Free Body Diagrams

1
Free Body Diagrams

• Calculating the net force
• Calculating the component of net force in the
  direction of motion
• Notice If we restrict our interest to the
  translational movement only (no rotation of the
  body) all forces can be considered to be attached
  to the bodys center of gravity.
• It is useful to indicate the magnitude of the
  force by the length of the arrow.

2
Example Hebb elevator

• Hebb elevator has a mass of 400kg. It is pulled
  up by a steel cable. Four people each weighing 75
  kg are in the elevator planning to go up to the
  lab.
• What is the tension on the cable when the
  elevator is at rest?
• What is the tension on the cable when the
  elevator is accelerating up at 1m/s2 ?
• What is the tension on the cable when the
  elevator is accelerating down at 1m/s2

3
Example Hebb elevator

• Hebb elevator has a mass of 400kg. It is pulled
  up by a steel cable. Four people each weighing 75
  kg are in the elevator planning to go up to the
  lab.
• What is the tension on the cable when the
  elevator is at rest?

T
T -mg -700kg(-9.8m/s2) 6860N Positive is
up.
mg
4
Example Hebb elevator

• Hebb elevator has a mass of 400kg. It is pulled
  up by a steel cable. Four people each weighing 75
  kg are in the elevator planning to go up to the
  lab.
• What is the tension on the cable when the
  elevator is accelerating up at 1m/s2 ?

T
T mg ma T ma-mg m(a-g) 700kg(1m/s2 -
(-9.8m/s2) 700kg 10.8m/s2 7560N
mg
5
Example Hebb elevator

• Hebb elevator has a mass of 400kg. It is pulled
  up by a steel cable. Four people each weighing 75
  kg are in the elevator planning to go up to the
  lab.
• What is the tension on the cable when the
  elevator is accelerating down at 1m/s2?

T
T mg - ma T -ma-mg m(-g-a) 700kg
(-(-9.8 m/s2) (-1 m/s2)) 700kg 8.8m/s2
6160N
mg
6
Interactive systems and environment
7
Newtons third law of motion

• Whenever one object exerts a force on the
  second object the second exerts an equal and
  opposite to force on the first.

8
Demo People on carts 3 trialsPerson A
pushing Person BPerson B pushing Person ABoth
pushing each otherWhat results do we expect?
9
Demo with the two carts on the track and force
probes.
10
Action-Reaction Pairs of Forces

• Have to act on different bodies.
• Have identical magnitude and act in the opposite
  directions
• Have the same origin (for example gravitational,
  elastic, magnetic, electrostatic)
• Act simultaneously

11
Action reaction force paradox

• I am pushing the table the table pushes me back
  with exactly the same force. Why it accelerates?
• Action reaction pairs on free body diagrams

12
Propulsion forces
13
Example 1 A tug with two barges
1
2
A tug of mass m1 20 000kg and an engine which
can create thrust of 100 000 N is starting its
trip. It is going to pull two barges one of mass
50 000 kg and one of the mass of 100 000 kg. What
is going to be the acceleration of the tug and
the barges. What is the tension on the cable
between tug and barge 1? What is the tension on
the cable between the barges?
14
What is the force propelling the tug?
15
Example 1 A tug with two barges
FP 100 000N m1 20 000kg
m2 50 000
m3 100 000
Free body diagrams? a ? T1 ? (Tension on
the cable between tug and barge 1) T2 ?
(Tension on the cable between barges)
16
We can consider the horizontal motion only (we do
not expect or observe vertical motion)
-T1 FP 100 000N
-T2 T1
T2
17

• Net force on the tug
• FP T1 ax 20 000
• Net force on barge 1
• T1 T2 ax 50 000
• Net horizontal force on barge 2
• T2 ax 100 000

18

• All three vessels are moving with the same
  acceleration ax
• FP T1 ax 20 000
• T1 T2 ax 50 000
• T2 ax 100 000
• T1 T2 ax 50 000
• T1 ax 50 000 ax 100 000 ax 150 000
• FP T1 ax 20 000
• FP ax 20 000 T1 ax 20 000 ax 150
  000
• FP ax 170 000
• ax 100000N/170 000kg 0.59 m/s2
• T2 0.59 m/s2 100 000kg 59 000N
• T1 T2 ax 50 000 88500N

19
Friction

• Kinetic friction
• Static friction
• Friction force does not depend on the contact
  area!
• Demo with the block pulled by a spring scale

20
Coefficients of friction

• Static
• S max(fs)/n
• fs ? ? S n
• Kinetic
• K fk /n
• fk ? K n
• ? S gt ? K