This provides some review of dvats, Newton's Laws, and electric fields.

Click here to open an IWP applet. The green dot represents a positively-charged particle.  When you start the animation, the particle will move under the influence of an electric field.  By convention, a positive E-field points in the +y direction.  You have the option to change the particle's charge, initial velocity (both magnitude and direction), and the magnitude of the E-field.  You can reverse the direction of the E-field by entering a negative number for it.  You can also make the particle negative by entering a negative sign in front of the charge.  The red vector represents the particle's velocity and will, of course, always be tangent to the particles' path.  The blue vector represents the particle's acceleration.  Of course, this is also the direction of the net force, which is all electric in this case.  If you haven't already clicked on the play button, do so now.  Stop the particle before it goes off the screen.  Then click Show Graph.  The Graph window is currently displaying the x- and y-velocity components.

In the following, ignore the gravitational force on the particle.

Do the following problems using the animation. Record your answers in the corresponding WebAssign assessment.

1. Change the electric field to 0. Reset and play the animation. Complete the following: The particle moves with constant <_> and zero <_>, because, according to Newton's 1st Law, the net, external force on the particle is <_>.

2. Change the angle of the initial velocity to 90° (vertically upward) and set the electric field back to the original value of 10,000 N/C. Reset and play. Complete the following: The velocity (insert a verb) <_> and the acceleration is <_> as the particle moves.
   
   Click Show Graph to examine the velocity vs. time and acceleration vs. time graphs. The velocity vs. time graph has <_> slope, and the acceleration vs. time graph has <_> slope.
   
   These results are consistent with Newton's 2nd Law, because the net force on the particle is simply the electric force. This force is constant, because the electric field is <_> and <_>. (Hint: The latter two fields are for two words that are frequently used interchangeably but actually have different meaning. For the first field, use the word that means invariable in time, and for the second field, use the word that means invariable in space.)

3. Change the angle of the initial velocity to -90° (or 270°), reset, and play. Which of the following motions is the motion of the particle most like?
    
   a satellite orbiting the Earth
   a ball projected horizontally on the surface of the Earth
   a ball thrown upward in a gravitational field
   a ball thrown downward in a gravitational field
    

4. Change the angle of the initial velocity back to 0° and play the animation. The name of the mathematical function that describes the path of the particle is a <_>. In what chapter of the textbook did you first encounter this kind of motion? (Give the number.) <_> In order to produce this kind of path, the horizontal velocity is <_>, and the vertical acceleration is <_>.

5. Make the electric field -10,000 N/C. Reset and play. Without changing the electric field again, make another change to restore the path to what it was before changing the field. This works because the electric force on a <_> charge is opposite the direction of the <_>.

6. Do a net force problem to determine the mass m of the particle in terms of charge q, electric field E, and acceleration a of the particle. Show your work completely as required for a net force problem.

7. In a moment, you'll take measurements from the applet in order to determine the acceleration of the particle to 2 significant figures. Use the Show Graph function. (Due to a bug, the time parameters don't show below the graph. However, you can read the value of time from the Animator.) First, complete the following:
   
   The graphical method for determining the acceleration of a uniformly-accelerating object is to find the <_> of the graph of <_> vs. <_>. In order to increase the accuracy of the calculation, one should pick the greatest <_> that one can.
   
   Now calculate the acceleration and give your result.

8. This is a practice symbolic question. This means your answer will be a formula. It must be formulated according to WebAssign specifications in order to be counted correctly. That means you must use variable names exactly as given (they're case sensitive, too), use parentheses correctly, and use the specific symbols for arithmetic operations.
   
   For this problem, we'll start you off by writing a simple equation. The equation will be the formula for area of a circle of radius r₁. For Greek letters like π, simply write pi. In order to indicate a subscript, use the form r_1.
   
   What you will write in the blank is the right-hand side of the equation only. There will be no equal sign. Click on the Symbolic Formatting Help to see how to indicate various operations. Before you submit your equation, click on the eyeball to the right of the equation window in order to preview your equation. We'll give you plenty of tries on this problem to give you a chance to practice. You can format your answer in different ways as long as you follow the usual rules for arithmetic operations. For example, multiplication is commutative, so you can switch the order of pi and r_1^2. You can add parentheses to either or both. You can even leave out the asterisk for multiplication. Try writing pi(1/r_1)^(-2) to see if that works.

9. Derive the formula needed to find the value of the particle's mass. Give your formula symbolically in terms of charge q, the electric field E, and the acceleration a. (Note that q represents the absolute value of q.)

10. Now calculate the particle's mass to 2 significant figures.

11. Here's a review of 2-dimensional dvats. Determine a formula for the y-coordinate of the particle in terms of x, a, and v_o only. Enter your formula symbolically. Use v_0 to represent initial velocity.

12. In order to check your result, set the input parameters to those given in WebAssign. Then use your equation from the previous problem to determine the magnitude of the initial velocity necessary for the particle to pass through the upper right-hand corner of the Animator window (0.20 m, 0.20 m).