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Find Magnitude & Direction for acceleration

  • #1
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Homework Statement


Block B has acceleration of 4 m/s2... Relative acceleration of block A w/ respect to B is 4 m/s2. Find magnitude & direction of accel for A?

Homework Equations


a_A = a_B + a_A/B

x_A = x_B + x_A/B

y_A = y_B + y_A/B

The Attempt at a Solution



x & y components:
-4cos(20) = -3.76
-4sin(20) = -1.37

-3.76 = 4 + x_A/B

x_A/B = -7.76

y_A/B = -1.37

|a| = sqrt( -7.76^2 + -1.37^2 ) = 7.88 m/s2

direction: tan -1 * (-1.37/-7.88) = 10.01 degrees
 

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Answers and Replies

  • #2
NascentOxygen
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aa|b :
x & y components:
-4cos(20) = -3.76
-4sin(20) = -1.37

aa = ab + aa|b
x components:
-3.76 = 4 + x_A/B
Hi ladkee. http://img96.imageshack.us/img96/5725/red5e5etimes5e5e45e5e25.gif [Broken]

Check above.
 
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  • #3
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what is the next step to find the magnitude of acceleration for a_A, are you saying use (-3.76, -1.37) as the x&y components?
 
  • #4
NascentOxygen
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I just added an extra line to my post. Can you fix your line I've marked with a cross?
 
  • #5
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I just added an extra line to my post. Can you fix your line I've marked with a cross?
 
  • #6
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Hi ladkee. http://img96.imageshack.us/img96/5725/red5e5etimes5e5e45e5e25.gif [Broken]

Check above.

I'm not sure what you mean by that? .....so are you saying for the x & y components I need to use are (-3.76, -1.37). How do you find the magnitude & direction for acceleration for this particular problem? please help, I need a clear response.
 
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  • #7
NascentOxygen
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Those are the x and y components of the smaller block's relative acceleration, yes. You worked them out.

I pointed out that you incorrectly applied the formula (which I highlighted by writing it in red). Can you apply that formula correctly to determine the x component of a's acceleration? So I'm saying there is something wrong in how you substituted values into that formula aa = ab + ...
 
  • #8
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Those are the x and y components of the smaller block's relative acceleration, yes. You worked them out.

I pointed out that you incorrectly applied the formula (which I highlighted by writing it in red). Can you apply that formula correctly to determine the x component of a's acceleration? So I'm saying there is something wrong in how you substituted values into that formula aa = ab + ...


so should it be something like .... a_A = (4*i + (- 3.76*j) ) + ( 0*i + (-1.37*j) ) = 0.24*i - 1.37*j
 
  • #9
NascentOxygen
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so should it be something like .... a_A = (4*i + (- 3.76*j) ) + ( 0*i + (-1.37*j) ) = 0.24*i - 1.37*j
You can do it that way if you wish. Next, you're asked to express as a magnitude and direction ....
 
  • #10
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You can do it that way if you wish. Next, you're asked to express as a magnitude and direction ....


Okay, for magnitude I did: |a| = sqrt ( (0.24^2) + (-1.37^2) = 1.39 m/s2

and direction I did inverse tangent of (y/x) which is ( -1.37 / 0.24 ) = - 80.06 deg ....which I'm not sure is right
 
  • #11
NascentOxygen
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Those look to be around what I was expecting.
 
  • #12
NascentOxygen
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You should be able to go back to your first post in this thread, and without doing any further calculations, sketch the triangle showing this vector relation: a_A = a_B + a_A/B

Hint: The first line in your first post tells you that the triangle will be isoscles.
 
  • #13
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I got the right answers, 1.39 & - 80.06, thanks for all ur help, highly appreciated
 

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