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Kinetic energy

  • Thread starter suppy123
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  • #1
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Homework Statement


A 3.00kg object has velocity 7.00j m/s. Then, a total force 12.0i N acts on the object for 5.00s.
Find the final kinetic energy from 1/2mvf^2 = 1/2mvf . vf


Homework Equations





The Attempt at a Solution


i got 1/2 * 3 * (20i+7j)(20i+7j)
then 600j^2 + 210ij + 73.5j^2

but the answer is 673.5 J, why?
since j.j =i.i=1 and i.j=0?
 
Last edited:

Answers and Replies

  • #2
Kurdt
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  • #3
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!? do i need to write the whole of that!!??

600j^2 + 210ij + 73.5j^2
600j.j + 210 i . j + 73.5j.j
600(1) + 210 (0) + 73.5(1)
is this alright
 
  • #4
Kurdt
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No thats not how a dot product works. You don't expand the brackets.

[tex] \mathbf{a} \cdot \mathbf{b} = a_xb_x + a_yb_y [/tex]

For vectors:

[tex] \mathbf{a} = (a_x,a_y) [/tex]
[tex] \mathbf{b} = (b_x,b_y) [/tex]
 
  • #5
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No thats not how a dot product works. You don't expand the brackets.

[tex] \mathbf{a} \cdot \mathbf{b} = a_xb_x + a_yb_y [/tex]

For vectors:

[tex] \mathbf{a} = (a_x,a_y) [/tex]
[tex] \mathbf{b} = (b_x,b_y) [/tex]

got it, a.b = axbx+ayby
a.b= 20i*20i+7j*7j= 449
 
Last edited:
  • #6
Kurdt
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A dot product gives a scalar answer and thats why it is sometimes called a scalar product. Drop the i's and j's and add the numbers together.
 

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