Solved: Help With Energy Problem Homework

[Kudo Shinichi]

HELP!Energy problem

Homework Statement

A 20kg object is acted on by a conservative force given by F=-3.0x-5.0x^2, with F in Newtons and x in meters. take the potential energy associated with the force to zero when the object is at x=0
a) what is the potential energy of the system associated with the force when the object is at x=2.0m?
b)If the object has a velocity of 4.0m/s in the negative direction of the x-axis when it is at x=5.0m, what is its speed when it passes through the origin?
c)What are the answers to a) and b) if the potential energy of the system is taken to be -8.0J when the object is at x=0.

The Attempt at a Solution

a)I can get the equation for finding out PE by integrating F=-3.0x-5.0x^2, which is -1.5x^2-5/3x^3
sub 2.0 into x
then the answer I got is -19.3
b) I don't really know how to approach this question, but I know that I have to somehow relate the conservative energy to speed...maybe to kinetic energy?1/2mv^2?
c)
a. -8=-1.5x^2-5/3x^3
x=-2.04m
but the question says when x=0, so I don't know what did i do wrong with this question
b. I didn't know how to do b), so I don't really know how to det the answer for this too.

I need some help on this. Thank you very much.

 

[Irid]

(b) is simple, just put in x=2 into your answer of part (a).

 

[Kudo Shinichi]

(b) is simple, just put in x=2 into your answer of part (a).

Then isn't the answer same as a)

 

[Irid]

Oh yeah, sorry :). For part (b) you have to use energy conservation. Kinetic energy (T=mvv/2) plus potential energy is a constant at any x, so just make an equation at for two points.

 

[Kudo Shinichi]

Oh yeah, sorry :). For part (b) you have to use energy conservation. Kinetic energy (T=mvv/2) plus potential energy is a constant at any x, so just make an equation at for two points.

E=K+PE
find PE by plugging in the x value
and plug in the x values and m into K then I got the energy...
sorry, but how can you get the speed from the answer I got for the energy
And also do you know whether i did part c right or not?

 

[Irid]

Consider points x_1=0 and x_2=5.
Then by energy conservation:

$$\frac{mv_1^2}{2} + V(x_1) = \frac{mv_2^2}{2} + V(x_2)$$

You have one of the speeds, so just solve for the other one.