VP5.22.2 A competition cyclist rides at a constant 12.5 m/s around a curve that is banked at 40.0°. The cyclist and her bicycle have a com- bined mass of 64.0 kg. (a) What must be the radius of her turn if there is to be no friction force pushing her either up or down the banked curve? (b) What is the magnitude of her acceleration? (c) What is the magni- tude of the normal force that the surface of the banked curve exerts on the bicycle?

4) This Atwood's machine includes two blocks connected by a cable, going over a pulley without slipping. Block 1 (30.0 kg) is connected to a spring (70.0 N/m), and slides on a horizontal surface with a coefficient of kinetic friction of 0.0100. Block 2 is 50.0 kg, and hangs vertically from the cable. The pulley is a disk with a radius of 0.500 m, and its moment of inertia about the center of mass is 10. 0 kg-m“. a) Draw the three free body diagrams, and write out Newton's 2nd Law for each. b) Derive the equation of motion (inhomogeneous 2nd order ODE) for this system. c) Use u-substitution to rewrite this as a homogeneous 2nd order ODE. d) Assume the position x as a function of time t is of the form x(t) = A cos (wt + p) I disk for undamped natural frequency w, phase angle P, and amplitude A. The initial conditions are: x(0) v(0) = -3. 00 m/s. Solve for the position of the mass as a function of time (you need to solve for w, 4, and A). = 2. 00 m and Mz

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Problem 1 (Lecture 03) Three forces act on the bracket shown to the right. Note that for this problem, the direction (0) of F1 is measured from the positive x' axis, positive clockwise. Complete the following: a) Determine the direction (0) and magnitude of F₁ so that the overall resultant force is directed along the positive x' axis and has a magnitude of 1 kN. b) Determine the unit vector u₂ (in Cartesian notation) for the direction of F2. y Ꮎ F₁ F₂ 45° 30° = 450 N F3 = 200 N X

A boxer delivers a hard blow to the chin of his opponent. The inertia of the boxer's hand (with glove) and forearm is 3.0 kg, and the inertia of the opponent's head is 6.5 kg. You learned in neurobiology class about 10 J of extra internal energy will render an opponent wobbly - kneed, and you guess that about half of the converted energy will end up in the opponent's head. Assuming a coefficient of restitution e = 0.20, with what speed does the boxer's fist have to contact the opponent's head in order to deliver the punch?

please answer this question with explination. many thanks !