Mechanics Resource Packet Contents by Topics

**Intepreting graphs**

- Given a graph of two interacting masses (x1(t) and x2(t) vs t) tell in words how each mass started out, and what happened between them during the time of the graph
- Given several graphs of x vs. t, identify regions of positive, negative, and zero acceleration

**1-D Kinematics** (x,v,a)

- calculate average velocity over a decreasing time interval
- calculate average acceleration over a decreasing time interval
- graph of v and a vs. t for a ball thrown vertically
- An ad talks about a student athlete who can hang in the air for 2.5 sec and understand why.
- Comment on good and bad 'hang times' for punts.
- A speed trap is set up based on time and distance. Draw three graphs corresponding to a speeder being i)above the speed limit, ii)below the limit, iii)at the speed limit when passing the second point in the speed trap.

**2-D Kinematics **(projectiles, etc.)

- ball launched to travel between two specified points
- balls thrown to collide in midair
- two connected arms rotating ('teacup' amusement park ride)

**Circular Motion**

- An
object travels along a circle, but not at constant speed.

Draw in its velocity and acceleration vector at various points. - A
mass suspended from the ceiling by a light string travels in a circular
path.

List all the forces acting on the mass, in order of decreasing magnitude, giving the direction of each force. - Describe the trajectory of a ball thrown in a rotating space station from one person toward another.

**Newton's Laws in 1-D**

- Stationary skier is pushed by friend; find skier's acceleration
- Wagon is propelled by a constant force, but is losing mass; calculate its acceleration
- Ball thrown vertically, graph position and velocity.
- Heavy mass suspended by a thread. Pull on thread below to break either upper or lower thread.
- grapefruit falling under air resistance
- ping pong ball with air resistance
- mass hanging from spring
- plot v vs. t for air drag linear in velocity; verify and interpret solution
- policeman and speeder

**Newton's Laws in 2-D**

- mass and spring on an incline
- mass and spring on incline with friction
- wheel and crank
- monkey and hunter student exercise w/ parametric plots

**Work, Dot Product**

- Forces are applied to a mass; say if the net work done on the mass is positive, negative or zero.
- dot product - which one is greatest, which one is least (qualitative comparison)?

**Work and Energy**

- In
moving a stationary book from the floor and setting it on a table, a person
does work.

But the book's KE does not change. Does this violate the work-KE theorem? - Where is an earthquake's energy stored just before the quake?

**Energy**

- skateboarder path after leaving ramp
- potential energy, conservative force, closed path
- Energy, force and equilibrium (force and equilibrium pts from given potential energy)

**Collisions and Impulse**

- Compare forces in a head-on collision between unequal masses
- Impulse of hammer on a plate
- Impulse of a tennis serve
- Impulse given by a fast charged particle to a nearby charge
- Airplane shooting at an enemy is stalled by gun recoil and crashes

**Springs and Masses**

- What happens to a spring's force constant if it is cut in half?
- For springs of different stiffness, which does more work when they are stretched equally?
- A car's bumper is connecected to the body by a spring. The body can stand 5.5 g's without crumpling. Will the design survive a 5-mph crash test? Is it a good design?
- Mass and spring on an incline
- Mass and spring on an incline with friction
- mass hanging vertically, supported by a spring
- frequency response of a mass-spring system
- why does an air cart collision take the same time at different speeds?
- collision of two masses via a spring (dsolve, odeplot)

**Rotation, Gravitation, Miscellaneous**

- moment of inertia of a long rod calculated by taking the rod to be a group of point masses
- Conservative force and potential energy
- Gravitational force by a long cylindrical rod
- Calculate torques on segments of a rod and see if this equals the torque calculated as if all the mass were at the CM of the rod (excel ss)
- Ditto but do the calculation in Maple
- Meter stick is kicked off-center. Describe its motion along the floor in the absence of friction.
- time for a stud wall to fall over