Physics 111-101 Exam #3 Cheat Sheet October 22, 2007

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Physics 111-101 Exam #3 Cheat Sheet October 22, 2007

Physics 111-101 Exam #3 “Cheat Sheet” October 22, 2007

REMEMBER:

Calculator mode on DEGREE

Write Equations out

Rearrange for unknown variable

Make sure ALL units are in every step

Four Significant Figures

Make sure all units cross each other out

Kinematic Equations for Constant Acceleration
v = v0 + at / x–x0 = v0t + ½at2 / v2 = v02 + 2a(x-x0)
Universal Gravitational Constant (G)
6.6726 x 10-11 Nm2/kg2
Static and Kinetic Friction
fs = μsFN / fk = μkFN
Work Done By Constant Force
W = F cosθΔx
Work-Energy Theorem
W = ΔK
Kinetic Energy
K = ½mv22 - ½mv12
Work as a dot product
W = F · Δx / W = |F| |Δx| cosθ
Gravitational Potential Energy
Ug = mgh
Conservation of Mechanical Energy
The negative of the change in potential energy (U) / W = -ΔU
Mechanical Energy (E)
E = K + U
Non-Conservative Forces & Work – Energy Theorem
WNC = E2 – E1 = (K2 + U2) – (K1 + U1)
Average/Instantaneous Power
P = Δw/Δt / P = F · V
Units of Power
1 Watt = 1 J/s / 1 hp = 550 ftlb/s = 746 Watts
Momentum
p = mv
Impulse
J = FΔt
Impulse-Momentum Theorem
J = Δp
System of Objects Experiencing No External Forces
F = 0 = Δp/Δt
Collision in One-Dimension
Linear momentum conserved, kinetic conserved only in elastic. Perfectly Inelastic: objects stick together.
Elastic  Kinetic Energy = each other. Inelastic  lose Kinetic Energy
Center of Mass
xcm = m1x1 + m2x2 / m1 + m2

Example Problems

  1. Let A = 3i + 4j -74k and B = 12i – 0j + 18k
  2. Find A · B
  3. Find angle between A & B
  1. The graph shows the net external force component F cosθ along the displacement as a function of the magnitude s of the displacement. The graph applies to a 65kg ice skater. How much work does the net force component do on the skater from:
  2. 0 to 3.0m
  3. 3.0m to 6m
  4. If the initial speed of the skater is 1.5 m/s when s=0, what is the speed when s=6.0m?
  1. Kevin has a mass of 87kg and is skating with in-line skates. He sees his 22kg younger brother up ahead standing on the sidewalk, with his back turned. Coming up from behind, he grabs his brother and rolls off at a speed of 2.4m/s. Ignoring friction, find Kevin’s speed just before he grabbed his brother.
  1. A 75kg man on a skateboard is traveling at 12 m/s. A 250kg man on a scooter is traveling at -5 m/s. The second man’s speed after the collision is -1 m/s. What is the first man’s speed after the collision and what kind of collision was it?
  1. Batman (m=91kg) jumps straight down from a bridge into a boat (m=510kg) in which a criminal is fleeing. The velocity of the boat is initially +11 m/s. What is the velocity of the boat after Batman lands?
  1. A 5kg block is set in motion up an incline with an initial speed of 8m/s. The block comes to rest after travelling along the plane, which is inclined at an angle of 30° to the horizontal.
  2. What is the change of kinetic energy of the block?
  3. What is the change in potential energy of the block?
  4. What is the frictional force exerted on the block? (assumed to be constant)
  5. What is the coefficient of Kinetic friction?