Find Final Kinetic Energy of 3.00kg Object

In summary, the dot product of vectors a and b is calculated by multiplying the corresponding components and adding them together, resulting in a scalar answer. In this case, the final kinetic energy is 673.5 J.
  • #1
suppy123
29
0

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:
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  • #3
!? 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
No that's 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
Kurdt said:
No that's 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
A dot product gives a scalar answer and that's why it is sometimes called a scalar product. Drop the i's and j's and add the numbers together.
 

1. How do you calculate the final kinetic energy of a 3.00kg object?

The final kinetic energy of a 3.00kg object can be calculated using the formula KE = 1/2 * m * v^2, where m is the mass of the object in kilograms and v is the final velocity of the object in meters per second.

2. What is the unit of measurement for kinetic energy?

The unit of measurement for kinetic energy is joules (J). This is a derived unit from the base units of mass (kilograms) and velocity (meters per second).

3. Can the final kinetic energy of an object be negative?

Yes, the final kinetic energy of an object can be negative. This typically occurs when the object's final velocity is in the opposite direction of its initial velocity, resulting in a negative value for the kinetic energy.

4. How does the mass of an object affect its final kinetic energy?

The mass of an object has a direct effect on its final kinetic energy. As the mass increases, the final kinetic energy also increases, assuming the velocity remains constant.

5. Can you use this formula to calculate the final kinetic energy of any object?

Yes, this formula can be used to calculate the final kinetic energy of any object, as long as the mass and final velocity of the object are known. However, it is important to note that this formula assumes the object is moving in a straight line and does not take into account any external forces acting on the object.

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