218: Mechanics Instructor: Dr. Tatiana Erukhimova

Lecture 16

Water SlideWho will come first?

http://curvebank.calstatela.edu/brach/brach.htm

The curve of fastest descent

Cycloid

Inverted cycloid:Brachistochrone

ENERGY DIAGRAMS

Potential Energy Diagrams

• For Conservative forces can draw energy diagrams

• Equilibrium points– Motion will move

“around” the equilibrium

– If placed there with no energy, will just stay (no force)

0 dxdU

xF

Stable vs. Unstable Equilibrium Points

The force is zero at both maxima and minima but…– If I put a ball with no velocity there would it stay?– What if it had a little bit of velocity?

A particle moves along the x-axis while acted on by a single conservative force parallel to the x-axis. The force corresponds to the potential-energy function graphed in the Figure. The particle is released from rest at point A.

a)What is the direction of the force on the particle when it is at point A?

b) At point B?

c) At what value of x is the kinetic energy of the particle a maximum?

d) What is the force on the particle when it is at point C?

e) What is the largest value of x reached by the particle during its motion?

f) What value or values of x correspond to points of stable equilibrium?

g) Of unstable equilibrium?

Quiz

Quiz

A block of mass m is attached to a vertical spring, spring constant k. The spring is unstretched at y=0.

A

If the spring is compressed an amount A and the block released from rest, how high will it go?