The equations of motion of the airplane in a straight line steady symmetrical flight are: OT-D=0 L-W=0 V md- =T-D dt L-W-0 V = md=T-W dt L-D=0
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- 4. A boy riding a bicycle with a constant speed of 800 m/min around a horizontal circu- lar path of radius r = 50 m leans inward at angle 8 with the vertical, as shown in Figure 9-27. Determine the angle of inclination needed to maintain a steady-state circular motion. mg R Figure 9-27 Boy riding a bicycle around a circular path.Assignment 4 1) A particle of mass 1 slug is moving in a constant force field given as F = 3i+ 10j - 5k lb the particle starts from rest at position (3,5,-4). What is the position of the par- ticle at time t = 8 seconds?State the equation that mathematically represents the system. All in domain X(s) hint: there are 3 equations 4:00-1-1-1-1!1! k₁ 0000 0000 B₂ B₁. m₁ 0000 k3 without friction x1 (1) m2 B3 -f(t) + - X2 (1)
- As shown in the figure. A plot of potential energy U versus position x of a 2 kg particle that can move along x-axis. The graph has these values U_A=9J, U_C=20J and U_D=24J. The particle is released at position x=5 m with kinetic energy 4 J where the potential energy is U_B=12 j. What is the kinetic energy of the particle at x =3.5 m. Upt ... Uc UAF-- 4 6 7 x (m) A) 8J B none of them C 7J D 7.5J3. Quarter car suspension model The figure below a model of the suspension of a car. r(t)is the position of the mass of the car from its equilibrium position while z is the profile of the road. Note that z is a function of the distance y along the road, but you need ż(t) which you can obtain from z(y) using the chain rule. The car is traveling to the right on the road at a speed v. Assume the mass of the car is 250 kg, the spring constant is 16 kN/m, and damping constant is 1000 Ns/m. (a) Derive the differential equation for the position of the car r(t). (b) If z(t) = Zoejot, determine the amplitude and the phase of the particular solution. (c) (MATLAB) If the car is travelling with constant velocity along a road with rolling hills that can be represented as a cosine function with amplitude Zo and wavelength A (wavelength is the distance between adjacent crests or adjacent troughs, determine the vertical motion of the car as a function of time. X(t) Z m 1 C Figure 1: Quarter car…hi Vo Vo V₁ = R - he A ball will be thrown from the initial position (pictured in green) to strike a target (pictured in red) while avoiding contact with the ceiling. The initial height is hi - 5 m, the ceiling is he - 25 m tall, and the target = = is ht = 20 m above the ground. The target is R = 40 ht m away, horizontally. Find the minimum initial speed V₁ that can achieve this m/s
- QI- the system as shown in figure below is beginning from rest, find the displacement, velocity and acceleration after 2 second? kN N.m F = - (t + 2) kN k = 8 m2 c = 6 s2 m = 1kg k F mEngineers are designing a system by which a falling mass m imparts kinetic energy to a rotating uniform drum to which it is attached by thin, very light wire wrapped around the rim of the drum (Figure 1). There is no appreciable friction in the axle of the drum, and everything starts from rest. This system is being tested on earth, but it is to be used on Mars, where the acceleration due to gravity is 3.71 m/s?. In the earth tests, when m is set to 15.0 kg and allowed to fall through 3.00 m, it gives 350.0 J of kinetic energy to the drum. Part A If the system is operated on Mars, through what distance would the 15.0 kg mass have to fall to give the same amount of kinetic energy to the drum? Express your answer with the appropriate units. HA hM = Value Units Part B Figure 1 of 1 How fast would the 15.0 kg mass be moving on Mars just as the drum gained 350.0 J of kinetic energy? Express your answer with the appropriate units. Drum HA Value Units v =A hanging mass m = 84kg is released from rest and accelerates downward. The winding drum A of mass me = 60kg with an effective diameter of d, = 410mm and a radius of inertia ka = 375mm meshes with gear B. Assume ws = 5wa, with subscript a related to the winding drum and ; to gear B. B Analyse the frictionless system and calculate: The moment of Inertia of the drum Ig = maka = 8.4375 |kgm? The linear acceleration a = 3.906 m/s/8 The angular accelerations for the drum ag = 19.532 rad/s/s as well as the gear s = 97.66 rad/8/s (*) The tension in the cord F N. Assume an observation period of 4 s from the instant the system is released from rest and calculate the change of linear speed Av = m/s and linear distance the hung mass moves Ah = m (*) During the 4 8 observation, the following changes of energy with the correct sign can be computer:
- 2 blocks with mass, 2 massless pulleys, give equation of motion for x(t): x(t) m, m, y(1)+ Problem 3 The winch delivers a horizontal towing force F to its cable at A which varies as shown in the graph. (Figure 1). Figure 79°F Mostly sunny B F F(N) 600 360 12 24 1 of 1 r(s) T Part A Determine the spel bucket is moving up its cable Express your ans appropriate units. v2 = Value Submit Regi Provide Feedback of 1 Part A Determine the speed of the 62 kg bucket when t= 19 s. Originally the bucket is moving upward at z, 3 m/s. v₂ = Express your answer to three significant figures and include the appropriate units. Submit HA 6 @ Value Provide FeedbackWhich quantity is always tangent to the curvilinear motion path?