Grains of wheat are planted in wet cotton wool around the edge of a dish of radi
ID: 1691866 • Letter: G
Question
Grains of wheat are planted in wet cotton wool around the edge of a dish of radius R = 0.15 m spinning with angular velocity of ?. As the seeds germinate it is observed that they grow at an angle to the vertical rather than straight up, which is how they grow under normal circumstances. It is assumed that their direction of growth is determined by the gravitational field direction.(a) Do the seeds grow inwards towards the centre or outwards? Why?
(b) Derive an equation for the angle of growth as a function of R, ? and g, where g = 9.8 m/s2 is the acceleration due to gravity.
(c) If the experiment is repeated a number of times for values of ? between 0 and 120 RPM, draw a graph in Excel showing the predicted angle? (in degrees) as a function of angular velocity.
Explanation / Answer
a.) Answer: Outward. Reason: When the dish is not spinning, the grain will grow vertically as normally. When the dish is spinning, there is a centripetal force that tries to push the plant outward (similar to when you're in a car that that keeps turning leftward, then you'd feel a force pushing you rightward (or outward). b.) Angle = Inverse tangent of [ (force of gravity)/(centripetal force) ] where force of gravity = (mass of wheat)*(g) and centripetal force = (mass of wheat)*(centripetal acceleration = (angular velocity)^2 * radius R) here is a link to a brief explanation of angular velocity/acceleration if you're rusty: http://hyperphysics.phy-astr.gsu.edu/hbase/rotq.html c.) basically you're plotting the equation from (b) the angle vs angular velocity Cramster has trouble generating graph but here: http://www.wolframalpha.com/input/?i=tan^-1%289.8%2F%280.15*x^2%29%29 take the positive portion of the graph is what you're interested in. The horizontal axis is angular velocity and the vertical axis is angle in radian. Note that the y intercept is 90 degrees.
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