Dynamics

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Dynamics

• the branch of mechanics that deals with the
  motion and equilibrium of systems under the
  action of forces, usually from outside the
  system.

40S Physics Cara Katz, Yael Shrom, Hannah Glinter
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Outline of Unit

• 30S Review of Forces
• formulas
• Net Force
• Free Body Diagrams
• Forces and Motions (friction)
• Forces in 2-D
• Equilibrium in 1-D and 2-D
• Forces at an angle
• Inclined Planes

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30S Review

• Formulas
• Fgmg
• Fnetma
• FfµFn
• Example Question A box has a mass of 5.0 kg. The
  applied force is 25 N. µk0.2. Find Fg, Fn, Ff
  and the acceleration of the box.
• Step 1 Fgmg, Fg (5.0)(-9.8), Fg 49 N (down)
• Step 2 FnFg, Fn 49 N (up)
• Step 3 FfµFn, Ff (0.2)(49), Ff 9.8 N (left)
• Step 4 Fnetma, 15.2 N/5.0 a, a 3.04 m/s²

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30S Review

• Net Force
• vector sum of all the forces which act
  upon an object (sum of all the forces)

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30S Review

• Free Body Diagrams

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30S Review

• Forces and Motion (Friction)
• using the formulas
• Example
• A force of 60 N is applied to a 20 kg. mass
  on a surface, where the force of the friction is
  25 N. At what rate does this mass accelerate?
• Fa 60N
• m 20 kg.
• Ff 25 N
• Fnet 60-25 35 N
• a Fnet/m, a35/20, Fnet 1.75m/s²

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Forces in 2-D

• Things to remember
• change all diagonal forces into x and y
  components
• analyze y and x axis SEPARATELY!
• solve for Fnet x, Fnety and Fnet
• solve for Fn last
• Example Questions
• Case 1 object on surface
• Case 2 Applying a force to the object
• Case 3 Pulling at an angle
• Case 4 Pushing at an angle

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Forces in 2-D

• Case 1 Object sitting on a surface

Y axis Fg 49 N down Fn 49 N up Fnety 0 N
X axis No forces Fnetx 0N
Fnet0
Fnet Fnetx and Fnety0 as long as object is
not falling!!!!
Case 2 Applying a Force
X axis Ff 10N left Fa 60 N right Fnetx 50 N
right Fnet 50 N right
Y axis Fg 196 N (down) Fn 196 N (up) Fnety 0N
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Forces in 2-D

• Case 3 Pulling at an angle

Y axis Fn 59N (up) Fg 49N (down) FAY 10N
(up) Fnet Y 0N
X axis Ff 20N (left) FAX 30N (right) Fnet X
10N (right) Fnet 10N (right)
If you were to look for acceleration, you
use Fnet ma In this case, 10 5a Acceleration
2m/s²
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Forces in 2-D

• Case 4 Pushing at an Angle

Y Axis Fn 69N (up) Fg 49N (down) FAY 20N
(down) Fnet Y 0N
X Axis Ff 20N (left) FAX 50N (right) Fnet X
30N (right) Fnet 30N (right)
Using what you know, find the acceleration!
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Equilibrium

• An Object is in equilibrium when it has zero
  acceleration.
• Fnet must be zero in x and y directions
• 1-D Problems
• Word Problem
• Suppose you had a sign with a mass of 20.0 kg.
  suspended by two ropes, one on each side of the
  sign. What would be the tension in each of the
  ropes?
• Answer Fg mg
• Fg (20)(9.8)
• Fg 196 N (down)
• Therefore each rope has a tension of 98 N.
• Picture Problem

What is the Fnet and is this an
equilibrium? Fnet 5 N (left)gt therefore because
there is an Fnet that is not 0, this is not an
equilibrium
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Equilibrium

• 2-D Problems
• Example Problem
• Suppose a sign is hanging from 2 wires, as
  shown in the diagram. The sign in 30 kg. What is
  the tension is each of the ropes?

T3 Fg Fg (30)(9.8) Fg 294 N (down) Sin45 147/
T1 T1 207.9 N Sin37 147/ T2 T2 244.3 N
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Forces at an Angle

• It requires less force to pull than push (this is
  due to the decreased normal force, which
  decreases the force of kinetic friction.
• Hint this is the same as Case 3 and 4, but this
  time youre given the angle!
• Example Problem
• A 20.0 Kg box is dragged along a horizontal
  floor with a force of 100.0 N. The force is
  applied at 40.0 above the horizontal and to the
  right. If the coefficient of kinetic friction is
  0.30, what is the net force on the box, and what
  is its acceleration?

Fg 196 N Cos40Fax/100, Fax76.6 N
(right) Sin40Fay/100, Fay 64.3 N
(up) FnFg-Fay, Fn 131.7 N Ff 39.5 N Fnet
37.1 N (right) (Fax- Ff) a 37.1/20, a 1.86 m/s²
Using the kinematics equations, you can find
time is asked to! Remember v10
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Inclined Planes
Things To Remember 1) Fn Fgy 2) Fnet Fgx
(because there is no Ff) 3) Fgx (Fg)(sin?)
Fgx- also known as parallel to plane 4) Fgy
(Fg)(cos?) Fgy- also known as
perpendicular force
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Good Luck On the Test!
We Know you'll do Fabulous!