A particle of mass m is moving in a bowl. The profile of the bowl is rotationally symmetric, and in cylindrical coordinates (r, y, z) the shape of the bowl can be described by a function z = (r(t), y(t), z(t)), but since the particle setup is described in Figure 2. h(r). The position of the particle is described by in contact with the bowl z(t) = h(r(t)). The h(r) gure 2: A particle of mass m moves in a rotationally symmetric bowl with shape h(r). Show that the x and y components of the particle's position are given a) by x(t) = r (t) cos 4(t), y(t) = r(t) sin o(t). b) Compute the x, y and z components of the particle's velocity. Compute the angular momentum L = (Lx, Ly, Lz) of the particle, and c) show that the z component is given by 2 dp(t) Lz = mr(t)²5 dt

A block of mass m = 240 kg rests against a spring with a spring constant of k = 550 N/m on an inclined plane which makes an angle of θ degrees with the horizontal. Assume the spring has been compressed a distance d from its neutral position. Refer to the figure.  (a)  Set your coordinates to have the x-axis along the surface of the plane, with up the plane as positive, and the y-axis normal to the plane, with out of the plane as positive. Enter an expression for the normal force, FN, that the plane exerts on the block (in the y-direction) in terms of defined quantities and g.   (b) Denoting the coefficient of static friction by μs, write an expression for the sum of the forces in the x-direction just before the block begins to slide up the inclined plane. Use defined quantities and g in your expression.  (c) Assuming the plane is frictionless, what will the angle of the plane be, in degrees, if the spring is compressed by gravity a distance 0.1 m?   (d) Assuming θ = 45 degrees and the…