2.2 
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Interactive Simulations   Position and displacement in one dimension    Displacement and position in two dimensions    Solve v=dx/dt for dt    Velocity, position, and time (basic version)    Velocity, position, and time (more advanced version)    Acceleration (basic version)    Acceleration (more advanced version)    Static equilibrium    Static equilibrium and the lever    Newton's second law (basic version)    Newton's second law (more advanced version)    Circular motion interactive simulation    Orbits of the planets and dwarf planets    Orbits simulation Interactive Calculators   Speed calculator    Velocity calculator    Acceleration calculator    Velocity in accelerated motion    Average velocity calculator    Hooke's law calculator    Torque calculator    Rotational equilibrium and torque    Newton's second law calculator    Momentum calculator    Angular velocity    Linear velocity and angular velocity    Centripetal acceleration    Centripetal force    Law of universal gravitation calculator
1 - Science of Physics
2 - Forces and Motion      Chapter 2 at a glance      2.1 - Motion      2.2 - Force, momentum, and Newton's laws      2.3 - Circular motion      2.4 - Solving harder physics problems      2.5 - Chapter review3 - Energy Transformations4 - Waves and Sound
5 - Electricity and Magnetism
6 - Light and Optics
7 - The Atom
8 - Linear Motion
9 - Vectors and Forces
10 - Forces
11 - Newton's Laws and Gravitation
12 - Circular Motion and Gravitation
13 - Torque and Static Equilibrium
14 - Momentum and Collisions
15 - Angular momentum
16 - Power and Machines
17 - Harmonic Motion
18 - Waves
19 - Sound
20 - Electricity
21 - Electric and Magnetic Fields
22 - Electromagnetism and Induction
23 - Light and Color
24 - Geometrical Optics
25 - Electromagnetic Radiation
26 - The Properties of Matter
27 - Thermodynamics and Heat Transfer
28 - The Atom
29 - The Quantum Theory
30 - TBD
31 - TBD
32 - TBD
33 - TBD
34 - TBD
35 - TBD
36 - TBD
37 - The atomic nucleus and radioactivity
38 - Nuclear reactions
39 - Relativity
40 - Particle physics and the standard model
41 - Electronics (semiconductors)
42 - Nuclear technology
43 - Lasers and photonics
44 - Metals, alloys and materials science
45 - Communications technology
46 - Buildings and structures
47 - Energy technology
48 - Biophysics
49 - Matter and Energy, Space and Time
50 - Energy Transformations
51 - Nanotechnology
52 - Website Videos
53 - ExtraStuff
55 - Modeling Motion, Friction, and Center of Mass
56 - Work and the Conservation of Energy
2D: Static equilibrium
How do we predict when something will move or not?
How do we determine forces we cannot measure?
Objects remain at rest only when the net force and the net torque are zero. The converse is also true: if an object is at rest you know the net force and the net torque must be zero. This last fact is used to determine unknown forces while the first statement predicts whether an object will remain at rest or begin to move.

Part 1: A simply supported beam
Doing the Investigation
In this interactive simulation, you will explore free-body force diagrams for static equilibrium.
How to use the interactive simulation
  1. Ths interactive model allows you to place up to four masses on a beam that is supported at its ends. You can adjust the placement of the masses by entering distances for each one.
  2. The beam is 5 meters long and has a mass of 25 kilograms (weight of 245 newtons).
  3. You can place two five, a ten, and a fifteen kilogram mass anywhere on the bar. Their distance (x) is measured from the left end of the bar.
  4. [Reset] clears all the masses and distances.
  5. The [Force] or [Torque] button toggles between displaying the force or torque diagrams below the bar.
  6. The force setting shows a free-body diagram of the situation and calculates the upwards forces and downward forces.
  7. The torque setting shows all the torques in the situation and calculates the clockwise and counterclockwise torques. In the torque setting, you can set where the fulcrum is considered, thus where the torques are measured from.
Analysis
  1. Find a solution in which two 5 kg masses create equal support forces from each end. The two masses may not be at the ends or in the same place. There are many possible answers. What is a common characteristic of all the possible answers?
  2. Create an equilibrium in which a force scale under the left support will measure a force of 300 N.
Assess Your Knowledge
  1. What is the relationship between the upwards and downwards forces on the free-body diagram?
  2. What is the relationship between the clockwise and counterclockwise torques when measuring torques?
  3. Describe what happens when you change the point around which torques are calculated. Does the solution depend on which point you select as the center of rotation? Why is this true?
Going Further
    Tim is a veteran window-washer. He is suspended 100 meters above the ground on a 100 newtons, 10 meter-long plank held up by ropes tied to the roof of the building. Tim carries his bucket with him when he washes, and together they weigh 800 newtons.
    • Draw a free-body diagram Tim washing the windows with him standing in the center of the plank. Include forces of Tim, the plank, and the ropes.
    Tim has had his equipment since he started washing windows many years ago, and his ropes are growing thin. Each rope can only provide 600 newtons of force without breaking.
    • Tim moves 2.5 meters from the center to wash. Will the ropes break? Will Tim's buckets fall on the people below?

Part 2: A lever
Doing the Investigation
In this interactive simulation, you will explore static equilibrium using a simple lever found in playground equipment such as a see-saw.
  1. The interactive model allows you to place the same four masses on a lever that is free to tip one way or the other.
  2. [Reset] clears all the masses and distances.
  3. The [Force] or [Torque] button toggles between displaying the force or torque diagrams below the bar.
  4. Additionally, the torque setting allows you to set whether the fulcrum (pivot point) is in the center or at either end.
Analysis
  1. Find a solution in which a 5 kg mass and a 10 kg mass are placed so that the lever is in equilibrium. What is the relationship between the torques created by the two weight forces?
  2. Create a situation in which the net torque is +100 Nm and another in which the net torque is −100 Nm. What happens to the lever in either case? Does it tip clockwise or counterclockwise?
Assess Your Knowledge
  1. Why is the lever harder to balance than the beam in the first part?
    Why can the lever not be balance when the fulcrum is on one end?
  2. How can the direction of tipping be predicted?
  3. Describe what happens when you change the point around which torques are calculated. Does the net torque of the solution depend on which point you select as the center of rotation? Why or why not?
  4. If you and your heavier friend are trying to balance a see-saw, which one of you should sit closer to the center?
Going Further
    Why is is easier to lift a heavy objects using a wheel barrow then without one?
    Estimate the force required to lift a 100 pound sandbag with a wheelbarrow.

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