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.

A small rock moves in water, and the force on it by the water is given by f=kv. The terminal speed of the rock is measured and found to be 2.0m/s. The rock is projected upward at an inital speed of 6.0m/s. You can ignore the buoyancy force on the rock

a) in the absence of fluid resistance, how high will the rock rise and how long will it take to reach this maximum height? I managed this one. b) when the effects of fluidresistance are included, what are the answers to the question in part a).

i manage to get the same z time as the solution on this website.

I and the website has the same equation for Vy.

the websites solution for Y = Vt*[1-e^(-k/mt))] which is the same expression as the example in the book.

But in the example in the book there is no initial speed Vy=0. In the question there is initla speed and therefor I think the expression for Y must be different from the examples expression. Therefore I think the solution of this question on this website must be wrong. Please comment me on this.

A particle is described by the wave function ψ(x) = b(a2 - x2) for -a ≤ x ≤ a and ψ(x)=0 for x ≤ -a and x ≥ a , where a and b are positive real constants.

(a) Using the normalization condition, find b in terms of a.

(b) What is the probability to find the particle at x = 0.33a in a small interval of width 0.01a?

(c) What is the probability for the particle to be found between x = 0.03a and x = 1.00a ?

What are the characteristics of an ideal radiation shield?

A posterior capsulotomy is a non-invasive laser procedure to eliminate the cloudiness that occasionally interferes with a patient's vision after cataract surgery. For this procedure a Nd:YAG laser with pulse duration of 30 ns is focused to 50 – 100 µm in diameter on the posterior capsule to cut a thin membrane which has become cloudy over time. Estimate the pulse energy necessary to achieve optical breakdown during this treatment, because otherwise all laser energy will be absorbed by the retina and other tissues lying underneath.

Q1) Two identical pucks collide on an air hockey table. One puck was originally at rest. If the incoming puck has a speed of 6.50 m/s and scatters to an angle of 30.0º,what is the speed of the second puck after the collision?

(You may use the result that θ₁−θ₂=90º for elastic collisions of objects that have identical masses.)

Q2)A block of mass m = 3.0 kg, moving on a frictionless surface with a speed 2.9 m/s makes a perfectly elastic collision with a block of mass M at rest. After the collision, the 3.0 kg block recoils with a speed of 0.8 m/s. In Fig. 1, the mass M (in kg) is closest to:

I have a slater determinant question.Please describe the concept of slater determinant. Describe in detail what purpose, which systems are used, on an example.

Two cars start from rest at a red stop light. When the light turns green, both cars accelerate forward. The blue car accelerates uniformly at a rate of 4.7 m/s² for 3.8 seconds. It then continues at a constant speed for 8.7 seconds, before applying the brakes such that the car’s speed decreases uniformly coming to rest 212 meters from where it started. The yellow car accelerates uniformly for the entire distance, finally catching the blue car just as the blue car comes to a stop.

1. How fast is the blue car going 2.7 seconds after it starts?

2. How fast is the blue car going 10.2 seconds after it starts?

3. How far does the blue car travel before its brakes are applied to slow down?

4. What is the acceleration of the blue car once the brakes are applied?

5. What is the total time the blue car is moving?

6. What is the acceleration of the yellow car?

A body with mass 95 kg moves with acceleration 2 m/s^2 under action of some force. What would be acceleration of a body with mass 10 kg if the same force would act on it?

A skilled volleyball player uses elbow motion (as well as shoulder motion) in a jump serve. With her shoulder positioned and maintained in flexion (about 100 degrees), a server initially starts the preparatory phase by flexing the elbow. At this time, the angular velocity of the elbow is 800 deg/s in flexion (positive) direction. As the server moves to strike the ball, the elbow undergoes extension, and immediately before the strike with the ball, the elbow’s angular velocity is 1500 deg/s in extension (negative direction). This change in angular velocity at the elbow joint occurs in 0.3 seconds. Which of the following statements is/are true about the angular acceleration of the elbow joint? Select statement(s) that is/are true. [1 pt.]

Group of answer choices

The elbow's angular acceleration is a positive value

The elbow's angular acceleration is a negative value

The elbow joint movement is speeding up

The elbow joint movement is slowing down