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2. A particle moves in the x-y plane. Its coordinates are given as functions of time...
1. A particle of unit mass moves along a trajectory , 2r) θ E (03), and θ E ( a coal, -a cose r(8...
Acceleration in polar coordinates is required
1. A particle of unit mass moves along a trajectory , 2r) θ E (03), and θ E ( a coal, -a cose r(8)--, expressed in plane polar coordinates. The angle 6(t) changes with time according to the equation θ wt. Here a, are positive constants independent of time. (a) [10 marks) Compute the transverse acceleration of the particle (b) [10 marks) Find the force acting on a particle and express it in terms...
#1 A particle of mass, m, moves along the path with its coordinates given as functions...
#1 A particle of mass, m, moves along the path with its coordinates given as functions of time: x=x, +at?, y = bt, z=ct, where xq, a,b,c are constants. Find angular momentum of this particle with respect to the origin, force acting on this particle and torque acting on this particle with respect to the origin as functions of time. Verify that your results satisfy Newton's second de law for rotation, which is " =FxF.
2) A particle moves in the x-y plane. Known information about the particle’s motion is given...
2) A particle moves in the x-y plane. Known information about the particle’s motion is given below: ???? = 150?? ft/sec. and at time t = 0, x = 6 ft ?? =5??3+50?? ft a) Derive, as functions of time, the position (x), acceleration (ax), velocity (vy), and acceleration (ay). b) Using your functions, calculate, at time t = 0.25 seconds, the total magnitude of velocity ?? of the particle and the angle ????the velocity vector makes with the x-axis....
1) 2D kinematics (rectangular coordinates) - A particle moving in the x-y plane has an acceleration...
1) 2D kinematics (rectangular coordinates) - A particle moving in the x-y plane has an acceleration in the y-direction given as ay -3t ft/s2 and an x-position ofx 3t + 2 ft. When t0, yo3ft and Vo, -4ft/s. a) Derive expressions for x, vx, ax, V, Vy, ay as functions of time. b) At times t 0,1,2 seconds, calculate the magnitude of velocity and the angle it makes with the x-axis. c) At times t 0,1,2 seconds, calculate the magnitude...
A particle moves horizontally in uniform circular motion, over a horizontal xy plane. At one instant,...
A particle moves horizontally in uniform circular motion, over a horizontal xy plane. At one instant, it moves through the point with coordinates (x, y) with a velocity of vi and an acceleration of -aj. In these expressions, v and a are the speed and the magnitude of acceleration, respectively, and thus are positive quantities. In terms of the variables given, what are the coordinates (a) xo and (b) Yo of the center of the circular path? (a) Xo =...
A particle moves on x-y plane according to the equations x = a cos (wt), y...
A particle moves on x-y plane according to the equations x = a
cos (wt), y = b sin (wt).
1 - Show that its trajectory is an ellipse?
2 - Calculate the values of its velocity v(t) = |v(t)| and
acceleration a(t) = |a(t)| ?
3 - What are the maximal and minimal values of v(t) and a(t)
?
I think for the first part the answer is as the following image.
Please correct me if my answer is...
(a) The velocity of a particle moving in the x - y plane is given by...
(a) The velocity of a particle moving in the x - y plane is given by ☺ = ((-3.2t+ 9.6 t)i + (2.4t + 4.0)j) m/s, where v is in meters per second and t in seconds. The particle is at the origin of the coordinate system at t = 0 s. i. Determine the magnitude of the acceleration of the particle at t = 2.5 s. ANS: ii. Determine the position of the particle at t = 2.5 s....
A particle moves along the x axis. Its position varies with time acording to the expression x =-4t + 2t2
Average and Instantaneous Velocity A particle moves along the x axis. Its position varies with time acording to the expression x =-4t + 2t2, where x is in meters and t is in seconds. The position-time graph for this motion is shown in the figure. Notice that the particle moves in the negative x direction for the first second of motion, is momentarily at rest at the moment t = 1 s, and moves in the positive x direction at times...
A 5.60-kg particle moves along the x axis. Its position varies with time according to x...
A 5.60-kg particle moves along the x axis. Its position varies with time according to x = t + 4.0t3, where x is in meters and t is in seconds. (a) Find the kinetic energy of the particle at any time t. (Use the following as necessary: t.) K = (b) Find the magnitude of the acceleration of the particle and the force acting on it at time t. (Use the following as necessary: t.) a = F = (c)...
Acceleration in polar coordinates is required
1. A particle of unit mass moves along a trajectory , 2r) θ E (03), and θ E ( a coal, -a cose r(8)--, expressed in plane polar coordinates. The angle 6(t) changes with time according to the equation θ wt. Here a, are positive constants independent of time. (a) [10 marks) Compute the transverse acceleration of the particle (b) [10 marks) Find the force acting on a particle and express it in terms...
#1 A particle of mass, m, moves along the path with its coordinates given as functions of time: x=x, +at?, y = bt, z=ct, where xq, a,b,c are constants. Find angular momentum of this particle with respect to the origin, force acting on this particle and torque acting on this particle with respect to the origin as functions of time. Verify that your results satisfy Newton's second de law for rotation, which is " =FxF.
1) 2D kinematics (rectangular coordinates) - A particle moving in the x-y plane has an acceleration in the y-direction given as ay -3t ft/s2 and an x-position ofx 3t + 2 ft. When t0, yo3ft and Vo, -4ft/s. a) Derive expressions for x, vx, ax, V, Vy, ay as functions of time. b) At times t 0,1,2 seconds, calculate the magnitude of velocity and the angle it makes with the x-axis. c) At times t 0,1,2 seconds, calculate the magnitude...
A particle moves horizontally in uniform circular motion, over a horizontal xy plane. At one instant, it moves through the point with coordinates (x, y) with a velocity of vi and an acceleration of -aj. In these expressions, v and a are the speed and the magnitude of acceleration, respectively, and thus are positive quantities. In terms of the variables given, what are the coordinates (a) xo and (b) Yo of the center of the circular path? (a) Xo =...
A particle moves on x-y plane according to the equations x = a
cos (wt), y = b sin (wt).
1 - Show that its trajectory is an ellipse?
2 - Calculate the values of its velocity v(t) = |v(t)| and
acceleration a(t) = |a(t)| ?
3 - What are the maximal and minimal values of v(t) and a(t)
?
I think for the first part the answer is as the following image.
Please correct me if my answer is...
(a) The velocity of a particle moving in the x - y plane is given by ☺ = ((-3.2t+ 9.6 t)i + (2.4t + 4.0)j) m/s, where v is in meters per second and t in seconds. The particle is at the origin of the coordinate system at t = 0 s. i. Determine the magnitude of the acceleration of the particle at t = 2.5 s. ANS: ii. Determine the position of the particle at t = 2.5 s....
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