a) If a conservative force acting on a particle produces a potential energy function given by: v k x Find the components of the force . b) Which of the following two forces is conservative: F1 = yi+2xyj F2 =y sin (2x) i + sin (x) j
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- Find the work (in J) done by the force F (6 N/m)yî + (27 N/m)xĵ between the points A = (0, 0) and B = (2 m, 2 m) over a circular arc of radius 2 m, centered at (0, 2 m). Evaluate the path integr %3D using Cartesian coordinates. (Hint: You will probably need to consult a table of integrals.) y(m)4 (2, 2) F(x, y) (0, 0) x(m)show workA block with mass m = 12 kg rests on a frictionless table and is accelerated by a spring with spring constant k = 4599 N/m after being compressed a distance x1 = 0.45 m from the spring’s unstretched length. The floor is frictionless except for a rough patch a distance d = 2.7 m long. For this rough path, the coefficient of friction is μk = 0.41. 1) How much work is done by friction as the block crosses the rough spot? 2) Instead, the spring is only compressed a distance x2 = 0.117 m before being released. How far into the rough path does the block slide before coming to rest? 3) What distance does the spring need to be compressed so that the block will just barely make it past the rough patch when released?
- Muhammad is running on the road. Find the velocity as a function of displacement x, taking into account the following force functions. so Muhammad mass=M and Let FO and K are positive, and let him start from rest. Then found the potential energy U(x) for these force equations. a) mohumed speeds up as it runs more: Fx = FO + kx b) He runs fast, tires himself, then runs again, repeatedly: (FX = Fo cos(kx))U(x)=9.0x^2-8.0x^3 Determine the force Fx associated with this potential-energy function Assuming no other forces act on the object, at what positions is this object in equilibrium? Which of these equilibrium positions are stable and which are unstable? (Hint: use the 2ndderivative)A luggage handler pulls a 20.0 kg suitcase up a ramp inclined at 34.0 ∘∘ above the horizontal by a force F⃗ → of magnitude 163 NN that acts parallel to the ramp. The coefficient of kinetic friction between the ramp and the incline is μk = 0.300. The suitcase travels 3.70 mm along the ramp. Calculate the work done on the suitcase by F⃗ →. Calculate the work done on the suitcase by the gravitational force. Calculate the work done on the suitcase by the normal force. Calculate the work done on the suitcase by the friction force. Calculate the total work done on the suitcase. If the speed of the suitcase is zero at the bottom of the ramp, what is its speed after it has traveled 3.70 mm along the ramp?
- Consider a force in R3 defined by f(x,y,z)=(6*x*y^3, 9*x^2*y^2+2*y,0). Find the potential energy U(x,y,z) such that U(0,0,0)=0.The potential energy of a system is given by: U(x,y,z)=5(J/m^2) x^2 + 7(J/m^3) xy^2 + 8(J/m^2) zy Find: The force acting on the system. Write the forces as the sum of its components. The magnitude of the force when x=1, y=0, z=2Problem Thirteen. A potential energy function is given by U(r)=U2 where o = 2.00 m r r and U, = 1.00 J. Find the magnitude of the force at r= 1.00 m. Give an answer in kN. 25.) (A) 280 (В) 106 (С) 420 (D) 470 (E) 530
- Needs Complete typed solution with 100 % accuracy.Problem 4: A 2.00 kg object moving in the x-y plane is under the influence of a force describe by the potential energy U (x,y) = (4.00 J/m³)x3 – (2.00 J/m4)y“. What is the magnitude and direction (angle) of the acceleration of the object at a point x=1 m and y = 2 m?A certain spring is found not to obey Hooke's law; it exerts a restoring force F(x) = -ax² - 6x³ if it is stretched or compressed, where: a = 10.0N/m², B = 300.0N/m³ The mass of the spring is negligible. Calculate the potential energy function U(x) for this spring, if U(x=0) = 0. Find the spring potential energy at x = 0.500 m