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- The box with dimensions indicated is to be constructed of materials that cost 1 cent per square inch for the lateral surface and 2 cents per square inch for the bases. What is the total cost of constructing the box?A student presses a book between his hands, as the drawing indicates. The forces that he exerts on the front and back covers of the book are perpendicular to the book and are horizontal. The book weighs 25.8 N. The coefficient of static friction between his hands and the book is 0.326. To keep the book from falling, what is the magnitude of the minimum pressing force that each hand must exert?Aspring whose equilibrium length is 15 cm exerts a force of 50 N when it is stretched to 20 cm. Find the work required to stretch the spring from 22 cm to 24 cm.
- Find the work required to pump the tank dry. Assume the outlet is right at the top of the tank.Cable AB passes over the small ideal pulley C without a change in its tension. What length of cable CD is required for static equilibrium in the position shown? What is the tension T in cable CD?Consider the motion of a soccer ball that is kicked from the point x0,y0=⟨0,0⟩ with an initial velocity of u0,v0=⟨35,9⟩ m/s. Assume the x-axis is horizontal, the positive y-axis is vertical (opposite g), the ground is horizontal, and only the gravitational force acts on the object. Determine the maximum height of the soccer ball.
- Prove that the force on the side of a rectangular plate of area A submerged vertically in a fluid is equal to p0A, where p0 is the fluid pressure at the center point of the rectangle.Find the work done by a force F = 5i (mag-nitude 5 N) in moving an object along the line from the origin to the point (1, 1) (distance in meters).How much work W is done by the force in moving an object a distance of 16m?
- If ƒx(a, b) = ƒy(a, b) = 0, does it follow that ƒ has a local maximum or local minimum at (a, b)? Explain.A body of mass n: moves along Y such that at time t its position is y(t) = at3/2 - bt + c, where a, b, c are constants. (a) Calculate the acceleration of the body. (b) What is the force acting on it?Find the moments of inertia about the coordinate axes of a thin rectangular plate of constant density δgm/cm2 bounded by the lines x = 3 and y = 3 in the first quadrant.