a block 6. GPI EC Review. A block having mass m and charge is connected to an WW

Question

a block

6. GPI EC Review. A block having mass m and charge is connected to an WWWh insulating spring having a force constant k, The block lies on a friction- less, insulating, horizon- tal track, and the system Figure P20.6. is immersed in a uniform electric field of magni- tude E directed as shown in Figure P20.6. The block is re- leased from rest when the spring is unstretched (at x 0) We wish to show that the ensuing motion of the block is simple harmonic (a) Consider the system of the block, the spring, and the electric field. Is this system isolated or non- isolated? (b) What kinds of potential energy exist within this system? (c) Call the initial configuration of the system that existing just as the block is released from rest. The final configuration is when the block momentarily comes to rest again. What is the value of x when the block comes to rest momentarily? (d) At some value of x we will call

Explanation / Answer

For part C, use the conservation of energy to set up an equation:

Ki + Ui = Kf +Uf

and substitute in corresponding components:

0 + QVi = 0 + (1/2 * k*x^2 + QVf)

so simplify to get

1/2 * k*x^2 +Q*E*x

Now solve for x:

x = (2*Q*E) / k

For part D the answer is particle in equilibrium because there is zero net force on it.

Part E, use conclusion from part D, to solve:

The two forces are the spring and the electric force, and we know that

Fs = -kx   and   Fe = EQ

Fs + Fe = 0

so Fs = - Fe

substitute in values and solve for x:

-kx = -EQ

and so x = EQ / k

Part G, the equation for tension is T = 2pi / angular frequency

and angular frequency = squareroot of (k/m)

so T = 2pi / squareroot of (k/m)

simplifying you get that

T = 2pi * squareroot of (m/k)

The system is isolated because there are no external forces present.

The only types of potential energy present are electrical and elastic potential energy. (kinetic energy is not even a potential energy not sure why its even an option)

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