Max Expansion of Block on Spring Connected to Electric Field

[bzaher]

A block having mass m and and a charge +Q is connected to a spring having a constant k. The block lies on frictionless horizontal track, and the system is immersed in a uniform electric field of magnitude E, directed east. If the block is released from rest when the spring is unstretched ( at x=0)

a)By what maximum does the spring expand
all i have is -kx1=Eq-kx2
x2=eq/k

b)What is the equilibrium position of the block?
in not sure of this isn't it the same as number one?

c) Show that the blocks motion is simple harmonic, and determine its period
I assume its just T=2pie*root m/k

d) What if? Repeat part (a) if the coefficient of kinetic friction between block and surface is Fu (u as in the coefficient of friction)

I don't want the answers I would love the tools to find them (though answers would be a bonus ) any help would be appreciated, thanks. oh and the spring is attached to the block

 

[Mindscrape]

I take it that you don't know differential equations? In your class, have you gone over a forcing function in simple harmonic motion?

 

[bzaher]

No we haven't, I have never done a question like this before, and it feels like I'm walking in the dark hoping to stumble on to something.

 

[Doc Al]

a)By what maximum does the spring expand
all i have is -kx1=Eq-kx2
x2=eq/k

No. Hint: Use energy conservation, not a force equation.

b)What is the equilibrium position of the block?
in not sure of this isn't it the same as number one?

Here's where you use a force equation to find the equilibrium point.

c) Show that the blocks motion is simple harmonic, and determine its period
I assume its just T=2pie*root m/k

OK.

d) What if? Repeat part (a) if the coefficient of kinetic friction between block and surface is Fu (u as in the coefficient of friction)

Use the same approach. You'll have an additional work/energy term.

(No need for any differential equations! Assuming you know the results for SHM, of course.)

 

[bzaher]

ok so here's what I think may be right.

a) ep=1/2*kd for a spring and Ep=EQ for the block so
ep=ep+ek
1/2ks=EQ/d+0
d^3=2EQ/k

b)if it is force that I use then
F=EQ
EK=kx
x=EQ/k

c) I understand now it is simple harmonic because no energy is lost right?

d)same as a but minus force of friction from electric potential?

 

[Doc Al]

a) ep=1/2*kd for a spring and Ep=EQ for the block so
ep=ep+ek
1/2ks=EQ/d+0
d^3=2EQ/k

No. What's the work done by the electric field as the block moves? What's the work done by the spring? (What's the energy stored in a stretched spring?)

b)if it is force that I use then
F=EQ
EK=kx
x=EQ/k

OK.

c) I understand now it is simple harmonic because no energy is lost right?

It's simple harmonic because the restoring force is proportional to the displacement from equilibrium.

d)same as a but minus force of friction from electric potential?

Again, part 'a' has to do with energy, not simply force. You'll have to consider the work done by friction as the block moves.

 

[bzaher]

Well, I'm out of ideas for a) then.

 

[Doc Al]

Well, I'm out of ideas for a) then.

At least look up the formula for the energy stored in a spring.

And for the work done by the constant electric field, recall that work = force X distance. (Careful not to use that for the spring, since the spring force isn't constant.)

 

[bzaher]

so then would it be
ep=deltaE
1/2kx^2=fd and solve for x?

 

[Doc Al]

so then would it be
ep=deltaE
1/2kx^2=fd and solve for x?

Yes. Replace 'd' with 'x'. And f is the force due to the electric field.

 

[bzaher]

Thanks a lot for all your help.