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
2E: Newton's second law
How do we predict the action of forces on motion?
How is the Second Law used?
Motion changes through the action of forces. The changes occur through acceleration because acceleration is a direct consequence of a non-zero net force. Models of motion start by calculating the acceleration from knowledge of forces. Acceleration is used to determine changes in velocity, which are used to determine changes in position.

Part 1: Modeling the action of a force
Doing the Investigation
In this interactive simulation, you will create a model for the motion of the ErgoBot by adjusting the values of the initial velocity, force, and mass. The goal is to cause the force to effect the ErgoBot's motion to pass through the target circles on the position vs. time graph.
How to use the interactive simulation
  1. The interactive model shows position and velocity versus time graphs. Red circles on the position vs. time graph are “targets.” Adjust the initial parameters, initial velocity (v0), force (F) and mass (m) so the curves hit both targets.
  2. [Run] starts the simulation. [Stop] stops it without changing values. [Clear] resets all variables to zero. [Reset] resets all variables and sets new targets.
  3. Enter values in the white boxes. The top score of 100 is achieved by hitting the center of each target.
Analysis
  1. Find a successful scenario using the same targets with a mass of 2 kg then change the mass to 4 kg. What single additional change makes the solution work again? Why?
  2. Compare how 1 N of force effects the motion of a 5 kg ErgoBot versus a 0.2 kg ErgoBot.
  3. Do you think the solution to this problem is unique or are there many possible solutions? Support your answer with evidence.
Assess Your Knowledge
  1. Describe the connection between force and acceleration.
  2. Describe in words how the three equations work together to determine motion.
Going Further
    A competitor at the lumberjack games competes in the log race. She must roll a 500 kilogram log 100 meters. To beat Paul Bunyan's record, she must complete the log roll in under one minute. What is the minimum amount of constant force she must apply to the log?

Part 2: Dynamic modeling
Doing the Investigation
Realistic motion simulations work in time steps. For each time step the net force is used to calculate the instantaneous acceleration. The acceleration determines the change in velocity for that time step. The change is added to the velocity from the previous time step and used to determine the position at the end of the time step.
In this interactive simulation, you will create a model for the motion of the ErgoBot by adjusting the values of the initial position, initial velocity, mass, and four periods of force. The goal is to cause the force to effect the ErgoBot's motion to pass through the four target circles on the position vs. time graph.
How to use the interactive simulation
  1. The second model allows you to set the force for four different time intervals, each 2.5 seconds long.
  2. In this model, unlike the first, you can set the starting position (x0) in addition to the initial velocity, mass, and four periods of force.
  3. Try to hit the centers of the four target red circles.
Analysis
  1. When the ErgoBot has a mass of 2 kg, put on a force of 1 N for the first section and −1 N for the second section. Observe how this effect the ErgoBot's motion. Explain why.
    Now apply those force in the opposite order. Observe and explain.
  2. How does the ability to set the starting position effect the difficulty of getting a perfect score?
  3. Do you think the solution to this problem is unique or are there many possible solutions? Support your answer with evidence.
Assess Your Knowledge
  1. What sections of the graphs are curved and which are linear? Why?
  2. If the ErgoBot's mass is doubled, how is the displacement effected?
Going Further
    A high quality sports car can go from 0 to 60 mph (26.8 m/s) in 3 seconds. The mass of this car is 1365 kg.
    • What is the force applied by the engine to accelerate this car?
    The same car can stop from that speed in 50 meters.
    • What is the force applied by the brakes to stop this car?

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