Classical Mechanics Answers

A particle of mass 'm' moves in x-y plane so that its position vector r = x_i + y_j with a parametric equation x= a cos wt, y= b sin wt, where a&b are constants, a>b and w is a positive constant. 1. Show that the force field is conservative. 2. Find the potential energy at point a&b. 3. Find the work done by the force in moving the particle from point a-b. 4. Find the total energy of the particle.

Obtain the corresponding potential energy function of the intermolecular force. 1. F(r) = -ar^-7 + br^-9. 2. at what value of 'r' will the potential energy function be minimum

Derive the potential energy function for a one dimensional motion and sketch its graph

A body of mass (m) falls from rest through a medium which exact a frictional drag force (bv) proportional to a applied force (f). 1. At what time does the body reach 1/e of it's terminal velocity. 2. Find its displacement. 3. Expand the displacement in power series up to t^4

A body of mass (m) falls from rest through a medium which exact a frictional drag force (bv) proportional to a applied force (f). 1. Expand the velocity in power series up to t^4

Find the center of mass of twelve identical particles

Obtain the corresponding potential energy function of the intermolecular force F(r) = -ar^-7 + br^-9

Derive the potential energy function for one dimensional motion

Sketch it graph

A light wooden uniform metre rule was clamped to the surface of a bench so that a length L of the metre rule was hanging over the edge. The overhanging end of the metre rule was loaded with a mass and the depression D produced at the loaded end was measured. Values of D were obtained for different lengths L.

L (mm) 200 300 400 500 600 700 800

D (mm) 2.0 6.0 13.0 28.0 49.0 75.0 109.0

Assume that D = KLⁿ, where K and n are constants, and draw a graph that would enable you to determine the values of n and K. Use a linear regression analysis of the data to fit the best straight line through the data and determine the value of D for L = 100 mm from the graph. 

A stuntman is placed in a cannon and fired at 40.0° with an initial speed of 35.0 m/s. A net is placed 60.0m from the cannon. In order to catch the stuntman, what is the height that the net should be placed?

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