conservative force
F = dU(x)/dx
F = d(1/2*k*x2) / dx
F = 1/2*k * dx2/dx
F = k*x
5. From the potential given below, calculate the resulting conservative force:
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...
A particle of mass 5 kg is subject to a conservative force whose potential energy (in joules) as a function of position (in meters) is given by the equation U(x) =-100x5e-1x [where x > 0] (a) Determine the position xo where the particle experiences stable equilibrium (b) Find the potential energy Uo of the particle at the position x 2106 The particle is displaced slightly from position x = xo and released (c) Determine the effective value of the spring...
so I know the answer to a) is U(x) = 4e(-2x) + 1 b) and the force is conservative, but how can I prove the force is conservative Given that The potential energy at x=0 is U=5.0 The force on the particle is given by F(x) = 8 a) The potential energy function is U=-F(x) dx +C U= 8e-*dx+C U= 4(4)+c Atx = 0 U=5.0J 5=4+C C=1 The potential energy of the system as a function of the particle position...
A 21 kg object is acted on by a conservative force given by F = -1.0x - 6.0x^2, with F in newtons and x in meters. Take the potential energy associated with the force to be zero when the object is at x = 0. (a) What is the potential energy of the system associated with the force when the object is at x = 1.7 m? (b) If the object has a velocity of 4.0 m/s in the negative...
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 potential energy is given by U(X) = 3xe^-x a) Determine the force b) Is the force conservative? Justify your answer
A 20 kg object is acted on by a conservative force given by F = −3.0x − 5.0x2, with F in newtons and x in meters. Take the potential energy associated with the force to be zero when the object is at x = 0. (a) What is the potential energy of the system associated with the force when the object is at x = 5.0 m? (b) If the object has a velocity of 2.0 m/s in the negative...
Find the potential º when F =-V¢, a conservative force of field defined by F = (3x*yz - 3yli +(rºz – 3x); +(x*y+22)
Find the potential when F =-Vº, a conservative force of field defined by F = (3x’yz – 3yli + (xºz – 3x)j + (x*y+2z)k
Find the potential o when F=-V¢, a conservative force of field defined by + = (3x’yz – 3y)i + (x?z – 3x)j + (x*y+ 2zł