Forest UCM NLM BlockOnIncline
Consider a block of massis sliding down the inclined plane shown below with a frictional force that is given by
How long does it take to fall a distance ?
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
Motion in thedirection described by Newton's second law is:
- Notice a terminal velocity exists when
- This means that the block does not stop sliding but instead it reaches a minimal (terminal) velocity.
Insert the terminal velocity constant into Newton's second law
before we had in the numerator and could do a substitution, but not this time, use an integral table.
solving for the fall time