Find the work (in J) done by the force F = (3 N/m)y î + (30 N/m)x ĵ between the points A = (0, 0) and B = (2 m, 2 m) over a circular arc of radius 2 m, centered at (2 m, 0).
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Find the work (in J) done by the force
between the points
and
over a circular arc of radius 2 m, centered at
Evaluate the path integral using Cartesian coordinates.
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- Consider a plane that is inclined by an angle of 45 degrees with the horizontal. A block of mass 5 kg starts at rest at the top of the inclined plane, at a height of 2 meters above the ground. The surface of the plane and the block have a relative coefficient of friction of (μk= 0.1). If the block is allowed to slide down the plane. (a) What is the work done by gravity during the slide down the plane? (b) What is the work done by friction during the slide down the plane? (c) Using the information from (a) and (b), find the speed of the object when it reaches the ground?Problem 4. A box of mass m = 2.0 kg is at rest at point B on a rough inclined plane with length s = 8.0 m (distance between A and B), and which makes an angle of 30° with the horizontal. The velocity of the box at point A is 2.5 m/s. (a) What is the work done by gravity between the top (B) and the bottom (A) of inclined plane? (b) Find the work done by the net force on the box. (c) Find the increase in thermal energy in the box-incline system as a result of friction. 30°A particle moves along a curved path y(x) = (10 m){1+cos[(0.1 m−1)x]} , from x = 0 to x = 10π m, subject to a tangential force of variable magnitude F(x) = (10 N)sin[(0.1 m−1)x]. How much work does the force do? (Hint: Consult a table of integrals or use a numerical integration program.)
- 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.Consider two vectors A= 6.75 i+(-3.53 k) and B= (-4.1j)+1.08 k. Find the angle between these two vectors.The force exerted by an electric charge at the origin on a charged particle at the point (æ, y, z) is F(7) KT where K is constant. (x, y, z) with position vector Assume K = 30. Find the work done as the particle moves along a straight line from (3,0,0) to (3,4,5)
- Problem 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) 530A person of weight 500 N skis 500 m down a frictionless slope covered by snow that makes an angle 30◦ to the horizontal. The person is at rest initially. There are two forces acting on the person – the weight and the normal reaction force. (a) How much work is done by the person’s weight and the normal reaction force. Find the velocity of the person at the 500 m mark down the slope using the Work-Energy Theorem and the velocity of the person at the 500 m mark using the conservation of mechanical energy. (b) If there is a friction of 50 N, find the velocity of the person at the 500 m mark. What is the work done by the person’s weight? What is the work done by friction?Needs Complete typed solution with 100 % accuracy.