Consider a particle on which a force acts that depends on the position of the particle. This force is given by R=(2y)î+(3x). Find the work done by this force when the particle moves from the origin to a point 5 meters to the right on the x- axis.
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A: (a) Let W be defined as the work done. Therefore, W=F→.ds→=F→.d→f-d→i
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- A cable exerts a constant upward tension of magnitude 1.66 ✕ 104 N on a 1.40 ✕ 103 kg elevator as it rises through a vertical distance of 2.30 m. (a)Find the work done by the tension force on the elevator (in J). (b) Find the work done by the force of gravity on the elevator (in J).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 force on a particle is described by 2x^3−6 at a point x along the x-axis. Find the work done in moving the particle from the origin to x=7.
- 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)Two force vectors are given P = Î+2ĵ+4k, and Q = 5î+8ĵ-2k. If the displacement vector is D = 1-5ĵ+2k, what is the total work done by these two forces?A 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?
- The figure shows three forces applied to a trunk that moves leftward by 3.23 m over a frictionless floor. The force magnitudes are F1 = 4.70 N, F2 = 8.63 N, and F3 = 3.16 N, and the indicated angle is 0 = 60°. (a) During the displacement, what is the net work done on the trunk by the three applied forces, the gravitational force, and the normal force? (b) Is there a net transfer of energy to or from the trunk? (c) Does the kinetic energy of the trunk increase or decrease? (a) Number i Units (b) (c) >Chapter 07, Problem 015 GO The figure shows three forces applied to a trunk that moves leftward by 2.87 m over a frictionless floor. The force magnitudes are F1 = 4.69 N, F2 = 9.16 N, and F3 = 3.25 N, and the indicated angle is 8 = 60°. (a) During the displacement, what is the net work done on the trunk by the three applied forces, the gravitational force, and the normal force? (b) Is there a net transfer of energy to or from the trunk? (c) Does the kinetic energy of the trunk increase or decrease? (a) Number Units (b) () the tolerance is +/-5% Click if you would like to Show Work for this question: Open Show WorkAn object moves in the x-y plane while acted on by the force F(x,y) = k1yi + k2xj, where k1 and k2 are constants with units of N/m. The object moves along a straight line path from Cartesian coordinate (x1, y1) to (x2, y2). Write an expression for the work done on the object by this force.