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# Scalar and Vector Operations

### Stokes and Gauss' Theorem

1. A vector ﬁeld v(x, y, z) is given by the formula v(x, y, z) = xyˆx − yˆ2y. Consider a square path in the xy plane which starts at (0,0,0) and moves along the corners (1,0,0), (1,1,0) and (0,1,0). Calculate the path integral of v, i.e. v · dr, and calculate the area integral of the divergence, R ∇ × v · da, an

### Center of Mass of Particles

A) Find the xcm coordinate of the center of mass of the system of particles shown in the figure. (See attached file for full problem description with diagram and values) Express your answer in meters to two significant figures. xcm = B) A straight rod has one end at the origin and the other end at the point (L,0) and

### Center of Mass and Coordinate System

A system of four buckets forms a square as shown in the figure. Initially, the buckets have different masses (it is not known how these masses are related). A student begins to add water gradually to the bucket located at the origin. As a result, what happens to the coordinates of the center of mass of the system of buckets? (Se

### Find the x coordinate of the center of mass.

Please see the attached file for full problem description with diagram. For the system of particles described above, find the x coordinate xcm of the center of mass. Assume that the particle of mass M is at the origin and the positive x axis is directed to the right. Express your answer in terms of L.

### Force; Calculating X and Y Components of a Quadrant

Could you show me how to perform the calculation asked for? It is part B. Calculate the theoretical x and y components of the first quadrant force vector using the cosine and sine of the measured angle and the measured first quadrant force. Then compare these values to the experimental scale readings along the x and y directi

### Finding the force on a helicopter given its position vector as a function of time.

(See attached file for full problem description with proper symbols) The position of a 2.75 x 10^5 N training helicopter under test is given by Vector r = (0.020 m/s3)t3î + (2.2m/s)t&#309; - (0.060 m/s2)t2k Find the net force on the helicopter at t =5.0 s. Express the vector F in the form Fx, Fy , Fz , where th

### Scalar and Vector Operations

(See attached file for full problem description with proper symbols) 1. Write each vector in terms of the unit vectors ^i and ^j. 2. Use unit vectors to express the vector C, where C = 3.00A - 4.00B. 3. Find the magnitude and direction of C.

### Direction and Work Done by Electric Field

(See attached file for full problem description) --- 4 a) Sketch arrows on the diagram (see attachment) to indicate the direction of the electric field, if any, at each of the points A, B, C, and D. A positively charged test particle is observed to move as described below. For each motion, tell whether the work done by

### Finding the Magnitude and Direction of Vectors from a Graph

Please see attachment for the graphs necessary to do these questions.

### Vector Addition and Visual Representation

1) Find the angle that the vector makes with vector . Express in terms of and any of the quantities given in the problem introduction ( , , and/or ) as well as any necessary constants. 2) In the coordinate system, what are the components of ? Express your answer as an ordered pair separated by a comma. Give your

### Obtaining a Unit Vector

Please see attachment for a unit vector problem I require help with.

### Vector Cross Product

The vector is 3.50 cm long and is directed into this page. Vector points from the lower-right corner of this page to the upper-left corner of this page and has the components , . 1) In the right-handed coordinate system, where the +x-axis directed to the right, the +y-axis toward the top of the page, and +z-axis out of th

### Vector calculation of a plane

A plane leaves the airport in Galisto and flies a distance 170 km at an angle 68.0 degree east of north and then changes direction to fly a distance 270 km at an angle 48.0 degree south of east, after which it makes an immediate emergency landing in a pasture. When the airport sends out a rescue crew, how far should this crew

### Vector Dot Product

How do I express these vectors as their product? Question attached.

### Vectors and Coordinate Systems

1) Find the components in the tilted coordinate system. Express your answer in terms of the length of the vector and the angle, with the components separated by a comma. 2) You are camping with two friends, Joe and Karl. Since all three of you like your privacy, you don't pitch your tents close together. Joe's tent is 25.0 m

### Vectors physics problem

Please see attached file for the full problem description. Find , the length of , the sum of and . Express in terms of , , and angle .

### Displacement Magnitude

A plane travels 3.8km at an angle of 26 degrees to the ground, then changes direction and travels 7.4km at an angle of 13 degrees to the ground. a) What is the magnitude of the plane's total displacement? Answer in units of km. b) At what angle above the horizontal is the plane's total displacement? Answer in units of de

### 8 Problems Vectors: Components of a vector, resultant vector

(See attached file for full problem description with diagrams) --- Please solve each and give a complete detailed step by step solution to solving each problem no matter how easy. I am trying to learn and not an expert. Give answer and way to solve. Adult student trying to make my way through all this and need your help!

### Force Impulse and Projectile Motion

In a slow-pitch softball game, a 0.200 kg softball crossed the plate at 20.00 m/s at an angle of 35.0° below the horizontal. The batter hits the ball toward center field, giving it a velocity of 40.0 m/s at 30.0° above the horizontal. (a) Determine the impulse delivered to the ball. (b) If the force on the ball increase

### What are the coordinates of the third mass of 3.0 kg?

The center of mass of three objects is located a (1,0). one object with a mass of 5.0 kg is at (-2,-1) and a second object with a mass of 2.0 kg is at (0,0). What are the coordinates of the third mass of 3.0 kg?

### Body on slope with friction

Please help with the following problem. Provide step by step calculations for each problem. You have a mass of 59 kg and are on a 28-degree slope hanging on to a cord with a breaking strength of 224 newtons. What must be the coefficient of static friction to 2 decimal places between you and the surface for you to be saved fr

### Scalar Components of a Vector

The force of magnitude 24Squareroot2 Newtons makes an angle of 225 degrees with the positive x axis. Find the x and y scalar components of the vector.

### Kinematics and Energy Kinematics

Could you provide workings out and answers to the following physics questions: 1.a. What is the difference between a scalar and a vector quantity? b. A hiker walks due north for 4.0 km to reach point A and then northeast for 6.0 km to reach point B. Find by calculation or by scale drawing: - the straight line distance from s

### Keeping a derrick from tipping

A load having a mass of 9.2 metric tons is to be lifted by means of a contractor's derrick as shown in fig 5-10. If the Vertical plane containing the boom bisects the angle ADB, what reactions must be provided at points A and B to keep the derrick from tipping? The boom has a mass of 1.84 metric tons, and it makes an angle of 4

### Physical principles; difference between a vector and scalar distance, difference between speed and velocity

1. Understanding physical principles is often very useful in everyday life. For example, a skater develops an intuitive understanding of angular momentum in order to master making turns, and virtually all of us as car drivers come to understand the principles of inertia, velocity, and linear momentum. Can you name at least

### Calculations for Vectors

Please provide formulas and step by step instructions on how to solve. A Vector F has a magnitude of 20 and is directed vertically downward. Find is components Fx and Fy in each of the coordinate frames. Please see attached.

### Solving Vector Problems

Hi, I am having a lot of difficulty understanding vectors, can you please assist me with these questions. Given: position vector A = i hat. position vector B = i hat + j hat + k hat. 1) Find A hat and B hat (unit vector in that direction). 2) Find position vector C in that plane perpendicular to position ve

### Area; Scalar; Vector; Cross Product etc...

Please assist me with the attached problems, including: 1. Find the area within the given set of points 2. Determine whether each product is a scalar or a vector or does not exist. Explain reasoning. See attachment for complete list of problems. Thanks

### MAGNITUDE OF A VECTOR

If A=(12i-16j) and B=(-24i+10j),what is the magnitude of vector C=(2A-B)?

### Solving for Vector Addition and Subtraction

Question: Two vectors act upon a body at an angle of 45 degrees between them. Vector A has a magnitude of 100.0 and vector B has a magnitude of 200.0. Draw an XY coordinate system. What are the x and y components of the resultant vector? What is the magnitude of the resultant, and it's directions angle with respect to the A vec