Work / Power done to a particle

[Warmacblu]

Homework Statement

A 1 kg particle starts from rest at x = 0 and moves under the influence of a single force Fx = 6.6 + 12.6x - 1.8x², where Fx is in Newtons and x is in meters.

Find the work done by this force on the particle as the particle moves from x = 0 m to x = 1.5 m.

Find the power delivered to the particle when it is at x = 1.5 m.

Homework Equations

Integrals
V = (2K/m)^1/2
P = Fv

The Attempt at a Solution

I solved the first part by solving the integral and plugging in 1.5. The answer was 22.05.

The second part I thought I had correct:

V = (2K/m)^1/2, where K = W
V = (2(22.05)/1.5)^1/2
V = 119.56 W

I tried variations on this number because I was certain I was correct, I even tried the negatives. Perhaps my equation for V is incorrect?

 

[Doc Al]

V = (2K/m)^1/2, where K = W
V = (2(22.05)/1.5)^1/2

m ≠ 1.5

 

[Warmacblu]

m ≠ 1.5

Wow, m equals mass?

V = (2K/m)1/2, where K = W
V = (2(22.05)/1)1/2
V = 6.64 m/s

W = 22.05 x 6.64

W = 146.43

 

[Doc Al]

Wow, m equals mass?

Uh, yeah... I hope you're not just plugging into formulas without knowing what they mean.

That formula for speed comes from the definition of kinetic energy, K = 1/2mv^2.

V = (2K/m)1/2, where K = W
V = (2(22.05)/1)1/2
V = 6.64 m/s

OK.

W = 22.05 x 6.64

Why are you multiplying W by the speed? (And then calling it W!)

 

[Warmacblu]

Uh, yeah... I hope you're not just plugging into formulas without knowing what they mean.

That formula for speed comes from the definition of kinetic energy, K = 1/2mv^2.


OK.

Why are you multiplying W by the speed? (And then calling it W!)

I was just becoming very frustrated with this question because it seemed so easy but I guess I don't really understand the concepts yet.

I am trying to solve for power which is P - Fv. I solved for v and I guess I thought that my previous answer was the force but it wasn't, it was just the average power.

I believe that in order to solve this problem, I have to plug in 1.5 into the Fx equation given to solve for the force and multiply that by the velocity.

Note - I already used up all of my tries for this problem so I would just like to understand the concept of the question now.

 

[Doc Al]

I believe that in order to solve this problem, I have to plug in 1.5 into the Fx equation given to solve for the force and multiply that by the velocity.

That's right. (In the future, try to take it slower. Double check each step.)

 

[Warmacblu]

That's right. (In the future, try to take it slower. Double check each step.)

Thanks, will do.