4) Find the most economical wide flange section for an A992 steel beam (E = 29 x 10³ ksi) using LRFD which spans 45 ft. with a dead load of 50 lb/ft² and a live load of 95 lb/ft² if the beams are spaced 12 ft apart and full lateral bracing is provided. Determine the total maximum deflection. (Because the beam is fully braced, you should utilize a reference table with wide flanges in descending order of Z as found in the note set.) Additional wide flange properties which the text does not show text is provided on the following pages %3D

A cat climbs up the side of a tree, tilted at a 10 degree angle relative to the vertical (the cat is on the top side). The cat's claws dig into the tree bark, which pushes the cat up the tree.  If the cat has a mass of 5 kg, how hard does it have to push into the tree in order to climb up at constant speed?

An aluminum cylinder with a radius of 1.1 cm and a height of 82 cm is used as one leg of a workbench. The workbench pushes down on the cylinder with a force of 3.2×10^4N. What is the compressive strain of the cylinder? Young's modulus for aluminum is 7.0×10^10Pa Express your answer using two significant figures. b)By what distance does the cylinder's height decrease as a result of the forces on it?

n the mid-20th century, engineers constructed a series of canals to move irrigation water from water sources to farming communities throughout the western United States. The volume of water a canal an move is partially dependent on its cross-sectional area. Suppose a canal is trapezoidal, 35.0 ft across the top and 15.0 ft across the bottom, with a planned depth of water of 10.0 ft as shown in the gure. Find the cross-sectional area of the canal when it is full (in ft). (Use the rules for working with measurements to give your answer to the appropriate accuracy and/or precision.) 35.0 ft 10.0 ft 15.0 ft

What dimensions will maximize the lateral surface area of an inverted cone, if V = 27 cm³?

The voltage across a component is given by v = V0e-t/CR. Determine the time taken for voltage v to drop from an initial voltage V0 of 150 volts to 100 volts,  if C = 5 x10-6 Farads and R = 40 kW.   A room 10 m wide has a span roof which slopes 300 on one side and 350 on the other. Find the length of the roof slopes, correct to the nearest cm.   A transmission line between two pylons hangs so that it’s height is described by y = 30 cosh(x/30) metres. Determine correct to 4 significant figures the value of x when y = 60 m.   The pressure loss p in a pipe is related to the flow rate Q by the equation P = KQn, where K and n are constants. If K = 190 x 103 determine the value for n when a flow rate of Q = 0.04 m3/s causes a pressure loss of 180 Pascals.

2) The sweep second hand of a watch is 15.0 mm long. What is the linear velocity of the tip?

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A cannonball is launched from an initial height of 10 meters with an initial launch angle of 21 degrees and an initial speed of 24 meters/second. We assume the cannonball has a mass of 17.6 kg, diameter of 0.18 meters, a drag coefficient of 0.47 and the density of air is 1.23 kg/m³ as modeled on the PhET simulation lab. (https://phet.colorado.edu/sims/html/projectile- motion/latest/projectile-motion_all.html ) This leads us to a value of μD =0.000418 for the coefficient of drag in the following calculations. Assume acceleration due to gravity is g = 9.8 m/s². Write the system of differential equations that would model the path of the cannonball. Use given values for any constants in the equation. Use Mathematica to compute the maximum height, time of impact and range of the cannonball and confirm your results with the PhET simulator. dv v. dt ᏧᎾ dt = II