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Mastering Physics Tutorial Question Series

Chapter 1 Vector Tutorial Question 1) In general it is best to conceptualize vectors as arrows in space, and then to make calculations with them using their components. (You must first specify a coordinate system in order to find the components of each arrow.) This problem gives you some practice with the components. Let vectors A

=(1,0,−3), B =(−2,5,1), and C =(3,1,1). Calculate the following, and

express your answers as ordered triplets of values separated by commas.

a) A −B =

b) B −C = c) −A +B −C = d) 3A −2C = e) −2A +3B −C = f)

2A −3(B −C ) =

2) Part A Find the magnitude of the vector A1→ represented by the pair of components

Ax1=9.10cm, Ay1= 2.40cm. Part B Let the direction of a vector be the angle that the vector makes with the +x-axis, measured counterclockwise from that axis. Find the direction of the vector A1. __________________________________________________________________________

Part C Find the magnitude of the vector A2→ represented by the pair of components Ax2= 9.50m , Ay2= -2.20m . __________________________________________________________________________

Part D Find the direction of the vector A2→. Let the direction of a vector be the angle that the vector makes with the +x-axis, measured counterclockwise from that axis. __________________________________________________________________________ 1

Mastering Physics Tutorial Question Series

Part E Find the magnitude of the vector A3→ represented by the pair of components Ax3= 7.35km , Ay3= -2.90km . __________________________________________________________________________

Part F Find the direction of the vector A3→. Let the direction of a vector be the angle that the vector makes with the +x-axis, measured counterclockwise from that axis. __________________________________________________________________________ 3)

Often a vector is specified by a magnitude and a direction; for example, a rope with tension T exerts a force of magnitude T in a direction 35∘ north of east. This is a good way to think of vectors; however, to calculate results with vectors, it is best to select a coordinate system and manipulate the components of the vectors in that coordinate system.

Part A

Find the components of the vector A with length a = 1.00 and angle α=20.0∘ with respect to the x axis as shown.

__________________________________________________________________________

Part B

Find the components of the vector B with length b = 1.00 and angle β=20.0∘ with respect to the x axis as shown.

__________________________________________________________________________

Part C

Find the components of the vector C with length c = 1.00 and angle ϕ= 35.0∘ as shown.

__________________________________________________________________________

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Mastering Physics Tutorial Question Series

4)

In each case, find the x- and y-components of vector A .

Part A

A = 4.8 i^− 5.9 j^ __________________________________________________________________________

Part B

A^= 12.2 j^− 4.91 i^ __________________________________________________________________________

Part C

A =− 12.0 i^+ 23.2 j^ __________________________________________________________________________

Part D

A =5.0B^, where B^= 6 i^− 8 j^

__________________________________________________________________________

5)

A spelunker is surveying a cave. She follows a passage 180m straight west, then 210m in a direction 45∘ east of south, and then 280 m at30∘ east of north. After a fourth unmeasured displacement, she finds herself back where she started.

Part A Use a scale drawing to determine the magnitude of the fourth displacement. __________________________________________________________________________

Part B Determine the direction of the fourth displacement. __________________________________________________________________________ 6)

A disoriented physics professor drives a distance 3.50 km north, then a distance 4.15km west, and then a distance 1.40km south.

Part A Find the magnitude of the resultant displacement, using the method of components. __________________________________________________________________________

Part B Find the direction of the resultant displacement, using the method of components. __________________________________________________________________________

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Mastering Physics Tutorial Question Series

7)

In nature, substances often possess a crystalline structure. The basic component of a crystal is the unit cell, such as the rectangular parallelpiped illustrated.

In the questions that follow express your answers in terms of the unit vectors that is, a vector with components

i^, j^, and k^,

Vx, Vy, and Vz in the x, y, and zdirections, respectively, is

written Vxi^+Vyj^+Vzk^.

Part A What is the vector V CO from point C to point O? __________________________________________________________________________

Part B What is the vector V OE from point O to point E? __________________________________________________________________________

Part C What is the vector V OF from point O to point F? __________________________________________________________________________

Part D What is the vector from A to B, V AB? __________________________________________________________________________

Part E What is the vector V BE from point B to point E? __________________________________________________________________________

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Mastering Physics Tutorial Question Series

Chapter 2 Motion Tutorial Question 1)

An object moves along the x axis during four separate trials. Graphs of position versus time for each trial are shown in the figure.

Part A During which trial or trials is the object's velocity not constant? Check all that apply.

Trial A Trial B Trial C Trial D Part B During which trial or trials is the magnitude of the average velocity the largest?

Trial A Trial B Trial C Trial D

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Mastering Physics Tutorial Question Series

2)

Two cars travel on the parallel lanes of a two-lane road. The cars’ motions are represented by the position versus time graph shown in the figure. Answer the questions using the times from the graph indicated by letters.

Part A At which of the times do the two cars pass each other? __________________________________________________________________________ Are the two cars traveling in the same direction when they pass each other? __________________________________________________________________________

Part C At which of the lettered times, if any, does car #1 momentarily stop? __________________________________________________________________________

Part D At which of the lettered times, if any, does car #2 momentarily stop? __________________________________________________________________________

Part E At which of the lettered times are the cars moving with nearly identical velocity? __________________________________________________________________________

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Mastering Physics Tutorial Question Series

3)

To describe the motion of a particle along a straight line, it is often convenient to draw a graph representing the position of the particle at different times. This type of graph is usually referred to as an x vs. t graph. To draw such a graph, choose an axis system in which time t is plotted on the horizontal axis and position x on the vertical axis. Then, indicate the values of x at various times t. Mathematically, this corresponds to plotting the variable x as a function of t. An example of a graph of position as a function of time for a particle traveling along a straight line is shown below. Note that an x vs. t graph like this does not represent the path of the particle in Now let's study the graph shown in the figure in more detail. (Figure 1) Refer to this graph to answer Parts A, B, and C.

Part A What is the total distance Δx traveled by the particle? __________________________________________________________________________

Part B What is the average velocity vav of the particle over the time interval Δt=50.0s? __________________________________________________________________________

Part C What is the instantaneous velocity v of the particle at

t=10.0s?

__________________________________________________________________________ Another common graphical representation of motion along a straight line is the v vs. t graph, that is, the graph of (instantaneous) velocity as a function of time. In this graph, time t is plotted on the horizontal axis and velocity v on the vertical axis. Note that by definition, velocity and acceleration are vector quantities. In straight-line motion, however, these vectors have only one nonzero component in the direction of motion. Thus, in this problem, we will call v the velocity and a the acceleration, even though they are really the components of the velocity and acceleration vectors in the direction of motion. 7

Mastering Physics Tutorial Question Series

Part D Which of the graphs shown is the correct v vs. t plot for the motion described in the previous parts?

Part E

Shown in the figure is the v vs. t curve selected in the previous part. What is the area A of the shaded region under the curve? __________________________________________________________________________

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Mastering Physics Tutorial Question Series

4) Consider the motion of a power ball that is dropped on the floor and bounces back. In the following questions, you will describe its motion at various points in its fall in terms of its velocity and acceleration.

Part A

(Figure 1) You drop a power ball on the floor. The motion diagram of the ball is sketched in the figure (Figure 1). Indicate whether the magnitude of the velocity of the ball is increasing, decreasing, or not changing. You drop a power ball on the floor. The motion diagram of the ball is sketched in the figure . Indicate whether the magnitude of the velocity of the ball is increasing, decreasing, or not changing.

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Mastering Physics Tutorial Question Series While the ball is in free fall, the magnitude of its velocity is increasing, so the ball is accelerating.

Part B

(Figure 3) Since the length of

v is directly proportional to the length of Δr , the vector connecting each

dot to the next could represent velocity vectors as well as position vectors, as shown in the figure here (Figure 3) . Indicate whether the velocity and acceleration of the ball are, respectively, positive (upward), negative, or zero. __________________________________________________________________________

Part C

(Figure 2) Now, consider the motion of the power ball once it bounces upward. Its motion diagram is shown in the figure here (Figure 2) . Indicate whether the magnitude of the velocity of the ball is increasing, decreasing, or not changing. Now, consider the motion of the power ball once it bounces upward. Its motion diagram is shown in the figure here . Indicate whether the magnitude of the velocity of the ball is increasing, decreasing, or not changing.

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Mastering Physics Tutorial Question Series Since the magnitude of the velocity of the ball is decreasing, the ball must be accelerating (specifically, slowing down).

Part D

(Figure 4) The next figure (Figure 4) shows the velocity vectors corresponding to the upward motion of the power ball. Indicate whether its velocity and acceleration, respectively, are positive (upward), negative, or zero. Use P, N, and Z for positive (upward), negative, and zero, respectively. Separate the letters for velocity and acceleration with a comma. __________________________________________________________________________

Part E The power ball has now reached its highest point above the ground and starts to descend again. The motion diagram representing the velocity vectors is the same as that after the initial release, as shown in the figure of Part B. Indicate whether the velocity and acceleration of the ball at its highest point are positive (upward), negative, or zero. __________________________________________________________________________

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Mastering Physics Tutorial Question Series

5)

(Figure 1) A graph of acceleration of the table versus time, termed a ballistocardiogram, is generated. Based on these measurements, the acceleration of the blood ejected by the heart can be determined. Patients with low blood accelerations generally have weakened heart muscles. A sketch of a single cycle of a ballistocardiogram is given in the figure. (Figure 1) . The units of the graph are arbitrary and linear for both time,t, and acceleration, a.

Part A At what time (in the arbitrary time units of the graph) is the speed of the table (and hence the speed of the blood in the opposite direction) a maximum? __________________________________________________________________________

6)

Part A At what time(s) do the rockets have the same velocity? __________________________________________________________________________

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Mastering Physics Tutorial Question Series

Part B At what time(s) do the rockets have the same x position? __________________________________________________________________________

Part C At what time(s) do the two rockets have the same acceleration? __________________________________________________________________________

Part D The motion of the rocket labeled A is an example of motion with uniform (i.e., constant) __________.

and nonzero acceleration velocity displacement time Part E The motion of the rocket labeled B is an example of motion with uniform (i.e., constant) __________

and nonzero acceleration velocity displacement time Part F At what time(s) is rocket A ahead of rocket B? __________________________________________________________________________

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Mastering Physics Tutorial Question Series

7)

Part A Which direction best approximates the direction of

a when the object is at position 1?

straight up downward to the left downward to the right straight down Part B Which direction best approximates the direction of

a when the object is at position 2?

straight up upward to the right straight down downward to the left Even though the acceleration is directed straight up, this does not mean that the object is moving straight up.

Part C Which direction best approximates the direction of

upward to the right to the right straight down downward to the right

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a when the object is at position 3?

Mastering Physics Tutorial Question Series

8) A rhinoceros is at the origin of coordinates at time t1=0. For the time interval from t1 to t2 = 13.0s, the rhino's average velocity has x-component -3.8m/s and ycomponent 5.2m/s .

Part A At time t2= 13.0s what is the x-coordinate of the rhino? __________________________________________________________________________

Part B At time t2= 13.0s what is the y-coordinate of the rhino? __________________________________________________________________________

Part C How far is the rhino from the origin? __________________________________________________________________________

9) A battleship simultaneously fires two shells toward two identical enemy ships. One shell hits ship A, which is close by, and the other hits ship B, which is farther away. The two shells are fired at the same speed. Assume that air resistance is negligible and that the magnitude of the acceleration due to gravity is g. Note that after Part B the question setup changes slightly.

Part A What shape is the trajectory (graph of y vs. x) of the shells?

straight line parabola hyperbola The shape cannot be determined. Part B For two shells fired at the same speed which statement about the horizontal distance traveled is correct?

The shell fired at a larger angle with respect to the horizontal lands farther away. The shell fired at an angle closest to 45 degrees lands farther away. The shell fired at a smaller angle with respect to the horizontal lands farther away. The lighter shell lands farther away.

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Mastering Physics Tutorial Question Series Now, consider for the remaining parts of the question below that both shells are fired at an angle greater than 45 degrees with respect to the horizontal. Remember that enemy ship A is closer than enemy ship B.

Part C Which shell is fired at the larger angle?

A B Both shells are fired at the same angle. Part D Which shell is launched with a greater vertical velocity, vy?

A B Both shells are launched with the same vertical velocity. Part E Which shell is launched with a greater horizontal velocity, vx?

A B Both shells are launched with the same horizontal velocity. Part F Which shell reaches the greater maximum height?

A B Both shells reach the same maximum height. Part G Which shell has the longest travel time (time elapsed between being fired and hitting the enemy ship)?

A B Both shells have the same travel time.

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Mastering Physics Tutorial Question Series

10) Consider a particle with initial velocity v that has magnitude 12.0 m/s and is directed 60.0 degreesabove the negative x axis. Part A What is the x component vx of v ? __________________________________________________________________________

Part B What is the y component vy of v ? __________________________________________________________________________ Breaking up the velocities into components is particularly useful when the components do not affect each other. Eventually, you will learn about situations in which the components of velocity do affect one another, but for now you will only be looking at problems where they do not. So, if there is acceleration in the x direction but not in the y direction, then the x component of the velocity will change, but the y component of the velocity will not.

Part C

(Applet)

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Mastering Physics Tutorial Question Series Look at the applet. The motion diagram for a projectile is displayed, as are the motion diagrams for each component. The x-component motion diagram is what you would get if you shined a spotlight down on the particle as it moved and recorded the motion of its shadow. Similarly, if you shined a spotlight to the left and recorded the particle's shadow, you would get the motion diagram for its y component. How would you describe the two motion diagrams for the components?

Both the vertical and horizontal components exhibit motion with constant nonzero acceleration. The vertical component exhibits motion with constant nonzero acceleration, whereas the horizontal component exhibits constant-velocity motion. The vertical component exhibits constant-velocity motion, whereas the horizontal component exhibits motion with constant nonzero acceleration. Both...