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use any external references, such as books or formula sheets. • The question booklet, answer sheet and scratch paper will be collected at the end of this exam. • To maintain exam security, do not communicate any information about the questions
• An integral is the space under a graph of an equation, the opposite of a derivative. For example: W= Z F(x)dx You can think of work as the area under the curve of the force vs. distance graph. • The notation ¨xrepresent d2x dt2. • Always draw a free body diagram when doing dynamics problems! 14
a) If f(x) is symmetric (or antisymmetric), so is F(k): i.e. if f(x) = f( x) then F(k) = F( k). b) If f(x) is real, F (k) = F( k). c) If f(x) is real and symmetric (antisymmetric), F(k) is real and symmetric (imaginary and antisymmetric). d) F.T.[f( x)] = 1 j j F k . e) F.T.[f(x+ a)] = eikaF(k). f) F.T.[e xf(x)] = F(k+ i ) (for real or complex .)
This textbook covers all the standard introductory topics in classical mechanics, including Newton’s laws, oscillations, energy, momentum, angular momentum, planetary motion, and special relativity.
F is applied to a system, the kinetic energy and the momentum undergo change according to the following equations: ~p = ~p 2 ~p 1 = X F~ t K = K 2 K 1 = X ~F ~s 1.2 Relationship Between Kinetic Energy and Momentum As you can see from the above equation, the P~ F (the net force) forms a rela-tionship between the change in momentum and the change ...
f k is the force of kinetic friction (in the –x direction), F N is the vertical normal force exerted by the floor (in the + y direction), and mg G is the force of gravity. The magnitud e of the force of friction is given by Eq. 6 -2: f k = k F N. Applying Newton’s second law to the x and y axes, we obtain 0 k N F f ma F mg respectively.
This booklet is a sequel to a similar collection of problems on kinematics and has two main parts: Section 3 — Statics and Section 4 — Dynamics; Section 5 contains revision problems. The main aim of this collection of problems is to present the most important solving ideas; using these, one can solve most (> 95%) of olympiad problems on ...
