Rail Given: Particle with mass m = 1kg was initially at A when time t =...
Hi, can you solve the question for me step by step, I will rate up if the working is correct. I will post the answer together with the question. Answer: Question 4 A particle of mass m is moving in a horizontal plane in a circle of radius R, with angular velocity 6, anti-clockwise given by é t+cos(2t) Implement plane polar unit vectors er and ee, in the horizontal plane, and k in the vertical direction, giving a right-handed coordinate...
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...
Q 4. (a) A body of mass m is moving in two dimensions in a constant z plane. Consider a coordinate system that rotates with constant angular speed 1 about the z-axis. In a fixed coordinate system (in the constant z plane), define the plane polar coordinates (r,0) while defining (r, ) as the corresponding plane polar coordinates in the rotating system. (i) In terms of the coordinate system rotating with constant angular speed 1, write down the kinetic energy...
Trajectory Problem 1 1. A particle A , of mass m, is acted on by the gravitational force from a second particle, B, which remains fixed at the origin. Initially, when A is very far from B(r - o0). A has a velocity vo directed along the line shown in the figure. The perpendicular distance between B and this line is D. The particle A is deflected from the figure. The shortest distance between this trajectory and B is found...
The particle of mass m is released when the spring of stiffness K is compressed by a, and travels without friction around the vertical loop ABCD of radius r. Determine the force exerted by the loop on the particle at point B. Gravity acceleration is g. The particle of mass m is released when the spring of stiffness k is compressed by a, and travels without friction around the vertical loop ABCD of radius r. Determine the force exerted by...
2. A particle moves in the x-y plane. Its coordinates are given as functions of time t(2 0) b x(t)-R(at-sina)t), )Sketch the trajectory of the particle. This is the trajectory of a point on the rim of a wheel y(t)-R(1-cosω t), where R and ω are constants. (a) (3 that is rolling at a constant speed on a horizontal surface. The curve traced out by such a point as it moves through space is called a cycloid. (b) (5 Find...
A particle travels along the circular path x2 +y-r, when the time t = 0 the particle it's at-r meter and y =0 m. If the y components of the particle's velocity is Vy 2r cos2t, determine: (a) the x and y components of its acceleration at any instant. (b) Draw the trajectory with the vector velocity and acceleration at t = π/4 sec. (c) calculate the average vector velocity between 0 and t/4 sec. (d) the distance travelled when...
Mechanics. 3. A particle of mass m moves in one dimension, and has position r(t) at time t. The particle has potential energy V(x) and its relativistic Lagrangian is given by where mo is the rest mass of the particle and c is the speed of light (a) Writing qr and denoting by p its associated canonical momenta, show that the Hamiltonian is given by (show it from first principles rather than using the energy mzc2 6 marks (b) Write...
A charged particle of mass m = 4.0 x 10- kg, initially moving with constant velocity in the y-direction, enters a region containing a constant magnetic field B = 4.0 T aliged with the positive z-axis as shown below. The particle enters the region at (x, y) = (d, 0) and leaves the region at (r,y)= (0, d), d = 0.5 m at a time t 600 is after it entered the region. d Figure 1 (a) With what speed...
marks] The position of a particle is given as a function of time by r(t)=(1-cos(27t)i+ (1-t)sin(2nt)j+ 4tk with i (1,0,0), j = (0,1,0) andk = (0,0,1) the Cartesian basis vectors of R3. (a) Sketch the particle trajectory from t 0 tot= 1, as a 3D perspective plot and as the 2D projection onto the xy-plane. (b) Determiner(t) as a function of time t. (c) Is r'(t) greater for t 0 than it is for t 1? Justify your answer. marks]...