In the figure below F = (x + y)i + (y + 1) j. a) Find the work done in going from (1,2) to (3,4) along Path 1. Answer: 8 + 12 = 20 b) Find the work done in going from (1,2) to (3,4) along Path 2. Answer: 8 + 8 = 16 c) Find the work done in going from (1,2) to (3,4) along Path 3. Answer: 18 d) Is F conservative? Justify your conclusion? Answer: No, W depends on the path we take. y Path 1 (1,2) Path 3 (3,4) Path 2

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?

The height of Niagara Falls on the American side is 51 m. (a) Calculate the potential energy of 1.0 g of water at the top of the falls relative to the ground level. Hint: The work done in ascending is given by mgh, where m is the mass (in kg), g is the gravitational acceleration  (9.8 m/s2), and h is the height (in meters).  J (b) What is the speed of the falling water if all the potential energy is converted to kinetic energy?  m/s (c) What would be the increase in temperature of the water if all the kinetic energy were converted to heat?    ° C

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.

An electric elevator with a motor at the top has a cable weighing 4.5 pounds per foot.When the car is at the first floor, 180 feet of cable are out, and effectively 0 feet are outwhen the car is at the top floor. The elevator car itself weighs 2000 pounds when empty   a) Find the work done by the motor lifting just the empty elevator car from the firstfloor to the top floor, ignoring the cable. b) Find the work done by the motor lifting just the cable from the first floor to the topfloor. Keep in mind, that the cable gets shorter and must therefore get lighter as theelevator goes up.

A block of mass 15.0 kg is pulled up from rest on a rough incline. The pulling force F =100.0 N that makes a 5.00° angle with the incline and the incline itself makes an angle of 10.0° with the horizontal. The coefficient of kinetic friction is 0.300, and the block is pulled 3.00 m on the incline. (a) How much work is done by the gravitational force on the block? (b) How much work is done by the 100.0-N force on the block? (c) How much work is done by the normal force? (d) Calculate work done by the friction force on the block. (e) What is the speed of the block after being pulled 3.00 m? F 5° 10°

A-D please!!

(1) Suppose you lift a stone that has a mass of 5.1 kilograms off the floor onto a shelf that is 2.5 meters high. How much work have you done? 124.95 Joules (2) Suppose you lift a laptop that weighs 5.3 pounds off the floor onto a shelf that is 2 feet high. How much work have you done? 347.68 x foot-pounds (3) The force on a particle is described by 6x work done in moving the particle from the origin to x = 9. - 2 pounds at a point r feet along the r-axis. Find the 9823.5 Vo foot-pounds

In the figure, a frictionless roller coaster car of mass m - 992 kg tops the first hill with speed vo- 11.9 m/s at heighth-47.0 m. How much work does the gravitational force do on the car from that point to (a) point A, (b) point B, and (c) point C? If the gravitational potential energy of the car-Earth system is taken to be zero at C, what is its value when the car is at (d) Band (e) A? First