In the figure below F = (y-1) î+ (x + 2) ĵ. a) Find the work done in going from (2,1) to (3,4) along Path 1. Answer: 12 + 3 = 15 b) Find the work done in going from (2,1) to (3,4) along Path 2. Answer: 0 + 15 = 15 c) Find the work done in going from (2,1) to (3,4) along Path 3. Answer: 15 d) Is F conservative? Justify your conclusion? Answer: Yes, W does not depends on the path we take. (3,4) Path 1 HA Path 2 Path 3 (2,1) X

A object of mass 3.00 kg is subject to a force Fx that varies with position as in the figure below.   (a) Find the work done by the force on the object as it moves from x = 0 to x = 4.00 m. (b) Find the work done by the force on the object as it moves from x = 4.00 m to x = 10.0 m. (c) Find the work done by the force on the object as it moves from x = 10.0 m to x = 17.0 m.

The force acting on a particle varies as in the figure below. (The x axis is marked in increments of 10.0 m.) F, (N) 6 4 2 0 A B C D E x (m) Find the work done by the force as the particle moves across the following distances. (a) from x = 0 m to x = 80.0 m (b) from x = 80.0 m to x = 120.0 m (c) from x = 0 m to x = 120.0 m

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A force F = 20.0 Newtons at a 20.0 degree angle with the X axis. This force is applied over a distance of 20.0 meters along the X axis. What work is done by the Force?

You push a stalled car with a constant force of 235 NN as it moves a distance 8.40 mm in a straight line. The amount of work that you do in this process is 1.47×103J1.47×103J. What is the angle between the direction of your push and the direction of the car's motion? Express your answer in degrees.

A shopper in a supermarket pushes a cart with a force of 33.0 N directed at an angle of 25.0° below the horizontal. The force is just sufficient to balance various friction forces, so the cart moves at constant speed. Find the work done by the shopper on the cart as she moves down a 54.2-m-long aisle. The shopper goes down the next aisle, pushing horizontally and maintaining the same speed as before. If the work done by frictional forces doesn't change, would the shopper's applied force be larger, smaller, or the same? What about the work done on the cart by the shopper? Is the work larger in part a, or is the work larger in part b; or is the work the same in both parts?

A object of mass 3.00 kg is subject to a force Fx that varies with position as in the figure below. (a) Find the work done by the force on the object as it moves from x = 0 to x = 4.00 m. (b) Find the work done by the force on the object as it moves from x = 4.00 m to x = 11.0 m. (c) Find the work done by the force on the object as it moves from x = 11.0 mto x = 17.0 m. (d) If the object has a speed of 0.600 m/s at x = 0,find its speed at x = 4.00 m and its speed at x = 17.0 m. speed at  x = 4.00 m         m/s speed at  x = 17.0 m         m/s

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)

A pail and its contents weigh 80 lbs. The pail is attached to the end of a 100 ft rope that weighs 10 lb and is hanging vertically. How much work is done in winding up the rope with the pail attached? For this problem, set up the appropriate integral(s), and evaluate the integral(s). The integral(s) can be evaluated by a calculator.