Catapulting mushrooms. Certain mushrooms launch their spores by a catapult mecha

Question

Catapulting mushrooms. Certain mushrooms launch their spores by a catapult mechanism. As water condenses from the air onto a spore that is attached to the mushroom, a drop grows on one side of the spore and a film grows on the other side. The spore is bent over by the drop's weight, but when the film reaches the drop, the drop's water suddenly spreads into the film and the spore springs upward so rapidly that it is slung off into the air. Typically, the spore reaches a speed of 1.60 m/s in a 5.00 µm launch; its speed is then reduced to zero in 1.20 mm by the air. Using that data and assuming constant accelerations, find the acceleration in terms of g during (a) the launch and (b) the speed reduction.

Explanation / Answer

Use your handy equation of motion: vf^2 - vi^2 = 2 a distance So to accelerate from rest: a = vf^2 / (2 distance) And to decelerate, use that same formula and the same speed with the deceleration distance. Don't worry about signs for this since they just want magnitudes. They ask you to express your answer in terms of g, so divide by g and that will give you the number of g's. Be careful to handle the millimeters and micrometers correctly. EDIT-- So you need more help. You have the equation for your answer. Fortunately, it was just an algebraic rearrangement of one of the equations of motion you should know by heart. Once you chose the right equation and did the algebra (which we did for you), you're 90% done. You just have to plug numbers into your calculator and get the units right. a = vf^2 / (2 distance) They give you a velocity. Square that. Then divide by 2. Then divide by the distance. You'll want your distance to be in meters, so don't forget to convert. 1000 mm per m. A million micrometers per meter. Then you'll have your answer in m/s^2. Divide that by g (9.8 m/s^2) and you'll have the g's. The only difference between the two parts is which distance you plug in. Obviously one distance is 200 times smaller, so the acceleration will be 200 times greater.

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