Variations on a Theme

The following 8 scenarios are the most common variations on the net force acting on an object. These scenarios will capture the essence of an object undergoing constant acceleration both with and without friction.

For each of the 8 scenarios, complete the following:

• Sketch the scenario, indicating the location of the essential variables (m1, m2, v0, θ, μs, μk, and g) involved.

• Sketch a velocity-time graph of the motion of the object 

  • Be sure to include important: 

    • Points (max, min, intercepts)

    • Slopes (relative values)

    • Areas under the curve (area of a v-t graph is the displacement of the object)

  • Comparative v-t graphs may be useful in describing the differences between frictionless and friction cases)

• Once you have the various forces identified, determine the sum (∑F) in the horizontal/vertical directions or parallel/perpendicular directions. 

  • Describe these forces in their root values (m, g, and θ)

• Create an algebraic equation to describe the acceleration in each of the 8 scenarios using the variables: m1, m2, v0, θ, μs, μk, and g as necessary.