Physics for Scientists and Engineers: Foundations and Connections
1st Edition
ISBN: 9781133939146
Author: Katz, Debora M.
Publisher: Cengage Learning
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Chapter 9, Problem 87PQ
To determine
Prove that
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Consider two vectors A = i +i+k and B = -i + j+ k. Which of the following statements about the
given vectors is not true?
O The dot product of the two vectors is equal to 1.
O The cross product between the two vectors has a z-component equal to zero.
O The magnitudes of the two vectors are the same.
O The angle between the two vectors is 70.52°
A
If the scalar product of two vectors, * and C, is
A = 2.0
equal to -3.5, if
two vectors when they are drawn starting from the
same point is equal to 130°, what is the magnitude of
and the angle between the
E. Engagement
Consider the vectors given below
A = Azî + Ayĵ + A,k
B = Bxî + Byj + B,k
Get the dot product of A andB by following the steps below.
A·B = (Azî + Ayĵ + A‚k)(Bxî + Byĵ + B,k)
Step 1: Multiply the vectors, the way you multiply polynomials. You should get 9 terms.
Ā ·B =
Step 2: Rearrange your terms. Set side by side the components and the unit vector.
A ·B =
Step 3: Apply the dot products to your unit vectors.
Recall: î · î = j· j = k · k = 1 and î ·j = î · k = j · k = 0
A·B =.
Step 4: Write the simplified and the final dot product
A·B =
Chapter 9 Solutions
Physics for Scientists and Engineers: Foundations and Connections
Ch. 9.4 - In the three cases shown in Figure 9.11, a force...Ch. 9.6 - Prob. 9.2CECh. 9.6 - Prob. 9.3CECh. 9.7 - Prob. 9.4CECh. 9.7 - Prob. 9.5CECh. 9.9 - Prob. 9.6CECh. 9 - Pick an isolated system for the following...Ch. 9 - Prob. 2PQCh. 9 - Prob. 3PQCh. 9 - Prob. 4PQ
Ch. 9 - Prob. 5PQCh. 9 - Prob. 6PQCh. 9 - Prob. 7PQCh. 9 - A 537-kg trailer is hitched to a truck. Find the...Ch. 9 - Prob. 9PQCh. 9 - A helicopter rescues a trapped person of mass m =...Ch. 9 - Prob. 11PQCh. 9 - An object is subject to a force F=(512i134j) N...Ch. 9 - Prob. 13PQCh. 9 - Prob. 14PQCh. 9 - Prob. 15PQCh. 9 - Prob. 16PQCh. 9 - Prob. 17PQCh. 9 - Prob. 18PQCh. 9 - Prob. 19PQCh. 9 - Prob. 20PQCh. 9 - Prob. 21PQCh. 9 - Prob. 22PQCh. 9 - A constant force of magnitude 4.75 N is exerted on...Ch. 9 - In three cases, a force acts on a particle, and...Ch. 9 - An object of mass m = 5.8 kg moves under the...Ch. 9 - A nonconstant force is exerted on a particle as it...Ch. 9 - Prob. 27PQCh. 9 - Prob. 28PQCh. 9 - Prob. 29PQCh. 9 - A particle moves in the xy plane (Fig. P9.30) from...Ch. 9 - A small object is attached to two springs of the...Ch. 9 - Prob. 32PQCh. 9 - Prob. 33PQCh. 9 - Prob. 34PQCh. 9 - Prob. 35PQCh. 9 - Prob. 36PQCh. 9 - Prob. 37PQCh. 9 - Prob. 38PQCh. 9 - A shopper weighs 3.00 kg of apples on a...Ch. 9 - Prob. 40PQCh. 9 - Prob. 41PQCh. 9 - Prob. 42PQCh. 9 - Prob. 43PQCh. 9 - Prob. 44PQCh. 9 - Prob. 45PQCh. 9 - Prob. 46PQCh. 9 - Prob. 47PQCh. 9 - Prob. 48PQCh. 9 - Prob. 49PQCh. 9 - A small 0.65-kg box is launched from rest by a...Ch. 9 - A small 0.65-kg box is launched from rest by a...Ch. 9 - A horizontal spring with force constant k = 625...Ch. 9 - A box of mass m = 2.00 kg is dropped from rest...Ch. 9 - Prob. 54PQCh. 9 - Return to Example 9.9 and use the result to find...Ch. 9 - Prob. 56PQCh. 9 - Crall and Whipple design a loop-the-loop track for...Ch. 9 - Prob. 58PQCh. 9 - Calculate the force required to pull a stuffed toy...Ch. 9 - Prob. 60PQCh. 9 - Prob. 61PQCh. 9 - Prob. 62PQCh. 9 - An elevator motor moves a car with six people...Ch. 9 - Prob. 64PQCh. 9 - Figure P9.65A shows a crate attached to a rope...Ch. 9 - Prob. 66PQCh. 9 - Prob. 67PQCh. 9 - Prob. 68PQCh. 9 - Prob. 69PQCh. 9 - Prob. 70PQCh. 9 - Prob. 71PQCh. 9 - Estimate the power required for a boxer to jump...Ch. 9 - Prob. 73PQCh. 9 - Prob. 74PQCh. 9 - Prob. 75PQCh. 9 - Prob. 76PQCh. 9 - Prob. 77PQCh. 9 - Prob. 78PQCh. 9 - Prob. 79PQCh. 9 - A block of mass m = 0.250 kg is pressed against a...Ch. 9 - On a movie set, an alien spacecraft is to be...Ch. 9 - Prob. 82PQCh. 9 - A spring-loaded toy gun is aimed vertically and...Ch. 9 - Prob. 84PQCh. 9 - The motion of a box of mass m = 2.00 kg along the...Ch. 9 - Prob. 86PQCh. 9 - Prob. 87PQCh. 9 - Prob. 88PQ
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- (a) For what values of the angle between two vectors is their scalar product positive? (b) For what values of is their scalar product negative?arrow_forwardGiven a vector A=4.5+4.5j and a vector B=4.5+4.5j, determine the magnitude of the cross product of these two vectors, AB. Hint: Make a sketch of both vectors including a coordinate system.arrow_forwardIn three cases, a force acts on a particle, and the particle is displaced from an initial position to a final position. Figure 9.11 (page 255) shows the position-versus-force graphs, indicating the initial and final positions of the particle in each case. Find the work done by the force on the particle and sketch the force and displacement vectors along with the appropriate axis in each case.arrow_forward
- February 3, 2009, was a very snowy day along Interstate 69 just outside of Indianapolis, Indiana. As a result of the slippery conditions and low visibility (50 yards or less), there was an enormous accident involving approximately 30 vehicles, including cars, tractor-trailers, and even a fire truck. Many witnesses said that people were driving too fast for the conditions and were too close together. In this problem, we explore two rules of thumb for driving in such conditions. The first is to drive at a speed that is half of what it would be in ideal conditions. The other is the 8-second rule: Watch the vehicle in front of you as it passes some object such as a street sign, and you should pass that same object 8 seconds later. On a dry road, the 8-second rule is replaced by a 3-second rule. a. Assume vehicles on a slippery interstate highway follow both rules. What is the distance between the vehicles? b. If a driver followed the first rule of thumb, driving at a lower speed, but used the 3-second rule instead of the 8-second rule, what is the distance between the vehicles? How does that distance compare with the visibility on the day of the accident? c. Suppose drivers do not follow either rule of thumb for slippery conditions. What is the distance between vehicles? How does that distance compare with the visibility on that day? d. Suppose a driver was not obeying either rule of thumb when she sees a tractor-trailer that stopped on the highway. She presses on her brakes, locking the wheels, and her car crashes into the truck. Estimate the magnitude of the impulse exerted on her car. e. Estimate the impulse on the car in part (d) had the driver followed both rules of thumb for slippery conditions instead of ignoring them.arrow_forwardA train moves along the tracks at a constant speed u. A woman on the train throws a ball of mass m straight ahead with a speed υ with respect to herself. (a) What is the kinetic energy gain of the ball as measured by a person on the train? (b) by a person standing by the railroad track? (c) How much work is done by the woman throwing he ball and (d) by the train?arrow_forwardThe two-dimensional vectors A and B both have magnitudes of 7.00 m. If A+B=4.00m, what is the angle between A and B?arrow_forward
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- PartA Glven two vectors A-400+3.60 3 and B 5.80 i-2.00 nd the scalar product of the two vectors A and B. Submit Request Answer Part B Find the angle between these two vectors.arrow_forwardPart A Find the angle between each of the following pairs of vectors A = Agi + Ayj and B = Bại + Byj. Az, = -1.60, Ay, =7.80; Bz, =2.90, Bu, =-3.30. You may want to review (Page). ΑΣΦ ? For related problemsolving tips and strategies, you may want to view a Video Tutor Solution of Finding an angle with the scalar product. Submit Previous Answers Request Answerarrow_forwardThe Vector Product Two vectors lying in the xy-plane are given by the equations A = 8î + 2j and B = -3î + 3j. Find Ax B and verify that à ×B = -B x A. SOLUTION Conceptualize Given the unit-vector notations of the vectors, think about the directions the vectors point in space. Draw them on graph paper and imagine the parallelogram for these vectors. Categorize Because we use the definition of the cross product discussed in this section, we categorize this example as-Select-- problem. Write the cross product of the two vectors: AxB = î + 2j ) x î + 3j Perform the multiplication: ĀxB = 8î x (-3î) + 8î × 3j +| j x (-3î) + 2j x Use the equations for the cross product of unit vectors to evaluate the various terms: AXB = To verify that AxB = -B x A, evaluate Bx A: BxA = (-31 + Perform the multiplication: BxA = (-31) x ]î +(-3î) × 2j + 3ĵ × 8î + j x 2j Use the equations for the cross product of unit vectors evaluate the various terms: BxA = Therefore, Ax B = -B xA As an alternative method for…arrow_forward
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