How Is Kinetic Energy Calculated from Force and Displacement?

[cereal turtle]

Homework Statement

If the resultant force acting on a 2.0kg object is equal to (3i + 4j) N, what is the change in kinetic energy as the object moves from (7i -8j)m to (11i -5j)m

Homework Equations

w = Fd
Ek = 1/2mv²

The Attempt at a Solution

I assumed that Ek = w so I tried to solve it by getting the change in displacement and then getting the dot product using the given force (did not use the mass at all)

d= (11i -5j) - (7i -8j)
= (4i +3j)

w= (3i +4j)(4i + 3j)
= (12i + 12j)

|w| = 17 J

... this answer was totally wrong, as the answer should be 24 J.

I can't really grasp the relationship with force and kinetic energy.. would appreciate some help. thank you.

 

[BeBattey]

Your dot product is incorrect. Remember it's also called the scalar product, because it produces a scalar, not a vector.

The dot product of two vectors, [a,b] and [c,d], is ac+bd, a simple number. In your case you have everything else correct.

Gotta kick that habit of tacking i and j back on there after evaluating the dot product!

You can also see how this is wonky because you're saying w, work, is a vector quantity, which energy is not!

 

[cereal turtle]

Ohhh! thanks so much! so i really didn't need the 2.0kg?

 

[BeBattey]

No, you really don't. The force over the distance is the work done, or change in kinetic energy. If you have a very massive object, the change in kinetic energy would be the SAME, but the resulting velocity would be lower!