Difference between revisions of "Forest UCM NLM BlockOnIncline"

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Find the blocks speed as a function of time.
 
Find the blocks speed as a function of time.
  
Step 1:  Identify the system
+
=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.
 
: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
+
=Step 2: Choose a suitable coordinate system=
  
 
: A coordinate system with one axis along the direction of motion may make solving the problem easier
 
: 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 3: Draw the Free Body Diagram=
  
 
[[File:TF_UCM_FBD_InclinedPlaneWfriction.png | 200 px]]
 
[[File:TF_UCM_FBD_InclinedPlaneWfriction.png | 200 px]]
  
Step 4: Define the Force vectors using the above coordinate system
+
=Step 4: Define the Force vectors using the above coordinate system=
  
 
:<math>\vec{N} = \left | \vec{N} \right | \hat{j}</math>
 
:<math>\vec{N} = \left | \vec{N} \right | \hat{j}</math>
Line 26: Line 26:
 
:<math>\vec{F_f} = - kmv^2 \hat{i}</math>
 
:<math>\vec{F_f} = - kmv^2 \hat{i}</math>
  
Step 5: Used Newton's second law
+
=Step 5: Used Newton's second law=
 +
 
 +
==:in the <math>\hat i</math> direction==
  
:in the <math>\hat i</math> direction
 
 
:<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>
 +
: \int dt = \int \frac{dv}{g\sin \theta - mkv^2}
  
 
[[Forest_UCM_NLM#Block_on_incline_with_friction]]
 
[[Forest_UCM_NLM#Block_on_incline_with_friction]]

Revision as of 02:48, 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 )= mg \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

:in the [math]\hat i[/math] direction

[math]\sum F_{ext} = mg \sin \theta -mkv^2 = ma_x = m \frac{dv_x}{dt}[/math]
\int dt = \int \frac{dv}{g\sin \theta - mkv^2}

Forest_UCM_NLM#Block_on_incline_with_friction