A constant force F=<-1, 2, -5> acts on a particle as it moves from A(2, 4, 1) to B(-2, 1, 3). Find the work done by the force.

I have trouble for finding the dot products.

A constant force F=<-1, 2, -5> acts on a particle as it moves from A(2, 4, 1) to B(-2, 1, 3). Find the work done by the force.

I have trouble for finding the dot products.

Tutors, sign in to answer this question.

Marked as Best Answer

A constant force field is conservative, so you can assume a straight line path for simplicity.

The displacement vector is **r** = <-2 - 2, 1 - 4, 3 - 1> = <-4, -3, 2>

With a force of **F** = <-1, 2, -5>, you get

W = **F**·**r** = <-4, -3, 2>·<-1, 2, -5> = 4 - 6 - 10 = -12.

A negative number means that the particle is doing work against the field.

Grigori S. | Certified Physics and Math Teacher G.S.Certified Physics and Math Teacher G.S.

By the definition work W is

W = Fr cos θ

where θ is the angle between vectors** F** and** r (**F and r are modules of those vectors). If vectors
**A** and **B **are given then the displacement** r** is defined as

**r** = **B**-**A = (-**2**i +j +**3**k) -(**2**i +**4**j +k) = -**4**i -**3**j + 2k**

Then

cos θ =( -4F_{x} + (-3)F_{y} +2F_{z})/Fr

where Fx, Fy, Fz are x,y,z components of **F: **Fx** =
**-1, Fy =2, Fz = -5. Thus, we have for W

W = (-4)(-1) + (-3)2 +2(-5) = 4=6 -10 = -12 units of work

Negative sign shows that the work is done by the component of force (F cos θ) which has a direction opposite to the direction of the displacement. This means that the particle willl slow down.

Already have an account? Log in

By signing up, I agree to Wyzant’s terms of use and privacy policy.

Or

To present the tutors that are the best fit for you, we’ll need your ZIP code.

Your Facebook email address is associated with a Wyzant tutor account. Please use a different email address to create a new student account.

Good news! It looks like you already have an account registered with the email address **you provided**.

It looks like this is your first time here. Welcome!

To present the tutors that are the best fit for you, we’ll need your ZIP code.

Please try again, our system had a problem processing your request.

Harry O.

Harry O: tutoring in ACT, algebra, geometry, physics and calculus

$12.50 per 15 min

View Profile >

Alix B.

Math and chemistry tutor

$13.75 per 15 min

View Profile >

Frederick M.

Science/Technology/Engineering/Math - Keeping it fun!

$15 per 15 min

View Profile >