Find the force for the following potential energy equations:
a) U(x) = (alpha)x^2 + (Beta)y^2 + (gamma)z^2 + C
b) U(x) = C(r^n)
in sperical coordinates.
Find the force for the following potential energy equations: a) U(x) = (alpha)x^2 + (Beta)y^2 +...
7. Assume X gammala, y) and Y-gamma(8,7) are independent. (a) Show that U = X + Y gamma(a +.). (b) Show that V = X/(X+Y) beta(a. 8). (c) Show that U and V are independent. (d) Show that W = 72 gamma(1/2, 1/2) if Z N (0,1).
3. In Cartesian coordinates, a potential energy field U = 3x + 5 xe + 2 cos(az). a) What are the potential energy at position (0, 0, 0), (1, 1, 0) and (1, 1, 1)? (5 pts) b) Derive the force function F(x, y, z). Is this force conservative? (10 pts) c) What are the forces at position (0, 0, 0), (1, 1, 0) and (1, 1, 1)? (5 pts)
12.) An electron Complete the following nuclear equations and identify them as alpha, beta, or gamma decay: 13.) 13K → -e + (alpha, beta, gamma) 14.) 23 Pu → He + (alpha, beta, gamma) 15.) Be + Be + (alpha, beta, gamma) 16.) 23 → 2307h (alpha, beta, gamma) 17.) Li → He + (alpha, beta, gamma) 18.) Write an equation showing pratartinium-229 aninn throunh nlnha darm. fanminn til... 26
Suppose X and Y are independent and
Prove the following
a) U=X+Y~gamma(α + β,γ)
b) V=X/(X + Y ) ∼ beta(α,β)
c) U, V independent
d) ~gamma(1/2,
1/2) when W~N(0,1)
X ~ gammala, y) and Y ~ gamma(6, 7) We were unable to transcribe this image
A particle of mass m moves in one dimension. Its potential energy is given by U(x) = -Voe-22/22 where U, and a are constants. (a) Draw an energy diagram showing the potential energy U(). Choose some value for the total mechanical energy E such that -U, < E < 0. Mark the kinetic energy, the potential energy and the total energy for the particle at some point of your choosing. (b) Find the force on the particle as a function...
A potential energy function for a two- dimensional force is of the form U= a ry+br, where a = 2.56 J/m' and b = -5 J/m. Find the magnitude of the force that acts at the point (x, y) for x = 69 m, y = 16 m. Answer in units of N.
Need help with both please!!
Question 15 2 pts Find the electric potential energy, U, of a test charge, 9. = 54.8 uc, placed at point p (at thecenter of the rectangle) as shown below. Take k = 9.0 x 109 Nm²/C2 1.0 uC = 10-6 C. Please round your answer to two decimal places. 9. = +30 uc 9. =-10uc 1.2 m p 9=-20uc 1.6 m 9 = +40 uc 931 43 94 Equations: First, determine the electric potential...
002 (part 1 of 3) 10.0 points An alpha particle (mass 6.64 x 1027 kg, Z - 2) approaches to within 1.29 x 10-14 m of a carbon nucleus (7-6). Find the maximum Coulomb force on the alpha particle. Answer in units of N 003 (part 2 of 3) 10.0 points Find the acceleration of alpha particle at this point. Answer in units of m/s. 004 (part 3 of 3) 10.0 points Find the potential energy of alpha particle at...
A potential energy function is given by U(x) = (x ^−8) *e^ (x ^2) . Let’s only focus on the region where x > 0. a) Find the position where the potential energy is a minimum b) For small oscillations around this minimum, what is the angular frequency ω? c) At what distance (either to the left or right) from the equilibrium point is the exact value of the force (derived from the full potential) more than 10% different from...
Consider the following. Find the force F_x associated with the potential-energy function U = Ax^5, where A is a constant. (Use the following as necessary: A and x.) F_x = At what value(s) of x does the force equal zero? x =