Physics 218: Mechanics Instructor: Dr. Tatiana Erukhimova Lecture 17

Nobel prize in physics 2011 Saul Perlmutter, Brian P. Schmidt, Adam G. Riess "for the discovery of the accelerating expansion of the Universe through observations of distant supernovae"

The Expanding Universe On large scales, galaxies are moving apart, with velocity proportional to distance. It’s not galaxies moving through space. Space is expanding, carrying the galaxies along! The galaxies themselves are not expanding!

Expanding universe: like a balloon Galaxies are at rest in the comoving (expanding) frame Due to the presence of matter, the universe is non-stationary: all distances change; scale factor R(t) is a function of time Like any analogy, the balloon analogy has its limits. In the analogy, the balloon expands into the region around it---there is space beyond the balloon. However, with the expanding universe, space itself is expanding in three dimensions---the whole coordinate system is expanding. Our universe is NOT expanding ``into'' anything ``beyond''.

A block of mass m starts at the top of an inclined plane. The coefficient of friction between the plane and the block is . Assuming the block slides down the plane calculate the work done by each force.

Work Energy Theorem

A person is pulling a crate of mass M along the floor with a constant force F over a distance d. The coefficient of friction is . (a)Find the work done by the force F on the crate. (b)Same if F changes as F 0 (1+x 2 /d 2 ). (c)Find the work done by the force of friction on the crate (F is constant). (d)Find the net work done on the crate if the crate is pulled with a constant velocity. (e)Find the final velocity of the crate if the crate is pulled with a non-zero acceleration starting from the rest. M

x

Problem 2 p.122 A 3 slug mass is attached to a spring which is pulled out one foot. The spring constant k is 100 pounds/ft. How fast will the mass be moving when the spring is returned to its unstretched length? (Assume no friction.)

Have a great day! Reading: Chapter 7 Hw: Chapter 7 problems and exercises