Physics 2710 Exam III
December 10, 2012
Please circle the letter corresponding to the best answer.
1. At room temperature the product k BT is closest to
(a) 6x106 eV
(b) 1/40 eV
(c) 1 eV
(d) 12,000 eV
Questions 2-3 refer to: A macroscopic system con
Collisions (1D, 2D; Elastic, Inelastic)
When there are no external forces present the momentum of a system will remain unchanged. (pi = pf)
If the kinetic energy before and after an interaction is the same, the "collision" is said to be elast
Momentum Impulse Conservation of momentum Center of mass Motion of the center of mass
Consider two interacting bodies:
Fnet t If we know the net force on each body then v = at = m
The velocity change for each mass will be different if
Relationship between conservative forces and PE Energy diagrams
How are conservative forces related to potential energy?
dW = F dr = -dU dU = -F dr
W = F dr
dU ( x ) Fx = - dx F=- U
The elastic potential energy of a spring:
Potential energy Conservative forces Mechanical energy Conservation of energy Appendix: Conservative forces
Potential energy is energy associated with the configuration of a system of objects that exert forces on one another.
Springs Hooke's law Work by nonconstant forces Power
If I pull the spring to the right, the spring pulls to the left on me.
Experiments with some springs show that Fapplied spring stretch so that F = kx (Hooke's law).
The work done
The material on these slides has been collected from student papers over several years. I have removed source information for the sake of clarity. Look for what is wrong with each snippet. Problems may be grammar-rel
Simple harmonic motion Mass and spring system
Simple harmonic motion (SHM) occurs when the restoring force (the force directed toward a stable equilibrium point) is proportional to the displacement from equilibrium.
The motion of a mass on
Kepler's three laws Application: Detection of exoplanets
Johannes Kepler used observations made by Tycho Brahe to "discover" three laws of planetary motion.
Kepler's 1st Law: The orbits of the pla
Gravity Weight Gravitational field strength Work by gravity/gravitational potential energy Escape velocity
Gravity is the force between two masses. Gravity is a longrange or field force. No contact is needed between the bodies. The force of g
The conditions for equilibrium are
F = 0 = 0
To have static equilibrium p = 0 and L = 0 too.
Center of gravity
If g is the same for all points within a body, then rcm = rcg.
An object that is 30 km tall will have a 1% variation in g
Angular Momentum Conservation of angular momentum
L = rp
The magnitude of L is
L = r p = rp
The direction of L is given by the right hand rule and its unit is kg m2/s.
Curl the fingers of your right hand so that they curl i
Rolling An object that is rolling combines translational motion (its center of mass moves) and rotational motion (points in the body rotate around the center of mass). For a rolling object
K tot = K T + K rot 1 2 1 2 = mvcm +
Torque Rotational form of Newton's 2nd law
A body can be set in rotational motion by the action of a torque. A rotating (spinning) body will continue to rotate unless it is acted upon by a torque.
hinge Q: Where on a door do you push to open
and as vectors Rotational kinetic energy Moment of inertia Parallel axis theorem
It will be a good idea to review lecture 9.
Linear and angular motion
Independent Time-t variable Variable coordinate First derivative Second derivative Constan
Work and Energy The scalar product Kinetic energy The work-energy theorem
Energy is a scalar quantity that is associated with a state (or condition) of an object.
Kinetic energy is associated with an object's state of motion. Potential energy
Example of 2D motion: Circular motion Conditions for circular motion Examples
is the angular position. Angular displacement:
= f - i
Note: angles measured CW are negative and angles measured CCW are positive. is measu
Examples using N2L
Example: A box slides across a rough surface. If the coefficient of kinetic friction is 0.3, what is the acceleration of the box?
FBD for box: fk;sb
Apply Newton's 2nd Law:
F = N
+ f k;sb + w eb = ma
Mass vs. weight Examples of forces Gravity (long-range force) Normal force (contact force) Tension (contact force) Friction (contact force) Drawing free body diagrams
Mass vs. weight
Mass is an inherent property of a body, independent of the b
Introduction to forces Newton's three laws Equilibrium
Isaac Newton was the first to discover that the laws that govern motions on the Earth also applied to celestial bodies.
Over the next few chapters we will study how bodies interact with on
Motion in two and three dimensions Example of 2D motion: Projectile motion
A particle moves along the blue path as shown. At time t1 its position is r0 and at time t2 its position is rf.
v0 r vf
The instantaneous velocity points tangent to t
Motion with constant acceleration Free Fall
Motion With Constant Acceleration
Consider an object with an acceleration a. What is the object's velocity as a function of time?
dv a= dt
This is a differential equation. Its solution is the functio
Time and position Distance and displacement Velocity and speed Acceleration
t1 would represent an instant of time as read from a clock.
The difference between two instants of time is a time interval: t = t2 t1.
Position, distance, and d
Vector vs. Scalar Vector addition Unit vectors
Vectors versus scalars:
A vector is a quantity that has both a magnitude and a direction. A force is an example of a vector quantity. Vector magnitudes have units.
A scalar is just a number usuall
Why study Physics? Physics Speak Units Approximations
Why Study Physics?
Physics is the foundation of every science (astronomy, biology, chemistry.) Many pieces of technology and/or medical equipment and procedures are developed with the help