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Use Hooke's Law to determine the work done by the variable force in the spring probiem. A force of 5 pounds compresses a 15*iCh spring a totai of 3 inches. How much work is done in compressing the spring 9 inches? \fNeglecting air resistance and the weight of the propellant, determine the work done in propelling a fouraton satellite to the following heights. (Use 4000 miles as the radius of Earth. Round your answers to one de(imal place) (a) 100 miles above Earth (b) 500 miles above Earth : m A rectangular tank with a base 4 feet by 5 feet and a height of 4 feet is full of water (see gure). The water weighs 62.4 pounds per cubic foot. How much work is done in pumping water out over the top edge in order tn empty the following amounts? (a) half of the tank :wa (b) all of the tank :ftm lJ ' Consider a 50*foot chain that weighs 6 pounds per foot hanging from a winch 50 feet above ground level. Find the work done by the winch in winding up the entire chain. Consider a 15foot hanging chain that weighs 3 pounds per foot. Find the work done in lifting the chain verticailyr to the indicated position. Take the bottom of the chain and raise it to the 15foot levei, ieaving the chain doubled and still hanging verticalii,l (see figure). EH: Find the center of mass of the given system of point masses lying on the X-axis. m1=6,m2=3,m3=4 X1=5,X2=U,X3=3 (UH: Consider a beam of length L with a fulcrum x feet from one end {see gure). There are objects with weights W1 and W2 placed on opposite ends of the beam, where W1