At t=0t=0 the current to a dc electric motor is reversed, resulting in an angular displacement of the motor shaft given by θ(t)=(θ(t)=( 260 rad/srad/s )t−()t−( 20.5 rad/s2rad/s2 )t2−()t2−( 1.49 rad/s3rad/s3 )t3)t3.

A- At what time is the angular velocity of the motor shaft zero?

B- Calculate the angular acceleration at the instant that the motor shaft has zero angular velocity.

C- How many revolutions does the motor shaft turn through between the time when the current is reversed and the instant when the angular velocity is zero?

D- How fast was the motor shaft rotating at t=0t=0, when the current was reversed?

E- Calculate the average angular velocity for the time period from t=0t=0 to the time calculated in part A.

An entrepreneur has proposed sending a probe to Alpha Centai 4 light years away. His idea is to use a "solar sail", which is a large area reflective sheet, and propelling the spacecraft to 10% of the speed of light using a high powered laser. If the laser sends 1200 nm light at the sail and the power reaching the reflective sheet is 1500 W:

(a) What is the force due to light pressure on the reflective sheet, assuming the light backscatters with 20% efficiency?
(b) If an engineer is testing the spacecraft far away from the solar system so that the gravity of the sun and planets can be ignored, and the spacecraft is 65 kg, what would be the power necessary to achieve 10% of the speed of light if the acceleration part of the journey was only 5.0 x 10^5 km? (ignore relativistic effects)

A small current loop can be used as a compass. (a) When it's placed in an external magnetic field, which plane will it be rotated into, and in which direction will its magnetic dipole moment p point? (b) Will the foop then be stretchedor compressedby B? (c) lf B varies with position, will the loop be forced toward positions where Bis greateror les!? (dl When a charged particle orbits in a magnetic field (see Ex 27-7, pg 7151, p is antiparallelto B. The force on the orbiting particle is inward (centripetal), but on the wire foop it must be outwardfor sl€bility-why?

Given: M1= 75kg; M2 = 50kg; V (M1) = 10 m/s North; V (M2) = 10 m/s West

Action: Collision, two masses stick together, move at unspecified angle in M2's initial direction

Question: Find magnitude of their speed together after collision.

An unstable nucleus of mass 1.7 ✕ 10⁻²⁶ kg, initially at rest at the origin of a coordinate system, disintegrates into three particles. One particle, having a mass of

m₁ = 1.8 ✕ 10⁻²⁷ kg,

moves in the positive y-direction with speed

v₁ = 5.4 ✕ 10⁶ m/s.

Another particle, of mass

m₂ = 8.0 ✕ 10⁻²⁷ kg,

moves in the positive x-direction with speed

v₂ = 3.2 ✕ 10⁶ m/s.

Find the magnitude and direction of the velocity of the third particle. (Assume that the +x-axis is to the right and the +y-axis is up along the page.)

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