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Technical University of Sofia Branch Plovdiv Theoretical Mechanics DYNAMICS * Navigation: Right (Down) arrow – next slide Left (Up) arrow – previous slide Esc – Exit Notes and Recommendations: [email protected] Lecture 2 Special Cases. The force is determined by the time. mx F t t F t dx 1 m F t dx dt x F t dt dt m m0 t t t 1 t dx 1 1 F t dt dx F t dt dt x F t dt dt dt m 0 m 0 0 m 0 Lecture 2 Special Cases. The force is determined by the time. Sample Problem 4 The bullet of mass m is given a velocity due to gas pressure caused by the burning of powder within the chamber of the gun. Assuming this pressure creates a force of F = F0sin(πt / t0) on the bullet, determine the velocity of the bullet at any instant it is in the barrel. What is the bullet’s maximum velocity? Also, determine the position of the bullet in the barrel as a function of time. Lecture 2 Special Cases. The force is determined by the velocity. mx F v v dv F v dv dt dv t m v dt m F v m F v v0 t v v 1 t t dx v 1 t dx 1 t dt x 1 t dt dt 0 Lecture 2 Special Cases. The force is determined by the velocity. Sample Problem 5 A car of mass m is traveling at a slow velocity v0. If it is subjected to the drag resistance of the wind, which is proportional to its velocity, i.e., FD = kv. Determine the distance and the time the car will travel before its velocity becomes 0,5 v0. Assume no other frictional forces act on the car. Lecture 2 Special Cases. The force is determined by the position. mx F x x F x dv dv dx dv F x v2 1 v vdv dx F x dx dt dx dt dx m m 2 m x0 x 2 v x F x dx m x0 x dx dx dx v x dt t dt x x x0 Lecture 2 Special Cases. The force is determined by the position. Sample Problem 6 The spring of constant k=200N/m is attached to both the support and the 2-kg cylinder, which slides freely on the horizontal guide, If a constant 10-N force is applied to the cylinder at time t=0 when the spring is undeformed and the system is at rest, determine the velocity of the cylinder when x=40 mm. Also determine the maximum displacement of the cylinder.