25. Kinetic energy If a variable force of magnitude F(x) moves an object of mass m along the x-axis from x1 to x2, the object's ve- locity v can be written as dx/dt (where t represents time). Use Newton's second law of motion F = m(dv/dt) and the Chain Rule dv dx dv dv dx dt dx dt to show that the net work done by the force in moving the object from x, to x, is F(x) dx = =mv;? – mv,?. where vị and v2 are the object's velocities at x1 and x2. In physics, the expression (1/2)mv² is called the kinetic energy of an object of mass m moving with velocity v. Therefore, the work done by the force equals the change in the object's kinetic energy, and we can find the work by calculating this change.
25. Kinetic energy If a variable force of magnitude F(x) moves an object of mass m along the x-axis from x1 to x2, the object's ve- locity v can be written as dx/dt (where t represents time). Use Newton's second law of motion F = m(dv/dt) and the Chain Rule dv dx dv dv dx dt dx dt to show that the net work done by the force in moving the object from x, to x, is F(x) dx = =mv;? – mv,?. where vị and v2 are the object's velocities at x1 and x2. In physics, the expression (1/2)mv² is called the kinetic energy of an object of mass m moving with velocity v. Therefore, the work done by the force equals the change in the object's kinetic energy, and we can find the work by calculating this change.
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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Transcribed Image Text:25. Kinetic energy If a variable force of magnitude F(x) moves an
object of mass m along the x-axis from x1 to x2, the object's ve-
locity v can be written as dx/dt (where t represents time). Use
Newton's second law of motion F = m(dv/dt) and the Chain Rule
dv dx
dv
dv
dx
dt
dx dt
to show that the net work done by the force in moving the object
from x, to x, is
F(x) dx = =mv;? – mv,?.
where vị and v2 are the object's velocities at x1 and x2. In physics,
the expression (1/2)mv² is called the kinetic energy of an object
of mass m moving with velocity v. Therefore, the work done by
the force equals the change in the object's kinetic energy, and we
can find the work by calculating this change.
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