Conceptual - Dot Product and Work

[mybrohshi5]

Conceptual ---- Work

Homework Statement

In general, the work done by a force F_vec is written as

$W=\int_{\rm i}^{\rm f} \vec{F}(\vec{r})\cdot d\vec{r}.$

Now, consider whether the following statements are true or false:

1) The dot product assures that the integrand is always nonnegative.
2) The dot product indicates that only the component of the force perpendicular to the
path contributes to the integral.
3) The dot product indicates that only the component of the force parallel to the path
contributes to the integral.

Homework Equations

n/a

The Attempt at a Solution

To be honest i have no idea about these. My professor doesn't teach, my book (which i just looked through for about 15 mins) doesn't talk about this anywhere, and yet it is on my homework :(

This is what i was thinking but i am really again not sure.

1) true
2) false
3) true

Thanks for any help.

 

[rootX]

Write (Provide) vector definition of the dot product.

 

[PhanthomJay]

By guessing or otherwise, you got two of them right, and one of them wrong. If a particle moves to the right and the force acting on it is to the right, is the work done by the force positive or negative? If the particle moves to the right and the force acting on it is to the left, is the work done by the force positive or negative?

 

[mybrohshi5]

This is what i found in my book.

Scalar product -> A . B = ABcos(theta)

 

[mybrohshi5]

By guessing or otherwise, you got two of them right, and one of them wrong. If a particle moves to the right and the force acting on it is to the right, is the work done by the force positive or negative? If the particle moves to the right and the force acting on it is to the left, is the work done by the force positive or negative?

moves to the right and force acting on it is to the right then work is POSITIVE.

moves to the right and force acting on it is to the left then work is NEGATIVE

so... is this saying that 1) is actually false because it can be negative?

 

[PhanthomJay]

moves to the right and force acting on it is to the right then work is POSITIVE.

yes...

moves to the right and force acting on it is to the left then work is NEGATIVE

yes...

so... is this saying that 1) is actually false because it can be negative?

I am hesitating to give answers to true-false questions, so it is up to you to decide...

 

[mybrohshi5]

Thank you :)