A certain toddler plans to launch a 0.25-gram pea from the handle of a 55-gram fork by pressing on the fork tines with an applied force of FA = 49 N, where the force will be applied perpendicular to the plane of the fork tines as shown. The fork will pivot about a point a distance LS = 5.6 cm from the tip of the fork, and the pivot is a distance of d = 5.8 cm from the fork’s center-of-mass. The child’s goal is to figure out in advance how far the pea will fly (its range). (a) (1 pt) First, determine the “effective length” of the fork – that is, the length of the black dashed line in the figure that represents the tip-to-end distance. Take LL = 16.5 cm as the horizontal distance from the pivot point to the end of the fork. Express your answer in meters.
(b)(1 pt) Next determine the moment of inertia for the fork (you may disregard the pea due to its very small mass) as it rotates about the indicated pivot point. Approximate the fork as a uniform rod with a length equal to the length you calculated in part (a). Express your answer in kg ∙ m%.
(c) (1 pt) Now determine the angular acceleration the fork experiences due to the force acting at the tip of the fork. The fork rotates as a solid object, so the angular acceleration of the tip is also equal to the angular acceleration of the end holding the pea. Don’t forget to include torque due to the gravitational force on the fork. Again, the pea can be neglected, as its low mass produces negligible torque. Express your answer in rad/s2.
(d)(1 pt) Assuming constant acceleration from rest, determine the tangential velocity of the end of the fork (where the pea is located). Note that the fork will rotate until the tines are flat on the table.
(e) (1 pt) What is the launch angle of the pea (the angle above the horizontal)? It might help to draw a diagram of the fork when the pea launches and figure out the angles from there. Note that the fork’s end does not start out horizontally.
(f) (1 pt) Using your results from (d) and (e), determine the range of the pea. Assume air resistance is negligible and that the pea lands at the same height it started from (on the table, for example). Express your answer in meters.