Styrofoam pellets. We will assume that when an object enters the pit its acceleration is given by 2 a g cs = − , where g is the acceleration of gravity, c is a constant and s is the distance below the surface of the particles in the pit. If the velocity of a mass is v 0 at the surface of the particles, find a) the distance it will need to stop, that is, the minimum depth of the loose particles so that the mass does not hit the bottom of the pit b) the time it will take to stop. Hint: You may assume that you know the velocity as a function of s in the particles, v ( s ) . For both parts a) and b) it is sufficient to leave your solution in the form of a definite integral with proper limits of integration.
Name: ________________________________ Problem 2. The cam is designed so that the center of the roller A which follows the contour moves on a limaçon defined by cos r b c θ = − , where b > c . If the cam does not rotate, determine the magnitude of the total acceleration of A in terms of b , c , and θ if the slotted arm revolves with a constant counterclockwise angular rate ! θ = ω .
Name: ________________________________ Problem 3. An excursion train traveling 30 mph from left to right in the picture encounters a rain shower. Point A lies 7 ft. directly beneath the lip of the overhang on the observation car. The raindrops are falling straight down at a constant speed of 25mph. a. What is the velocity of a raindrop with respect to an observer in the train? b. How far onto the observation platform will the raindrops land? v train Observation platform
Name: ________________________________ Problem 4. In a 5-meter-high tunnel, a projectile is launched at an angle of θ = 35° from the floor, as shown. Determine the correct launch velocity to maximize the horizontal range of the projectile without hitting the top of the tunnel. Do not calculate the range.
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- Spring '08