Two force vectors F1 and F2 are applied at the origin of the system of coordinates, point O of coordinates (0,0,0). The two force are expressed in Newton units (N). The vector expressed of the first fore is F1=(-120i+60j+40k) N. The second force F2 has a magnitude of 85 N and its direction is defined by the line between point O and B (4, -3, 5), where these coordinates are in meters (m). (a) Find unit vector ef1alone F1. (b) Find unit vector ef2alone F2. (c) find the angle O between F1 and F2 using the dot product operation. (d) Find the force vector resultant R=F1+F2. (e) find the direction cosine, cosOxof vector R.

## Two force vectors F1 and F2 are applied at the origin of the system of coordinates, point O of coordinates (0,0,0). The two force are expressed in Newton units (N). The vector expressed of the first fore is F1=(-120i+60j+40k) N. The second force F2 has a magnitude of 85 N and its direction is defined by the line between point O and B (4, -3, 5), where these coordinates are in meters (m). (a) Find unit vector ef1alone F1. (b) Find unit vector ef2alone F2. (c) find the angle O between F1 and F2 using the dot product operation. (d) Find the force vector resultant R=F1+F2. (e) find the direction cosine, cosOxof vector R.

Chapter 3 Practice Problems (Practice – no credit) Due: 11:59pm on Wednesday, February 12, 2014 You will receive no credit for items you complete after the assignment is due. Grading Policy Tactics Box 3.1 Determining the Components of a Vector Learning Goal: To practice Tactics Box 3.1 Determining the Components of a Vector. When a vector is decomposed into component vectors and parallel to the coordinate axes, we can describe each component vector with a single number (a scalar) called the component. This tactics box describes how to determine the x component and y component of vector , denoted and . TACTICS BOX 3.1 Determining the components of a vector The absolute value of the x component is the magnitude of the 1. component vector . 2. The sign of is positive if points in the positive x direction; it is negative if points in the negative x direction. 3. The y component is determined similarly. Part A What is the magnitude of the component vector shown in the figure? Express your answer in meters to one significant figure. A A x A y A Ax Ay |Ax| Ax A x Ax A x A x Ay A x

## Chapter 3 Practice Problems (Practice – no credit) Due: 11:59pm on Wednesday, February 12, 2014 You will receive no credit for items you complete after the assignment is due. Grading Policy Tactics Box 3.1 Determining the Components of a Vector Learning Goal: To practice Tactics Box 3.1 Determining the Components of a Vector. When a vector is decomposed into component vectors and parallel to the coordinate axes, we can describe each component vector with a single number (a scalar) called the component. This tactics box describes how to determine the x component and y component of vector , denoted and . TACTICS BOX 3.1 Determining the components of a vector The absolute value of the x component is the magnitude of the 1. component vector . 2. The sign of is positive if points in the positive x direction; it is negative if points in the negative x direction. 3. The y component is determined similarly. Part A What is the magnitude of the component vector shown in the figure? Express your answer in meters to one significant figure. A A x A y A Ax Ay |Ax| Ax A x Ax A x A x Ay A x

To identify the correct notation for a point and a vector, determine the position vector of a point relative to another point , and calculate the corresponding unit vector. although vectors are often constructed from points , points are not vectors, vectors are commonly constructed from either : (1) the origin to a point or (2) a starting point to an ending point. Part A ) as shown on the coordinate system, points A and B have the following distance from the origin : xA = 2.70 ft , zA = 2.50 ft , xB = 1.10 ft , and zB = 1.70 ft. which of the following statements correctly describes the location and position vector of point A from the origin ? Use appropriate notation for the location and position vector of a point,

## To identify the correct notation for a point and a vector, determine the position vector of a point relative to another point , and calculate the corresponding unit vector. although vectors are often constructed from points , points are not vectors, vectors are commonly constructed from either : (1) the origin to a point or (2) a starting point to an ending point. Part A ) as shown on the coordinate system, points A and B have the following distance from the origin : xA = 2.70 ft , zA = 2.50 ft , xB = 1.10 ft , and zB = 1.70 ft. which of the following statements correctly describes the location and position vector of point A from the origin ? Use appropriate notation for the location and position vector of a point,

Chapter 5 Practice Problems (Practice – no credit) Due: 11:59pm on Friday, March 14, 2014 You will receive no credit for items you complete after the assignment is due. Grading Policy Tactics Box 5.1 Drawing Force Vectors Learning Goal: To practice Tactics Box 5.1 Drawing Force Vectors. To visualize how forces are exerted on objects, we can use simple diagrams such as vectors. This Tactics Box illustrates the process of drawing a force vector by using the particle model, in which objects are treated as points. TACTICS BOX 5.1 Drawing force vectors Represent the object 1. as a particle. 2. Place the tail of the force vector on the particle. 3. Draw the force vector as an arrow pointing in the proper direction and with a length proportional to the size of the force. 4. Give the vector an appropriate label. The resulting diagram for a force exerted on an object is shown in the drawing. Note that the object is represented as a black dot. Part A A book lies on a table. A pushing force parallel to the table top and directed to the right is exerted on the book. Follow the steps above to draw the force vector . Use the black dot as the particle representing the book. F  F push F push

## Chapter 5 Practice Problems (Practice – no credit) Due: 11:59pm on Friday, March 14, 2014 You will receive no credit for items you complete after the assignment is due. Grading Policy Tactics Box 5.1 Drawing Force Vectors Learning Goal: To practice Tactics Box 5.1 Drawing Force Vectors. To visualize how forces are exerted on objects, we can use simple diagrams such as vectors. This Tactics Box illustrates the process of drawing a force vector by using the particle model, in which objects are treated as points. TACTICS BOX 5.1 Drawing force vectors Represent the object 1. as a particle. 2. Place the tail of the force vector on the particle. 3. Draw the force vector as an arrow pointing in the proper direction and with a length proportional to the size of the force. 4. Give the vector an appropriate label. The resulting diagram for a force exerted on an object is shown in the drawing. Note that the object is represented as a black dot. Part A A book lies on a table. A pushing force parallel to the table top and directed to the right is exerted on the book. Follow the steps above to draw the force vector . Use the black dot as the particle representing the book. F  F push F push

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