A truck ascends a ramp that follows the path y=x/2 (with both y and x in meters) from the origin to the point (40,20). a) What is the grade of the ramp? (Wikipedia Link) b) How much work is done by gravity along this path? Please start from the basic definiton of work. c) If the truck ascends the ramp at constant speed of 10m/s and has a mass of 3000kg, how much power is required in kW?
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A truck ascends a ramp that follows the path y=x/2 (with both y and x in...
An object moves across a level, frictionless surface marked with a set of x-y axes, with all coordinates measured in meters. East is defined as the positive y-direction; north is the positive y-direction. Throughout its movement, the object is subjected to several forces, one of which is this: F_1(x, y) = [axy, by] N where a = 7, and b = 4. Find the units of a and b. Find the work done by F_1, on the object as it...
Please solve these three questions! (1) Length of graphs a) Let a path C be given by the graph of y g(x), a 3 < b, with a piecewise C1 function g : [a, b - IR. Show that the path integral of a continuous function f: IR2- R over the path C is b) Let g : [a, b] - IR be a piecewise C1 function. The length of the graph of g on (t, g(t)). Show that [a,b]...
The force field F (x, y) = (x + 4y)i + (x^2 − 3)j acts on an object traveling from (0, 0) to (0, 1). The object moves along the path x = c(y − y^2 ) with 0 ≤ y ≤ 1. Determine the value of c that minimizes the work done on the object by the force field. Please use the line work integral, and optimization
(1) Integrate f(x, y,z)+Vy - z2 over the straight line segment path from (0,0,0) to (1,1,1) (2) Consider the field F (2xyz+2,x2z, x2y), (a) (b) (c) Show that the field is conservative. Find a potential function for the field. Find the work the field does on an object that follows the path consisting of the line segment from (0,0,0) to (1,2,2), followed by the line segment from (1,2,2) to (2,4,3) Find the work done by the field ß-(x, 3y,-5z) along...
2) Find the area of the region enclosed by each group of equations. a) y x, y sin x, b) y x2-2x, y= x+ 4 x 3) A particle moves along a straight line with a velocity of 5 cm/s and then accelerates at a rate of a(t) t2+2. What is its displacement after 5 seconds of acceleration (acceleration is in cm/s2) 4) A cylindrical can (radius 10 millimeters) is used to measure rainfall in Stormville. The can is initially...
1. Power is a quantity Watts. 2. 1 hp is equal to 3. Energy is neither created nor destroyed, only determine the work done on an object, the angle 0, is measured between the Force and the 5. The SI units for Power are 6. Another name for the unit of Work, which is a N m, is called 7. Work done on an object slowing down is 8. Yo u push a lawn mower 6 times as far as...
Question 1 1 pts What is the kinetic energy of a man who weighs 980N who is riding in a car traveling 40 km per hour? Express your answer in Joules, but don't type the unit in the answer box. Round to the nearest whole number. (Careful with the units) 1 pts Astudent slides her 80.0-kg desk across the level floor of her dormitory room a distance 4.00 m at constant speed. If the coefficient of kinetic friction between the...
Read the article below and in your own words, (1-2 sentences) what is the "true direction" or right way to interpret nature, according to Bacon? True Directions Concerning the Interpretation of Nature (1620) Francis Bacon Those who have taken it on themselves to lay down the law of nature as something that has already been discovered and understood, whether they have spoken in simple confidence or in a spirit of professional posturing, have done great harm to philosophy and the...