Physics for Scientists and Engineers
6th Edition
ISBN: 9781429281843
Author: Tipler
Publisher: MAC HIGHER
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Chapter 7, Problem 5P
(a)
To determine
Whether the statement is true or false.
(b)
To determine
Whether the statement is true or false.
(c)
To determine
Whether the statement is true or false.
(d)
To determine
Whether the statement is true or false.
(e)
To determine
Whether the statement is true or false.
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Find the work done by the force F= <(y+z), -(x+z), (x+y)> along each of the following closed paths:
a. The circle x^2+y^2=1 in the z=0 plane, taken counterclockwise
b. The circle x^2+z^2=1 in the y=0 plane, taken counterclockwise
Calculate the work done by the force F(x, y) = y2 i + xy j in moving a particle along the line whichconnects (−1, 1) to (0, 0) and then along the parabola y = x2 from (0, 0) to (1, 1)
The force F= (yzi + zxj + xyz)/xyz acts on the particle P(x,y,z) which moves in space. (a) Using the relation derived in Prob. 13.79, show that this force is a conservative force. (b) Determine the potential function associated with F.Reference to Problem 13.79:Prove that a force F(x,y,z) is conservative if, and only if, the following relations are satisfied:
Chapter 7 Solutions
Physics for Scientists and Engineers
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- Consider a particle on which a force acts that depends on the position of the particle. This force is given by . Find the work done by this force when the particle moves from the origin to a point 5 meters to the right on the x-axis.arrow_forwardA mysterious force acts on all particles along a particular line and always points towards a particular point P on the line. The magnitude of the force on a particle increases as the cube of the distance from that point; that is Fr3 , if the distance from P to the position of the particle is r. Let b be the proportionality constant, and write the magnitude of the force as F=br3. Find the potential energy of a particle subjected to this force when the particle is at a distance D from P, assuming the potential energy to be zero when the particle is at P.arrow_forwardA force F = (6i 2j) N acts on a panicle that under-goes a displacement r = (3i + j) m. Find (a) the work done by the force on the particle and (b) the angle between F and r.arrow_forward
- Repeat the preceding problem, but this time, suppose that the work done by air resistance cannot be ignored. Let the work done by the air resistance when the skier goes from A to B along the given hilly path be —2000 J. The work done by air resistance is negative since the air resistance acts in the opposite direction to the displacement. Supposing the mass of the skier is 50 kg, what is the speed of the skier at point B ?arrow_forwardCheck Your Understanding Find the work done by the same force in Example 7.4 over a cubic path, y=(0.25m-2)x3 , between the same points A=(0,0) and B=(2m,2m) .arrow_forwardIf the dot product of two vectors vanishes, what can you say about their directions?arrow_forward
- A particle moves along a curved path y(x)=(10m){1+cos[0.1m1]x} , from x=0 to x=10m , subject to a tangential force of variable magnitude F(x)=(10N)sin[(0.1m-1)x] . How much work does the force do? (Hint: Consult a table of integrals or use a numerical integration program.)arrow_forwardConsider a particle moving in the region x > 0 under the influence of the potential where U0 = 1 J and α = 2 m. Plot the potential, find the equilibrium points, and determine whether they are maxima or minima.arrow_forwardTwo bodies are interacting by a conservative force Show that the mechanical energy of an isolated system consisting of two bodies interacting with a conservative force is conserved. (Hint: Start by using Newton’s third law and the definition of work to find the work done on each body by the conservative force.)arrow_forward
- Consider a particle on which several forces act, one of which is known to be constant in time: . As a result, the particle moves along the x-axis from x=0 to x=5 m in some time interval. What is the work done by ?arrow_forwardA mouse of mass 200 g falls 100 m down a vertical mine shaft and lands at the bottom with a speed of 8.0 m/s. During its fall, how much work is done on the mouse by air resistance?arrow_forwardAn external force acts on a particle during a trip from one point to another and back to that same point. This particle is only effected by conservative forces. Does this particle’s kinetic energy and potential change as a result of this trip?arrow_forward
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Mechanical work done (GCSE Physics); Author: Dr de Bruin's Classroom;https://www.youtube.com/watch?v=OapgRhYDMvw;License: Standard YouTube License, CC-BY