Chapter 13, Problem 45P

The figure below shows a diver going through general motion. The diver's center of gravity can be assumed to undergo a projectile motion. Assume that the diver takes off from a diving board such that his center of gravity is a height ho = 11m above the water level and enters the water at a horizontal distance 1 = 4m from the end of the board. If the total time the diver remains in the air is t2 = 2.3s, calculate the speed, vo, and angle of takeoff ,O, of the diver's center of gravity. Also determine the height, hi, the diver reaches at the top of the dive. (Note that tr is NOT half of t2.)

A particle P of mass m = 4 kg arrives at point O with a horizontal velocity vo and starts rolling down a circle with radius R = 3.5 m. The particle is attached to the point O by means of a linear spring of stiffness k = 60 N/m that is unstretched when the particle is at O. Assume that during the motion of P along the circle, the spring follows the circle. Let = {În, ŵy} be a fixed reference frame as shown in the figure and let B = {bx, by} be a reference frame attached to P so that ĥ is tangent to the circular path and by is perpendicular to the circular path. For convenience, take g = N = 10 m/s² in this question. ny nx IP a) Determine the Direction Cosine Matrices N[C]B and BCN. b) Determine for P in the frame N the position vector NrP, velocity vector NP, and acceleration vector NaP. e) For each value of leaves the circular path at 0 = 00. Draw a Free Body Diagram of the particle, clearly indicating all forces acting on the particle, and use the Free Body Diagram to determine the…

Find the normal force at the point Q

The object of the pinball-type game is to project the particle so that it enters the hole at E. When the spring is compressed and suddenly released, the particle is projected along the track, which is smooth except for the rough portion between points B and C, where the coefficient of kinetic friction is μk. The particle becomes a projectile at point D. Determine the correct spring compression δ so that the particle enters the hole at E. Solve in general terms, and then evaluate for k = 299 N/m, m = 0.55 kg, μk = 0.40, ρ = 190 mm, and d = 714 mm. State any necessary conditions relating the lengths d and ρ.

The 0.5-lb projectile A is subjected to a drag force of magnitude kv2, where the constant k = 0.0003 lb-sec²/ft2. This drag force always opposes the velocity v. At the instant depicted, v = 210 ft/sec, 0 = 41°, and r = 495 ft. Determine the corresponding values of r and 0. y | ku² Answers: i M. 0 = i 0 T A V 170 --x ft/sec² rad/sec²

A rocket runs out of fuel in the position shown and continues in unpowered flight above the atmosphere. If its velocity in this position was 600 mi/hr, calculate the maximum additional altitude h acquired and the corresponding time t to reach it. The gravitational acceleration during this phase of its flight is 29.2 ft/sec². v = 600 mi/hr Vertical 133 Answers: h = t = mi sec

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Determine the angle and the tension in the cord when the speed of the sphere is 20 ft/s. The sphere has a weight of 40 lb and its speed is 12 ft/s at the instant it is at position A (horizontally aligned with the pulley P). Treat the sphere as a particle. B Tension in cord, T = 0 Angle at position B, when vs is 20 ft/s, 0 = Pulley P ← 5 ft | in degrees A

a) Determine the Direction Cosine Matrices N[C]B and B[C]N