Physics 2211 Spring 2005

1
Physics 2111 Lecture 7

• More discussion of dynamics
• Review
• The Free Body Diagram
• The tools we have for making solving problems
• Ropes Pulleys (tension)
• Hookes Law (springs)

2
Review Newton's Laws

• Law 1 An object subject to no external forces
  is at rest or moves with a constant
  velocity if viewed from an inertial reference
  frame.

3
Gravity

• What is the force of gravity exerted by the earth
  on a typical physics student?

• Typical student mass m 55kg
• g 9.8 m/s2.
• Fg mg (55 kg)x(9.8 m/s2 )
• Fg 539 N (weight)

4
ExampleMass vs. Weight

• An astronaut on Earth kicks a bowling ball and
  hurts his foot. A year later, the same astronaut
  kicks a bowling ball on the moon with the same
  force.
  His foot hurts...

Ouch!
(1) more (2) less (3) the same

• The masses of both the bowling ball and the
  astronaut remain the same, so his foot will feel
  the same resistance and hurt the same as before.

5
ExampleMass vs. Weight
Wow! Thats light.

• However the weights of the bowling ball and the
  astronaut are less

W mgMoon gMoon lt gEarth

• Thus it would be easier for the astronaut to pick
  up the bowling ball on the Moon than on the Earth.

6
The Free Body Diagram

• Key phrase here is for an object.

7
The Free Body Diagram

• Consider the following case

• What are the all the forces acting on the
• P plank
• F floor
• W wall
• E earth ?

8
The Free Body Diagram

• What are the forces acting on the plank ?

• Isolate the plank from
• the rest of the world.

9
The Free Body Diagram

• What are the forces acting on the plank ?

• Isolate the plank from
• the rest of the world.

• This is a free body diagram.

10
Aside statics

• In this example the plank is not moving...
• It is certainly not accelerating!

• This is the basic idea behind statics in
  engineering mechanics.

11
Example

• Example dynamics problem
• A box of mass m 2 kg slides on a horizontal
  frictionless floor. A force Fx 10 N pushes on
  it in the x direction. What is the acceleration
  of the box?

12
Example

• Draw a picture showing all of the forces

13
Example

• Draw a picture showing all of the forces.
• Isolate the forces acting on the block.

14
Example

• Draw a picture showing all of the forces.
• Isolate the forces acting on the block.
• Draw a free body diagram.

• Solve Newtons 2nd Law for each component

15
Example

• FX maX
• So aX FX / m (10 N)/(2 kg) 5 m/s2.
• FY maY or FFB - mg maY
• But aY 0
• So FFB mg.
• The vertical component of the forceof the floor
  on the object (FFB ) isoften called the Normal
  Force (N ).
• Since aY 0 , N mg in this case.

16
Example Recap
N mg
y
FX
aX FX / m
x
mg
17
ExampleNormal Force

• A block of mass m rests on the floor of an
  elevator that is accelerating upward. What is
  the relationship between the force due to
  gravity and the normal force on the block?

18
ExampleNormal Force

• Draw a free body diagram

• All forces are acting in the y direction, so use

19
Tools Ropes Strings

• Ropes strings can be used to pull from a
  distance.
• Tension (T) at a certain position in a rope is
  the magnitude of the force acting across a
  cross-section of the rope at that position.
• The force you would feel if you cut the rope and
  grabbed the ends.
• An action-reaction pair.

20
Tools Ropes Strings

• Consider a horizontal segment of rope having mass
  m
• Draw a free-body diagram (ignore gravity).

• Using Newtons 2nd law (in x direction)
  FNET T2 - T1 ma
• So if m 0 (i.e., the rope is light) then T1
  ??T2

21
Tools Ropes Strings

• An ideal (massless) rope has constant tension
  along the rope.

• If a rope has mass, the tension can vary along
  the rope
• For example, a heavy rope hanging from the
  ceiling...

• We will deal mostly with ideal massless ropes.

22
Tools Ropes Strings

• The direction of the force provided by a rope is
  along the direction of the rope

Since ay 0 (box not moving),
23
Tools Pegs Pulleys

• Pegs and pulleys are used to change the direction
  of forces
• An ideal massless pulley or ideal smooth peg will
  change the direction of an applied force without
  altering the magnitude

24
Tools Pegs Pulleys

• Pegs and pulleys are used to change the direction
  of forces
• An ideal massless pulley or ideal smooth peg will
  change the direction of an applied force without
  altering the magnitude

25
Springs

• Hookes Law The force exerted by a spring is
  proportional to the distance the spring is
  stretched or compressed from its relaxed position
  (linear restoring force).
• FX -k x Where x is the displacement from
  the relaxed position and k is the constant
  of proportionality.

26
Springs

• Hookes Law The force exerted by a spring is
  proportional to the distance the spring is
  stretched or compressed from its relaxed position
  (linear restoring force).
• FX -k x Where x is the displacement from
  the relaxed position and k is the constant
  of proportionality.

27
Springs

• Hookes Law The force exerted by a spring is
  proportional to the distance the spring is
  stretched or compressed from its relaxed position
  (linear restoring force).
• FX -k x Where x is the displacement from
  the relaxed position and k is the constant
  of proportionality.