# Forest UCM NLM BlockOnIncline

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# the problem

Consider a block of mass is 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 5: Used Newton's second law

Motion in the direction 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.

Integral table

Identities

substituting

Solving for

Integral table

solving for the fall time