Prove that the Force : F = (x^2 y z) i - ( x y z^2) k Is Non Conservative Force
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Q: emonstrate whether or not this force is conservative.
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- Problem 2: A student pushes a baseball of m = 0.18 kg down onto the top of a vertical spring that has its lower end fixed to a table, compressing the spring a distance of d = 0.14 meters from its equilibrium length. The spring constant of the spring is k = 740 N/m. Let the gravitational potential energy be zero at the position of the baseball in the compressed spring. Randomized Variables m = 0.18 kg k = 740 N/m d = 0.14 mprove this force are conserved F(x,y)=2a(x-y)i-a(2x-y)j Where a is constant(a) For one-dimensional motion of a particle of mass m acted upon by a force F(x), obtain the formal solution to the trajectory x(t) in the inverse form: m = ₂√ 2 {E – V(x)} where V (x) is the potential energy and x0 is the position at t = 0. (b) If the force, F(x) is a constant then what is the equation of the particles trajectory (x vs t). t(x): = dx
- (b) Write a necessary condition for a transformation (q,p) to (Q,P) to be connonical. Prove that P-2(1+√qcosp)√q sinp:Q-log(1+√qcosp)Consider the functions f(x) = x and g(x) = sin x on the interval (0, ). (a) Complete the table and make a conjecture about which is the greater function on the interval (0, ). (b) Use a graphing utility to graph the functions and use the graphs to make a conjecture about which is the greater function on the interval (0, ). (c) Prove that f(x) > g(x) on the interval (0, ). [Hint: Show that h′(x) > 0, where h = f − g.]The Brachistochrone Problem: Show that if the particle is projected withan initial kinetic energy 1/2 m v02 that the brachistochrone is still a cycloidpassing through the two points with a cusp at a height z above the initialpoint given by v02 = 2gz.
- Find the distance from the point (2, –7, –6) to the line L = (-5,–10, -5) + t (8,7,6) , -∞Let F = (z^2 cos y, −xz^2 sin y, 2xz cos y − cos z).a) Show that F is irrotational.b) Find a potential function f (x, yz) such that F = ∇f , and f (0, π, π/3) = 2(5) When variables p, V,T are related by F(p, V,T) = 0, show the following: (a) ),- = 1/), ƏT V др (b) ),+), ), = 0 ƏT ),H,O, = -1 (Chain relation) (c) T