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 18PQ
To determine
Show that the dot product of vector gives square of vector
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A.determine the work done by the force on the particle with the appropriate units.
B.what is the angle between the force and the particles displacement.
8) Consider two vectors À and B where:
A = -6.00 ¢ + 3.00 ¡ + 3.00 k
B = 6.00 1 - 8.00 ¡ + 4.00 k
If we want to find the angle between these two vectors, we have two options: we can use the magnitude of the dot product, or the magnitude of the cross product.
À • B = AB cos(e)
A x BI = AB sin(e)
However, these approaches give conflicting answers for the value of e.
a) What is the correct value of theta?
b) Why does the other formula give the wrong answer?
a) Show that a constant force field does zero work on a particle that moves once uniformly around the circle x2 + y2 = 1 (b) Is this also true for a force field , where is a constant and ?
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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- Given 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_forward(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_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
- A light spring is attached to a block of mass 4m at rest on a frictionless, horizontal table. A second block of mass m is now placed on the table, in contact with the free end of the spring, and the two blocks are pushed together (Fig. P10.78). When the blocks are released, the more massive block moves to the left at 2.50 m/s. a. What is the speed of the less massive block? b. If m = 1.00 kg, what is the elastic potential energy of the system before it is released from rest? FIGURE P10.78arrow_forwardOn a movie set, an alien spacecraft is to be lifted to a height of 30.0 m for use in a scene. The 200.0-kg spacecraft is attached by ropes to a massless pulley on a crane, and four members of the films construction crew lift the prop at constant speed by delivering 185 W of power each. If 20.0% of the mechanical energy delivered to the pulley is lost to friction, what is the time interval required to lift the spacecraft to the specified height?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_forward
- In an attempt to produce exotic new particles, a proton of mass mp = 1.67 1027 kg is accelerated to 0.99c (c = 3.00 108 m/s is the speed of light) and crashed into a helium nucleus of mass mHe = 6.64 1027 kg initially at rest. The collision is elastic. a. What is the kinetic energy of the helium nucleus after the collision? b. What is the kinetic energy of the proton after the collision? (In Chapter 39, well learn what Einstein says about making such calculations.)arrow_forwardA) Find the scalar product of the two vectors A = 4.00î + 7.00ĵ and B=5.00î - 2.00ĵ , b) find the angle between these two vectors, c) find the cross products in 3 ways.arrow_forward(a) Take U = 5 for a system with a particle at position x = 0 and calculate the potential energy of the system as a function of the particle position x. The force on the particle is given by (8e-2x) î . (b) Explain whether the force is conservative or nonconservative and how you can tell.arrow_forward
- (a) If an electron is projected horizontally with a speed of 3.0 * 106 m/s, how far will it fall in traversing 1.0 m of horizontal distance? (b) Does the answer increase or decrease if the initial speed is increased?arrow_forwardConsider the vectors a = i + 8j + 4k and b = 7i − 6j − 6k, where i, j, and k are mutuallyperpendicular unit vectors forming a right-handed system. (a) Calculate (v) The vector product a × b. (vi) The direction cosines of a.arrow_forward
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