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d. The electric field outside both spheres is Q/4πε0r2. Using this and the reference point of V

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d. The electric field outside both spheres is Q/4πε0r2. Using this and the reference point of V = 0 Volts at infinity, find an expression for the potential at a point outside the sphere and a distance r from the center of the sphere. V = – ∫ E(r’) • dr’ and integrate from r = infinity (where V = 0 Volts) to a point r.i. Note that the primed r’s indicate a variable for purposes of integration, where r is a specific limit position for purposes of the integration.e. Measure the voltage at some point outside the sphere and find the charge on both spheres. Verify that the total charge is the same.Conductorr=________ Vmeasured=________ Vtheory=_______Insulatorr=________ Vmeasured=________ Vtheory=_______Now for the voltage inside the uniformly charged insulator. Here the electric field is Qr/(4πε0R3) where R is the radius of the sphere itself. In this case, to find the electric potential as a function of r, you again need to integrate V = – ∫ E • dr, but this time you must break up the integral and integrate from infinity to R using E = Q/4π ε0r2 (to find the electric potential associated with getting all the charges to the surface of the sphere) and then integrate from R to r (an arbitrary point inside the sphere) using the expression for the electric field inside the insulating sphere.f. Verify that your calculation gives the same results as shown on the graph. (for an R inside the surface of the insulator)Insulatorr=________ Vmeasured=________ Vtheory=_______Additional QuestionConsider the insulator. The charge was uniformly distributed throughout the volume. Qualitatively discuss how things would change if the density changed as a function of r. This is similar to the Earth where the mass density varies as one moves from the crust to the core (not that anyone can do that …except in some science fiction movies).

## 6. Compare and contrast the bony, ligamentous, articular and cartilaginous

Question 6. Compare and contrast the bony, ligamentous, articular and cartilaginous aspects of the medial knee joint with those of the lateral knee joint – relative structure size, static structure size, etc.7. For the following questions #7, 8 and 9, consider moving from a seated position to a standing position, focusing on the KNEE JOINT ONLY analysis.When you stand, what motion is occurring at the knee?a. Flexionb. Extensionc. Diagonal Adductiond. Both b and c.8. For the following questions #7, 8 and 9, consider moving from a seated position to a standing position, focusing on the KNEE JOINT ONLY analysis. When you stand, what muscle (s) are activating at the knee?a. Iliopsoas and Hamstringsb. Quadriceps complexc. Gluteus Maximus and Hamstringsd. None of the above.9. For the following questions #7, 8 and 9, consider moving from a seated position to a standing position, focusing on the KNEE JOINT ONLY analysis. When you stand, what type of contraction occurs of the muscle (s) of the knee joint you identified?a. Isometricb. Concentric shorteningc. Eccentric lengtheningd. None of the above

d. The electric field outside both spheres is Q/4πε0r2. Using this and the reference point of V = 0

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d. The electric field outside both spheres is Q/4πε0r2. Using this and the reference point of V = 0 Volts at infinity, find an expression for the potential at a point outside the sphere and a distance r from the center of the sphere. V = – ∫ E(r’) • dr’ and integrate from r = infinity (where V = 0 Volts) to a point r.i. Note that the primed r’s indicate a variable for purposes of integration, where r is a specific limit position for purposes of the integration.

## -A 52 g bullet hits a stationary 853 g wooden block sitting

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-A 52 g bullet hits a stationary 853 g wooden block sitting on a frictionless surface, against a spring attached to the wall (see diagram). If the spring constant is 278 N/m and the spring compresses 13.2 cm upon impact: -Determine the bullet’s initial velocity. -Show that the bullet hitting the wood is an inelastic collision.

## Can you identify the relevant physical principles and summarize them in words?

Question Can you identify the relevant physical principles and summarize them in words? Please draw free body diagrams for blocks in part (a). Include an appropriate coordinate system for each and the vector lengths have the correct relative lengths. Also, please highlight any interaction forces.Can you write out Newton’s Second Law in two dimensions for each block in part (a)?

## A 900 kg car moving at 60 m/s overtakes a 1500 kg car moving at 50

Question A 900 kg car moving at 60 m/s overtakes a 1500 kg car moving at 50 m/s in the same direction and collides with it. (a) Find their final velocity if the two cars remain in contact. (b) What is the magnitude of the kinetic energy lost in the collision?

## If a spring is stretched too far, it will become deformed and stop obeying Hooke’s law. Suppose that it obeys a

Question If a spring is stretched too far, it will become deformed and stop obeying Hooke’s law. Suppose that it obeys a modified Hooke’s law of the form Fs = -(kx bx^2), where k and b areconstants with appropriate units. (Notice that for small values of x, thelinear term would dominate which leads to Hooke’s law, but for largevalues of x, the quadratic term would dominate, leading to a restoringforce that is larger than predicted by Hooke’s law.)If the spring is attached to a ceiling, and a mass of 1.0 kg is hung fromit, then the spring stretches to a distance d = 4.0 cm from it’sequilibrium position. If the spring is attached to a wall, and a 1.0 kgblock is attached to the spring and pulled back to a maximum positionxmax = 3.0 cm before being released on a frictionless table, themaximum speed the mass reaches is 6.0 cm/s. Find the potential energyexpression for such a spring (in units of J) as a function of x (thedisplacement from the equilibrium position at x = 0 in units of cm).(A) Us = 2.9x^2 0.012x^3(B) Us = 1.9x^2 0.050x^3(C) Us = 3.8x^2 0.074x^3(D) Us = 1.2x^2 0.085x^3(E) Us = 4.5x^2 0.083x^3