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An accelerometer record for the motion of a given part of a
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Vector Mechanics For Engineers
- 6 Two cars A and B travelling at constant speeds are in the positions shown in Figure Q.6 at time t = 0. The velocity of A is 40 km/h and that of B is 60 km/h. Determine:(i) The velocity of A relative to B and the magnitude and direction of the velocity vector.(ii) The position vector of A relative to B as a function of time.arrow_forwardA part of a machine consists of two arms OA and AP so that the angle between OA and AP is always half of that between O.A and the --axis. The following demonstrates the movement of these two arms. a. At a = Q rad, location = C. Path of P x(a): Y(a) = PO → Hint: (x(a), (y(a)) = OP = OA+AP. Try to set up OA and AP using angles in standard position. Length = a Arm O.A is 3.7 cm long and arm AP is 5.4 cm long. Find the location of P (in cm) when a = 0 rad, rad, /2 rad and /3 rad. Round your answers to at least 2 decimal places and enter them as points (x, y). cm a/2 O A At a rad, location = At a = π/2 rad, location = At a = π/3 rad, location = b. Find the parametric equations (a) and y(a) (in cm) that give the path of P for all & € [0₂]. The parameter a should represent the angle given in the diagram. Check your answer with the results from part (a). Use exact values or round the values to at least 5 significant figures. a = 0.7 Drag the slider to move the points. Try to reload the page if…arrow_forwardQuestion 3: Kinematics The position vector of a particle is given as function of time as r = (3t³î - 4t²ĵ+ 5tk) m. If the particle started moving from rest at = (3î+ 4ĵ- 5k) m and that t is in second, determine the: (a) (b) (c) displacement vector and its magnitude after time t = 3 s vecocity vector and its magnitude after time t = 3 s acceleration vector and its magnitude after time t = 3 s Retarrow_forward
- A car P travels along a straight road with a constant speed v = 64 mi/hr. At the instant when the angle 0 = 60°, determine the values of r in ft/sec and 8 in deg/sec. Assume = 113! Answers: r = 1 0 = F MI x חומון V ft/sec deg/secarrow_forwardAngular Impulse and Momentum Principles To apply the principle of angular impulse and momentum to describe a particle's motion. The moment of a force about a point O, fixed in an inertial coordinate system, MO, and the angular momentum about the same point, HO, are related as follows: ∑MO=H˙O where H˙O is the time derivative of the angular momentum, HO=r×mv. Integrating this equation with respect to time yields the following equation: ∑∫t2t1MO dt=(HO)2−(HO)1 This equation is the principle of angular impulse and momentum, and it is often rearranged to its more familiar form (HO)1+∑∫t2t1MO dt=(HO)2 A centrifugal governor consists of a central rotating shaft that has two thin, pin-connected rods attached to it; a heavy sphere caps the end of each rod. (Figure 1) A centrifugal governor mechanically limits an engine's speed. A part of the engine turns the centrifugal governor, and if the speed exceeds a set amount, the height of the spheres decreases the driving force of the engine by…arrow_forwardAngular Impulse and Momentum Principles To apply the principle of angular impulse and momentum to describe a particle's motion. The moment of a force about a point O, fixed in an inertial coordinate system, MO, and the angular momentum about the same point, HO, are related as follows: ∑MO=H˙O where H˙O is the time derivative of the angular momentum, HO=r×mv. Integrating this equation with respect to time yields the following equation: ∑∫t2t1MO dt=(HO)2−(HO)1 This equation is the principle of angular impulse and momentum, and it is often rearranged to its more familiar form (HO)1+∑∫t2t1MO dt=(HO)2 A centrifugal governor consists of a central rotating shaft that has two thin, pin-connected rods attached to it; a heavy sphere caps the end of each rod. (Figure 1) A centrifugal governor mechanically limits an engine's speed. A part of the engine turns the centrifugal governor, and if the speed exceeds a set amount, the height of the spheres decreases the driving force of the engine by…arrow_forward
- For the helicopter of Prob. 11.168, it was found that when the helicopter was at B , the distance and the angle of elevation of the helicopter were r= 3000 ft and 0= 20°, respectively. Four seconds later, the radar station sighted the helicopter at r= 3320 ft and 0= 23.1°. Determine the average speed and the angle of climb β of the helicopter during the 4-s interval.arrow_forwardmoments = 0) in order to determine a force or moment requires a complete free body diagram. Absence of a free body diagram may result in a grade of 'O' for the problem. %3D 1. The acceleration of a particle is directly proportional to time, t, i.e., a = at where a is a constant. At t = 0 s, the position of the particle is -150 mm. Knowing that v = 200 mm/s and x = 75 mm whent = 3 s, determine the position and velocity when t = 5 s.arrow_forwardThe planar two-link space-station assembly robot shown in Figure 1 consists of two identical links of lengths a = b=2 metres. (c) Derive expressions for the horizontal and vertical positions and velocities of point E in terms of 0,, 0,, 0, and Ô, . (i) (ii) For the case when 0, = 0.4 radians and 0, = 0.2 radians, and 0, = 0, = 0.6 radians/sec, calculate the position of point E, and the magnitude of the linear velocity of point E. E y b Xarrow_forward
- Problem 7 The equation of motion of a particle is given, acceleration (a) in terms of time (t) as below: a= 3t2 + 2t+4, in which acceleration is in m/s2 and time t is in seconds. It is observed that the velocity of the particle is 12 m/s after 4 seconds; and the displacement of the particle is 8 m after 4 seconds. Determine (i) Velocity after 8 seconds (ii) Displacement after 2 secondsarrow_forward1. A chain of blocks is moving upward at 3 m/s. The tension in the cable connected to the top of the chain is To = 800 N. a. What is the acceleration of the chain of blocks? b. What is the tension in the cable connecting Block C and Block D? v = 3 m/s To = 800 N mA = 21 kg mB = 25 kg mc = 20 kg mp = 18 kg mg = 17 kg mp = 15 kg a = ? TCD = ?arrow_forward33. (a) a (t) = a + Jt; v_(t) = v + a_+*; x(1) = x, + v + ļa t² + &ji°arrow_forward
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