Difference between revisions of "Forest UCM NLM BlockOnIncline"
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:<math>\sum F_{ext} = mg \sin \theta -mkv^2 = ma_x = m \frac{dv_x}{dt}</math> | :<math>\sum F_{ext} = mg \sin \theta -mkv^2 = ma_x = m \frac{dv_x}{dt}</math> | ||
− | : <math>\ | + | : <math>\int_0^t dt = \int_0^v \frac{dv}{g\sin \theta - kv^2}</math> |
Integral table <math>\Rightarrow</math> | Integral table <math>\Rightarrow</math> |
Revision as of 03:35, 20 August 2014
the problem
Consider a block of mass m sliding down the inclined plane shown below with a frictional force that is given by
Find the blocks speed as a function of time.
Step 1: Identify the system
- The block is the system with the following external forces, A normal force, a gravitational force, and the force of friction.
Step 2: Choose a suitable coordinate system
- A coordinate system with one axis along the direction of motion may make solving the problem easier
Step 3: Draw the Free Body Diagram
Step 4: Define the Force vectors using the above coordinate system
Step 5: Used Newton's second law
in the direction
Integral table
Identities
Solving for
- v = \tan \left ( \sqrt{gk\sin \theta} i t \right )
- =