An object with a mass of 5.86kg moves along the x -axis under the influence of one force whose potential energy is given by the graph. In the graph, the vertical spacing between adjacent grid lines represents an energy difference of 2.57J , and the horizontal spacing between adjacent grid lines represents a displacement of a . When the object is at position x=0 , it is moving in the positive x -direction with speed vi . Part (a)  In units of meters per second, what is the minimum value of vi , the speed of the particle at x=0 , so that the object just reaches position x=7a ? Part (b)  Suppose that the initial speed was 2.48 times that calculated in part (a). What would be the speed, in units of meters per second, of the object when it reaches position x=9a ?

Problem1. A block slides on a rough horizontal surface from point A to point B. A force (magnitude P = 2.0 N) acts on the block between A and B, as shown. Points A and B are 1.5 m apart. (a) How much work is done on the block by the force P? (b) If the kinetic energies of the block at A and B are 6.0 J and 4.0 J, respectively, how much work is done on the block by the net force as the block moves from A to B? (c) What is the work done by the friction force? 40° B

A sledge loaded with bricks has a total mass of 17.6 kg and is pulled at constant speed by a rope inclined at 19.5° above the horizontal. The sledge moves a distance of 19.7 m on a horizontal surface. The coefficient of kinetic friction between the sledge and surface is 0.500. (a) What is the tension in the rope? Your response differs from the correct answer by more than 100%. N (b) How much work is done by the rope on the sledge? Your response differs significantly from the correct answer. Rework your solution from the beginning and check each step carefully. kJ (c).What.is.the.mechanical energy lost due to friction? Enter a number. differs significantly from the correct answer. Rework your solution from the beginning and check each step carefully. kJ Additional Materials

A small boat is crossing a lake on a windy day. During some interval of time, the boat undergoes the given displacement Af = (3.21 m) î + (2.71 m)ĵ During the same interval of time, the wind exerts the given constant force F on the boat. F = (269 N)î – (131 N)ĵ What is the total work done on the boat by the wind over this period of time? work: J What is the angle between the direction of the wind force and the direction of the boat's motion during this time interval? angle:

2 kg and M=3 kg, are connected by a very light string passing over a massless and frictionless pulley. The M block moves 3 m to the right with constant speed. A Two blocks of maSses M 147 %3D During this process, how much work is done on the M block by the tension in the string? (Take g= 10 m/s) %3D