U(x) = 1/x^2 - 1/x
F = -dU/dx
= -d (1/x^2 - 1/x) /dx
= - ( -2/x^3 + 1/x^2)
= 2/x^3 - 1/x^2
so F(x) = 2/x^3 - 1/x^2
12. A ball moves in on dimension. The potential-energy function is U() = 1/22 - 1/x....
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 particle of mass m moves in one dimension along the positive x axis. It is acted on by a constant force directed toward the origin with magnitude B, and an inverse-square law repulsive force with magnitude A/x^2. Find the potential energy function, U(x). Sketch the energy diagram for the system when the maximum kinetic energy is K_0 = 1/2 mv_0^2 Find the equilibrium position, x_0.
2. If one dimension, if we have a potential energy function U(x) along with initial values for x and v, we can determine x and v for all subsequent times. A) Explain why this works. B) There's actually an exception to this think about starting at the top of a hill), why does your reasoning for A) no longer apply?
The potential energy is given by U(X) = 3xe^-x a) Determine the force b) Is the force conservative? Justify your answer
How do I approach these questions? Problem 9: The potential energy function for a conservative force Fc along the x-axis is U(x) = x3. (a) Use the potential energy function U(x) to calculate the force along the x-direction Fx. Answer: Fx = -3x2 (b) Calculate the work done by Fc when a particle moves from ti = 2 m to xf = 3. Answer: -19 J (c) This particle has a mass m= 2 kg. If the particle has a...
U(U) x(m) 5 10 15 A particle moves under the influence of a conservative force. The graph shows the potential energy U as a function of position x. Which of the following graphs best shows the force F exerted on the particle as a function of r? F(N) ->x(m) F(N) →x(m) (W)x+ F(N) (W)x+ F(N) (W)x+ F(N)
Suppose we have a single particle moving in one dimension whose potential energy as a function of xx is U(x)U(x). Show (using the chain rule and the relationship F(x)=−U′(x)F(x)=−U′(x)) dEtotal/dt=0 , Conservation of Energy, for this system.
Given a potential energy function U(x), the corresponding force F is in the positive x direction if:a) u is positiveb) u is negativec) u is an increasing function of xd) u is an decreasing function of x
A 4-kg particle moves along the x-axis under the influence of a conservative force. The potential energy is given by U(x) = bx^3 , where b = 8.0 J/m^3 . What is the magnitude of the acceleration of the particle (in m/s2 ) when it is at the point x = 2 m?
The figure showsthe force Fx exerted on a particle that moves along the x-axis. Draw a graph of the particle's potential energy as a function of position xfrom x=0m to x=1.1m . Let U be zero at x=0m .