Viewed Questions
Find the area of the parallelogram with vertices $A(-3,0),$ $B(-1,3), C(5,2),$ and $D(3,-1)$
Vectors and the Geometry of Space
The Cross Product
$14-15$ Find $|\mathbf{u} \times \mathbf{v}|$ and determine whether $\mathbf{u} \times \mathbf{v}$ is directed into the page or out of the page.
$9-12$ Find the vector, not with determinants, but by using properties of cross products. $$(\mathbf{i}+\mathbf{j}) \times(\mathbf{i}-\mathbf{j})$$
A conducting spherical shell with inner radius $a$ and outer radius $b$ has a positive point charge $Q$ located at its center. The total charge on the shell is $-3 Q,$ and it is insulated from its surroundings (Fig. $\mathbf{P 2 2 . 4 2}$ ). (a) Derive expressions for the electric-field magnitude $E$ in terms of the distance $r$ from the center for the regions $r<a, a<r<b,$ and $r>b .$ What is the surface charge density (b) on the inner surface of the conducting shell; (c) on the outer surface of the conducting shell? (d) Sketch the electric field lines and the location of all charges. (e) Graph $E$ as a function of $r$
Questions asked
Ankur S
Numerade educator
You stand on top of a 45.0 m tall building and throw a ball straight up with a speed of 10.0 m/s. How long did the ball take to hit the ground below?
Supratim Pal
The equation for mass undergoing simple harmonic motion is given by x = (0.5 cm) cos (1.047t). For parts (b.) through (d.), the changes made always refer back to this original equation. (a.) Sketch the mass's position on the axes provided for the entire time values given. (b.) If a mass which is nine times larger than the original is attached to the same spring but no other changes are made to the system, plot the position. (c.) If the original mass is attached to a spring whose constant is four times larger than the first but no other changes are made to the system, plot the position. (d.) If the original mass is attached to the original spring but the amplitude is doubled with no other changes are made to the system, plot the position.
Kirsty Gledhill
#3 This graph shows the height versus time for the location ( x=0 ) as a transverse wave propagates through it. For the given wave speeds and times, sketch the corresponding height-versus-location graph for all points of the medium. Explain how you determined your answer.
#1 A mass connected to a spring that is undergoing horizontal simple harmonic motion has the position-versus-time graph shown. (a.) What is the period of the motion? Hint: There's a more precise way than just estimating where the cycle ends. The period is not 2.5 s. (b.) What is the amplitude of the motion? (c.) Fill in the following table giving the times when certain behaviors occurred. For full points your must explain how you determined your answers. | Behavior | Times | Explanation | | :--- | :--- | :--- | | Moving to the left at maximum speed | | | | Moving to the right at maximum speed | | | | Instantaneously at rest | | |
Timothy James
Which of the following objects would undergo simple harmonic motion? Check all that apply. A tomato is placed on a hanging scale at the grocery store. The scale goes up and down with no friction. A rock is tied to a string and allowed to swing back-and-forth starting at a "small" angle and without friction. The heart of a sprinter beats faster as she runs around the track. A mass, connected to a spring, oscillates back-and-forth a few times before being stopped by friction. A child on a swing goes through an increasing arc due to her parent's push.
A satellite is in elliptical orbit around the earth. Given are the satellite's gravitational and total energies (both negative as discussed in problem #1) at perigee. Assume the earth's gravity is the only force acting on the satellite, that the orbit's semi-minor axis is 1.3 times larger than the perigee distance, and the orbit's eccentricity is e = 0.25. (By the way, notice how circular that looks!) Finish the bar graph for perigee and then sketch the energy bar graphs at the "halfway" point M and at apogee. Your values should be roughly to scale and for full points you must explain how you determined the energy values used. At Perigee P K Ug E At Point M K Ug E At Apogee A K Ug E
#1 Given that Newton's Law of gravity makes the gravitational potential energy negative, we have the very intriguing possibility that a satellite could have a total energy of zero! (a.) What special condition must the kinetic and gravitational potential energies obey in order for the total energy to be zero. (b.) Show that the angular-momentum conservation condition derived in class for the speed and distances at apogee and perigee (or aphelion and perihelion for something in orbit around the sun) va ra = vp rp, makes it impossible for a satellite in elliptical orbit to have a total energy of zero but that it could happen in circular orbit. Hint: Write an equation for the energy at apogee and one for the energy at perigee. Show that if one of them equals zero, that the va ra = vp rp condition requires that other one cannot be zero unless the orbit is circular. (c.) In fact, explain why it makes sense that the total energy of a satellite would be negative. Hint: Use the same argument as the one used in class when deriving the escape speed equation.
Paul Gabriel
Each figure below shows a block attached to the end of a spring resting on a frictionless surface. In each figure, the springs are to be stretched to the right by a distance given in the figure and released. The blocks will then proceed to oscillate. The mass is given for each different block, and the force constant is given for each different spring. Rank the figures from greatest to least on the basis of the period of the vibratory motion. That is, rank the figures on the basis of how long each will take to go through one complete cycle. A 0.4 m stretch 5 N/m 1 kg E 0.5 m stretch 1 N/m 1 kg B 0.2 m stretch 5 N/m 2 kg F 0.5 m stretch 4 N/m 4 kg C 0.2 m stretch 6 N/m 3 kg G 0.4 m stretch 10 N/m 2 kg D 0.2 m stretch 4 N/m 5 kg H 0.5 m stretch 1 N/m 5 kg Greatest 1 ___ 2 ___ 3 ___ 4 ___ 5 ___ 6 ___ 7 ___ 8 ___ Least Or, all of the periods would be the same. ___ Please carefully explain your reasoning. How sure were you of your ranking? (circle one) Basically Guessed Sure Very Sure 1 2 3 4 5 6 7 8 9 10
1. A mass on a spring is observed to complete 15 oscillations in 30 seconds. What are the period and the frequency of motion? Don't forget units. To = fO =
R x m
