Problem Statement

Charges -2nC and 2nC are located at x= -0.1cm and x=0.1cm respectively. Determine the electric field at the points (-1 cm, 0 cm), (1 cm, 0 cm), (0 cm, 1cm), (0 cm, -1 cm) and (1 cm, 1 cm).

Visual Representation

• Draw a sketch of the charge distribution.

• Establish a coordinate system and show the locations of the charges.

• Identify the point P at which you want to calculate the electric field.

• Draw the electric field of each charge at point P. ⃗

• Use symmetry to determine if any components of Enet are zero.

Mathematical Representation ⃗

• For each charge, determine its distance from P and the angle of E i

• Determine the field strength of each charge.

• Write each vector in component form. ⃗

• Sum the vector components to determine E net.

• Check result for correct units and that it is reasonable.

A guy was dumped by his girlfriend and wants to jump off from a building 200 ft high. What is the required velocity he must start in order to touch down on her new boyfriend who stands on the ground, 30ft from the building. a) if he jumped out horizontally b)the guy jumped down with a depression angle of 30 degrees. Find the impact velocity and speed. Does he have any chance?

My question is would this lab procedure be a valid method of calculating the coefficient of static friction when you are only allowed to make measurements of distance and not of mass. What steps should I add or change?

Lab Objective: Find the coefficient of static friction between a CPO sled and a smart track by only measuring the distance.

1. Angle the straight track so that it acts as a ramp

2. Draw the freebody diagram of the sled on the straight track showing a normal force perpendicular to the ramp surface

3. Break the horizontal and vertical forces into their x and y components and sum them together. Make sure to break the force of gravity apart into its x and y components, applying Newtons’s 2nd law equations to establish relationships between gravity, Fn, and static friction. The x and y components of gravity are the normal force as its y component, Fg (y) = Fn = mgcosθ and F g (x) = mgsinθ as the x component.

4. Measure the horizontal and vertical distances of the ramp by using a meterstick.

5. Calculate the angle at the horizontal (angle of incline) by using inverse tan(height of ramp /base length).

6. Calculate the tangent of the angle of incline using the equation of tanθ=sin θ/cos(θ). The coefficient of static friction is tangent to the angle at which the sled slides.

Problem 1 [6] Compute the eigenvalues of Hˆ = pˆ 2 2m + 1 2 mΩ 2xˆ 2 + λxˆ using two different methods: 1. Complete the square in 1 2mΩ 2x 2+λx (that is, write the term as 1 2mΩ 2 (x− x0) 2+C with suitable constants x0 and C) and use the exact eigenvalues En = (n+ 1 2 )¯hω of a harmonic oscillator with potential V (x) = 1 2mω2x 2 . 2. Apply second-order perturbation theory in λ

Problem 2 [2] Compute the eigenvalues of the matrix Hˆ = 2 λ λ 3 − 2λ ! and Taylor expand them to second order in the real number λ

A gas is compressed at a constant pressure of 0.800 atm from 9.00 L to 2.00 L. In the process, 350 J of energy leaves the gas by heat.

(a) What is the work done on the gas?
J

(b) What is the change in its internal energy?
J

a.) show that a simple pendulum has a stable equilibrium point at theta=0.

b.) Find the natural frequency w of the system. (show work)

A4μCchargeisplacedatthepoint⃗r1 =2ˆicmandan-4μCchargeisplacedat ⃗r2 = −2 ˆi cm. The charges do not move. a. What is the electric field (magnitude and direction) at the origin? b. What is the electric field (magnitude and direction) at the point (0,2)? c. What is the electric field at the point (4,4)? For this part give your answer in both unit vector (ˆi, ˆj) notation and in magnitude and direction relative to ˆi.

The bright yellow sodium line in the sodium spectrum is actually a pair of closely spaced lines at 589.0 nm and 589.6 nm. You observe the sodium spectrum using a diffraction grating with a spacing of 1700 nm . Find the angular separation between the two sodium lines in first order. Find the angular separation between the two sodium lines in second order. Express your answer to two significant figures and include the appropriate units.

You are part of a searchand- rescue mission that has been called out to look for a lost explorer. You’ve found the missing explorer, but you're separated from him by a 200-m m -high cliff and a 30-m m -wide raging river. To save his life, you need to get a 5.8 kg k g package of emergency supplies across the river. Unfortunately, you can't throw the package hard enough to make it across. Fortunately, you happen to have a 0.90 kg k g rocket intended for launching flares. Improvising quickly, you attach a sharpened stick to the front of the rocket, so that it will impale itself into the package of supplies, then fire the rocket at ground level toward the supplies. (Figure 1) Figure1 of 1A figure shows an explorer stranded across a 30-meter-wide river at the bottom of a 200-meter-height cliff. A rescuer attempts to deliver a package to the explorer by placing the package at the edge of the cliff and shooting a rocket horizontally at it. A figure shows an explorer stranded across a 30-meter-wide river at the bottom of a 200-meter-height cliff. A rescuer attempts to deliver a package to the explorer by placing the package at the edge of the cliff and shooting a rocket horizontally at it. Part A What minimum speed must the rocket have just before impact in order to save the explorer’s life? Express your answer to two significant figures and include the appropriate units.

a.) Derive the equations of motion for an object with mass(m1) that is orbiting the second object of mass (m2>>m1) in a perfectly circular orbit with radius(R) and orbital period (T).

(Use lagrangian mechanics & show work)

b.) Find the hamiltonian of the system and describe how it is related to the system energy.