1. A vertical spring with a spring constant of 450N.m ismounted on the floor. Fr

Question

1. A vertical spring with a spring constant of 450N.m ismounted on the floor. From directly above the spring , which isunstrained, a 0.30kg block is dropped from rest. It collides withand sticks to the spring. the spring is compressed by 0.025m inbringing the block to a momentary halt. Assuming air resistance isnegligible, from what height above the compressed spring was theblock dropped? 2. A large tank that is open at the top is filled with waterto a depth of 15m. A spout located 10.0m above the bottom of thetank is then opened as shown in the drawing . Assume there isnegligible change in the height of the column. With what speed willthe water emerge from the sprout? 3. A cup of coffee is sitting on a tray in an airplane that isflying at a constant altitude and a constant velocity. Thecoefficient of static friction between the cup and the table is0.30. Suddenly the plane accelerates, its altitude remainingconstant. What is the maximum acceleration that the plane can havewithout the cup sliding backward on the tray? 1. A vertical spring with a spring constant of 450N.m ismounted on the floor. From directly above the spring , which isunstrained, a 0.30kg block is dropped from rest. It collides withand sticks to the spring. the spring is compressed by 0.025m inbringing the block to a momentary halt. Assuming air resistance isnegligible, from what height above the compressed spring was theblock dropped? 2. A large tank that is open at the top is filled with waterto a depth of 15m. A spout located 10.0m above the bottom of thetank is then opened as shown in the drawing . Assume there isnegligible change in the height of the column. With what speed willthe water emerge from the sprout? 3. A cup of coffee is sitting on a tray in an airplane that isflying at a constant altitude and a constant velocity. Thecoefficient of static friction between the cup and the table is0.30. Suddenly the plane accelerates, its altitude remainingconstant. What is the maximum acceleration that the plane can havewithout the cup sliding backward on the tray?

Explanation / Answer

Spring constant K = 450 N m Mass m = 0.30 kg Compression x = 0.025 m Kinetic energy justbefore colllision = potential energy atmaximum compression                           ( 1/ 2) m v ^ 2 = ( 1/ 2) k x ^ 2 fromm this required speed v = 0.9682 m / s

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