Classical Dynamics of Particles and Systems
5th Edition
ISBN: 9780534408961
Author: Stephen T. Thornton, Jerry B. Marion
Publisher: Cengage Learning
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In the figure, a body with a mass of 2 kg moves under the influence of two constant forces F1 = 5N and F2 = 4N in the xy plane. At time t = 0, the object is at point 0 and its speed is V = 2i + j (m / s). What is the acceleration of the particle and its position after 2 seconds in terms of the unit vector?
A projectile of mass [m] is launched with initial velocity [v0] at angle [theta] from the +x direction. From the origin, the projectile is connected toa massless spring with force constant k, as shown.
From the equations of motion, one can show that the horizontal and vertical positions of the mass as functions of time can be written asx(t) = A cos wt + B sin wty(t) = C cos wt + D sin wt + Eprovided that the coefficients satisfy the conditions that initially, x(0) = y(0) = 0,vx (t = 0) = v0 cos [theta], and
vy (t = 0) = v0 sin [theta].
Determine the coefficients A,B,C,D, and E in termsof the given variables.
Given that the velocity of a particle in rectilinear motion varies with the displacement xaccording to the equation =
v=bx^-3
where: b is a positive constant, find the force acting on the particle as a function of x.(Hint: F= ma= mv dv/dx.)
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