Physics 218: Mechanics Instructor: Dr. Tatiana Erukhimova Lecture 21

Quiz This is a one-dimensional problem. Suppose a particle is attracted to the origin with a force Find the potential function.

Examples Strategy: write down the total mechanical energy, E, E = KE + U at the initial and final positions of a particle:

Work-energy theorem: Mechanical energy is conserved!

Then use or

H

Water Slide Who hits the bottom with a faster speed?

Roller Coaster You are in a roller coaster car of mass M that starts at the top, height H, with an initial speed V 0 =0. Assume no friction. a)What is the speed at the bottom? b)How high will it go again? c)Would it go as high if there were friction? H

Roller Coaster with Friction A roller coaster of mass m starts at rest at height y 1 and falls down the path with friction, then back up until it hits height y 2 (y 1 > y 2 ). Assuming we don’t know anything about the friction or the path, how much work is done by friction on this path?

A gun shoots a bullet at angle θ with the x axis with a velocity of magnitude V m. What is magnitude of the velocity when the bullet returns to the ground? How high it will go?

Block of mass m has a spring connected to the bottom. You release it from a given height H and want to know how close the block will get to the floor. The spring has spring constant k and natural length L. H y=0