Difference between revisions of "Forest UCM NLM BlockOnIncline"

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Line 23: Line 23:
  
 
:<math>\vec{N} = \left | \vec{N} \right | \hat{j}</math>
 
:<math>\vec{N} = \left | \vec{N} \right | \hat{j}</math>
:<math>\vec{F_g} = \left | \vec{F_g} right | \left ( \sin \theta \hat{i} - \cos \theta \hat{j} \right )</math>
+
:<math>\vec{F_g} = \left | \vec{F_g} \right | \left ( \sin \theta \hat{i} - \cos \theta \hat{j} \right )</math>
 
:<math>\vec{F_f} = - kmv^2 \hat{i}</math>
 
:<math>\vec{F_f} = - kmv^2 \hat{i}</math>
  

Revision as of 02:39, 19 August 2014

Consider a block of mass m sliding down the inclined plane shown below with a frictional force that is given by

[math]F_f = kmv^2[/math]


200 px

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

200 px

Step 4: Define the Force vectors using the above coordinate system

[math]\vec{N} = \left | \vec{N} \right | \hat{j}[/math]
[math]\vec{F_g} = \left | \vec{F_g} \right | \left ( \sin \theta \hat{i} - \cos \theta \hat{j} \right )[/math]
[math]\vec{F_f} = - kmv^2 \hat{i}[/math]

Step 5: Used Newton's second law


Forest_UCM_NLM#Block_on_incline_with_friction