1. Physics 218: Mechanics Instructor: Dr. Tatiana Erukhimova Lecture 13

2. A block of mass M is on a horizontal surface and is attached to a spring, spring constant k. If the spring is compressed an amount A and the block released from rest, how far will it go before stopping if the coefficient of friction between the block and the surface is  ? How will this answer change is the block is not attached to the spring?? Quiz Ch 7 (b) Consider the spring force given by F x = –kx+nx 2 Consider  =  0 (1 + x/d).

3. Quiz Ch7 (c) A block of mass m slides down on the larger block of mass M (see the figure below). There is non-zero coefficient of friction between the two blocks. Neglect the friction between the block of mass M and the table. 1) Plot the free body diagram for each of the blocks; 2) Find the work done by gravity on the block of mass m (the smaller one) in two coordinate systems shown above, if the height of the inclined plane is H. y x x y a) b)

4. 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?

5. Quiz A sled slides down a hill H m high with a slope of θ. The total mass of the sled plus contents is M. It starts from rest. There is no friction. Use the Work Energy Theorem to find the velocity of the sled at the bottom, and to show that it doesn’t depend on the angle of the hill.

6. All force are CONSERVATIVE or NON-CONSERVATIVE

7. A force is conservative if: The work done by the force in going from to is independent of the path the particle follows The work done by the force when the particle goes from to around a closed path, back to, is zero. or

8. Non-conservative: doesn’t satisfy the above conditions

9. If a force can be written as the derivative of some 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:

10. does NOT depend on path! 1D case:

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

12. Force of gravity: Potential energy function: Spring: Potential energy function: