Question An electron moves along the z-axis with vz=4.8×107m/s. As it passes the origin, what are the strength and direction of the magnetic field at the following (x, y, z) positions? (2 cm, 0 cm, 0 cm) (0 cm, 0 cm ,1 cm) (0 cm, 2 cm , 1 cm )

In M25a experiment, you are going to observe Newton’s Second Law for rotational motion, experimentally determine moment of inertia of a platform and of a hollow cylinder (“hoop”), and compare your experimental values with theoretical/calculated values. It is possible that a number of students will be conducting this experiment before the material is covered in a lecture course. Since many concepts could be new for you, it is important to read your text, the lab handout, and become familiar with the concepts related to the experiment and the calculations you will be expected to do in the lab. You can also ask your lecture instructor for help, if needed. M25a Prelab: Rotational Equilibrium and Rotational Dynamics Read lab instructions before answering the questions IMPORTANT In M25a experiment, you are going to observe Newton's Second Law for rotational motion, experimentally determine moment of inertia of a platform and of a hollow cylinder ("hoop"), and compare your experimental values with theoretical/calculated values. It is possible that a number of students will be conducting this experiment before the material is covered in a lecture course. Since many concepts could be new for you, it is important to read your text, the lab handout and become familiar with the concepts related to the experiment and the calculations you will be expected to do in the lab. You can also ask your lecture instructor for help, if needed. Once you are fully prepared answer the following questions: PARTI 1. Give the definition of a lever arm. 2. Write down the equation to calculate the torque if the magnitude of a force and the lever arm are given. 3. A ruler is suspended on a pivot point and a mass is hanging on each side of the suspension point. The system is in equilibrium. How does the torque on the right side compare to the torque on the left side? PART II 4. In the second part of the experiment, the rotation of the system occurs because a hanging mass moves with linear acceleration a, and is attached to a pulley with radius r. Write down the equation that you will use to calculate the linear . acceleration using the measured radius and angular acceleration. 5. Write down the equation you will use to calculate tension in the string using the linear acceleration a mass m, and free-fall acceleration g. 6. The force that exerts the torque on the disk/hoop system is the tension applied to the string. Write down the equation to calculate this torque using the tension and the radius.

The Anderson County board of supervisors has agreed to fund an ambitious project that will spend money now to save much more money in the future. A total of $16.2 million will be awarded to the York Corporation for energy improvements in 40 buildings, 27 parks, and 37 traffic intersections. These improvements include lighting upgrades, solar hot water collectors, more efficient heating/cooling systems, and light-emitting diodes for traffic signals. Bonds paying 7% per year over the next 15 years will be used to pay for these improvements. If the annual savings fail to average $2 million, York Corporation will reimburse the county the difference. Will York need to pay any money to the county? If so, how much?

Problem 5. [15 pts) Work out the curl of integrand F in the following line integrals to determine whether it is path independent. If yes, find out the corresponding potential function f and calculate the integration from (0, 0, 0) to (a, b, c). (a) [5 pts) Sexydx + x2ydy + 6zędz (b) [10 pts] Sc sin(x2 + 2y2 + z2) (2xdx + 4ydy + 2zdz)

 The area bounded by the curve y^2 = 12x and the line x = 3 is revolved about the line x =3. What is the volume generated? Show full solution

A researcher conducts an experiment comparing four treatment conditions with a separate sample of n=6 in each treatment. An ANOVA is used to evaluate the data, and the results of the ANOVA are presented in the following table. Complete all missing values in the table. Hint: Begin with the values in the df column. SourceSdfMSBetweenF =treatmentsWithintreatmentsTotal58

4. A 2-wire d.c. distributor is 250 m long. It is to be loaded as shown in Fig 13.10 at 50 m intervals. If the maximum voltage drop is not to exceed 10V and the resistivity of core material is 0-7 x 2-54 µN cm, determine the maximum cross-sectional area of each conductor. [1-602 cm*] Supply End 120 A 90 A 60 A 50 A 80 A