Question

Need help with the whole problem. Thank you!

Even if the problem comes with a figure, draw your own set-up. Identify the key points on your drawing: those would be the center of the objects, or the knots of the ropes - if ropes are connected to each other. Once you identified those points place an xy system of coordinators in each of them, so that one of the axis points in the direction of the motion, or in the direction of the rope. Draw a free-body diagram (FBD) for each object or knot under consideration, and label all external forces acting on it. Resolve all forces into x and y components - if they are not already pointing along these axis. Write the equations sigma F_x =ma_x and sigma F_y = ma_y for each FBD. Keep track of the signs of the various components. If the object is at rest or moves with constant velocity then a_x and/or a_y is zero. Imagine each FBD in a bubble. When you write sigma F consider only the forces inside the bubble. Application of step 5 leads to a set of n equations with n unknowns. Set that system up in a bracket. Step 7 Solve the simultaneous equations for the unknowns in terms of the known quantities. A seaplane of total mass m lands on a lake with initial speed upsilon_i i. The only horizontal force on it is a resistive force on its pontoons from the water. The resistive force is proportional to the velocity of the seaplane: R = - bv. Newton's second law applied to the plane is - b upsilon i = m(d upsilon/dt) i. From the fundamental theorem of calculus, this differential equation implies that the speed changes according to integral_dv/v = - b/m integral_0^1 dt Carry out the integration to determine the speed of the seaplane as a function of time, (b) Sketch a graph of the speed as a function of time, (c) Does the seaplane come to a complete stop after a finite interval of time? (d) Does the seaplane travel a finite distance in stopping?

Answer 1

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