Physics 218: Mechanics Instructor: Dr. Tatiana Erukhimova Lectures 25, 26

Second exam Tuesday, October Heldenfels Sections 818 and 819 start at 7 pm Sections 820 and 821 start at 8:05 pm

Work Energy Theorem

If a force can be written as the gradient (slope) of some scalar function, that force is conservative. U(x) is called the potential energy function for the force If such a function exists, then the force is conservative 1D case:

does NOT depend on path! 1D case:

does NOT depend on path! If F x (x) is known, you can find the potential energy function as

or

Newton’s 2nd Law

Work does not depend on the choice of coordinates! You can calculate work of each force in the most convenient system of coordinates. Do not forget to work with components!

Usually there are several ways to solve the problem. Indicate the law or the theorem you use!

Average 76.9 Median 81 Sec Sec Sec Sec

Center of Mass

Find the position of the center of mass of the system of the sun and Jupiter. (Since Jupiter is more massive than the rest of the planets put together, this is essentially the position of the center of mass of the solar system.) Does the center of mass lie inside or outside the sun?

Motion of the Center of Mass

The center of mass of a system moves as if all of the mass of the system were concentrated at that point and as if all of the forces were acting at that point There is only the external forces that affect the motion of the center of mass ( ) Only external forces affect the motion of the center of mass

Momentum is a vector! Vector equation!

If

Conservation of Momentum If there is no external force on a system, then the total momentum of the system is a constant

True in X and Y directions separately!