Trajectory Problem 1 1. A particle A , of mass m, is acted on by the...
PROBLEM 2 (10 POINTS) A particle of mass m moving along a straight line is acted on by a retarding force (one directed against the motion) F = beau, where b and a are constants and u is the velocity. At に0, it is moving with velocity 10. Find the velocity at later times always
particle 13.9 A particle of mass 3m is located 1.00 m from a of mass m. (a) Where should you put a third mass M so that the ull of the sun on net gravitational force on M due to the two masses is exactly zero? ume the distance (b) Is the equilibrium of M at this point stable or unstable () for y the distance of points along the line connecting m and 3m, and (ii) for points dix...
1.14) A particle of mass m is acted upon by a net force F. As a result of the force, the particle starts from rest and moves along a curved path for which the acceleration relative to an inertial Cartesian coordinate system with an origin at the location where the particle is at rest is given by a - with At, B+Ct, and constants. You may assume that the units associated with t are seconds and = D where A,...
1. Non-Linear Collisioin A particle A which has a mass m and travels with a speed vo along some direction i collides with a stationary particle B having mass 2m. As indicated in the figure, after the collision A moves in a direction at an angle of 30° from i and B moves in a direction at angle 50° from i . The only forces acting on the particles are those which they exert on each other. a) Apply the...
A particle of mass m moves in one dimension along the positive x axis. It is acted on by a constant force directed toward the origin with magnitude B, and an inverse-square law repulsive force with magnitude A/x^2. Find the potential energy function, U(x). Sketch the energy diagram for the system when the maximum kinetic energy is K_0 = 1/2 mv_0^2 Find the equilibrium position, x_0.
In figure. 1 below, a particle of mass m is initially at point A, a distance d from the center of one uniform sphere and distance 4d from the center of another identical uniform sphere, both of mass M>>m. State whether, if you moved the particle to point D, the following would be positive, negative, or zero and why: a) the change in the gravitational potential energy of the particle. b) the work done by the net gravitational force on...
A particle with a mass of 3.00 kg is acted on by a force F, acting in the x-direction. If the magnitude of the force varies in time as shown in the figure below, determine the following.(a) Impulse of the force (in kg · m/s) (b) final velocity of the particle (in m/s) if it is initially at rest (c) Find the final velocity of the particle (in m/s) if it is initially moving along the x-axis with a velocity of -2.00...
A particle with a mass of 1.75 kg is acted on by a force Facting in the x-direction. If the magnitude of the force varies in time as shown in the figure below, determine the following F, (N) 8 6 n 4 2 t(s) 2 3 4 5 (a) impulse of the force (in kg. m/s) kg. m/s (b) final velocity of the particle (in m/s) if it is initially at rest m/s (c) Find the final velocity of the...
In the figure, particle A moves along the line y = 33 m with a constant velocity v→ of magnitude 3.5 m/s and directed parallel to the x axis. At the instant particle A passes the y axis, particle B leaves the origin with zero initial speed and constant acceleration a→ of magnitude 0.46 m/s2. What angle θ between a→ and the positive direction of the y axis would result in a collision?
(1 point) Suppose 41 yl i(1) = (a) Find ci and c2 (b) Sketch the phase plane trajectory that satisfies the given initial condition. Which graph most closely resembles the graph you drew? B (c) What is the approximate direction of travel for the solution curve, as t increases from -oo to o0? OA. along the line y toward the origin and then along the line y-z away from the origin 41 yl B. along the line y z toward...