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 20PQ
To determine
To show that dot product is associative:
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(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.
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 ?
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.
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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- In 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_forwardA 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_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_forward
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- The 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_forwardA helicopter rescues a trapped person of mass m = 65.0 kg from a flooded river by lifting the person vertically upward using a winch and rope. The person is pulled 12.0 m into the helicopter with a constant force that is 15% greater than the persons weight. a. Find the work done by each of the forces acting on the person. b. Assuming the survivor starts from rest, determine his speed upon reaching the helicopter.arrow_forwardA side view of a half-pipe at a skateboard park is shown in Figure P8.51. Sketch a graph of the gravitational potential energy of the skateboarderEarth system as a function of position for a skateboarder who travels from the left side of the half-pipe to the right side. Let the leftmost point be where x = 0 and the lowest point in the half-pipe be where U = 0. FIGURE P8.51arrow_forward
- A constant force of magnitude 4.75 N is exerted on an object. The forces direction is 60.0 counterclockwise from the positive x axis in the xy plane, and the objects displacement is r=(4.22.1j+1.6k)m. Calculate the work done by this force.arrow_forwardThe potential energy function for either one of the two atoms in a diatomic molecule is often approximated by U(x)=a/x12b/x6 where x is the distance between the atoms. (a) At what distance of separation does the potential energy have a local minimum (x=) ? What is the force on an atom at this separation? (c) How does the force vary with the separation distance?arrow_forward8) 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?arrow_forward
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