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Fig. P15.194
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Vector Mechanics For Engineers
- An automobile P is traveling along a circular track of radius R=958.4 m. At position "A" on the track, the automobile has a speed of UA = 10.3 m/s. At this position, the driver of the automobile applies the brakes causing the speed of the automobile to change with distance s traveled along the track according to the following equation: U(S) = VA COS(0.001s) m/s (cos is in radians), where s is given in meters. Determine the magnitude of the acceleration for the driver when the automobile reaches position "B" on the track where "B" is a quarter of the distance around the track from position "A". R B O circular trackarrow_forwardThree belts move on two pulleys without slipping in the speed reduction system shown in the figure. At the instant shown, the velocity of point A on the input band is 5.5 ft/s to the right, decreasing at a rate of 9.9 ft/s2. 3 to the lights T 4 in. ↓ 8 in. B C (a) Determine for that instant the velocity of point C, in ft/s, on the exit band. b) Determine for that instant the acceleration of point C, in ft/s2, in the output band. (c) Determine for that instant the acceleration of point B, in ft/s2, at the output pulley.arrow_forwardA 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_forward
- Two ships A and B are moving with constant speeds VA = 20 m/s and vB = 14 m/s, respectively, along straight intersecting courses. The navigator of ship B notes the time rates of change of the separation distance r between the ships and the bearing angle 0. If r= 116 m and e = 113°, what does the navigator measure for i, ï, Ô and Ö? Check that i – ro = 0 and rö + 2rÒ = 0. A. UB 65° Answers: i m/s i m/s2 = i rad/s = i rad/s2arrow_forwardHi, I need help with this question please. Block A is connected to a fixed pin O with a string 100 mm long. The block and the channel are at rest when a motor on a shaft through O starts to rotate the channel with angular velocity ω = sin(0.2t) rad/s and the string starts to pull the block towards O with speed v = sin(0.2t) mm/s. 1. At the time instant t = 2.5π s, determine: a) the components of the velocity and acceleration of the ball in polar coordinatesb) the speed of the ballc) the components of the velocity and acceleration of the ball in normal coordinatesd) sketch the polar and normal components of the velocity and acceleration of the ball on the figure.arrow_forwardQuestion 2 [2/105]: A car P travels along a straight road with a constant speed v = 65 mi/hr. At the instant when the angle 0 = 60°, determine the values of r in ft/sec and è in deg/sec. 100' y 1 1 Ve O -x 15 Varrow_forward
- Q.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. y 3.5 km 2 km Figure Q.6arrow_forwardA cylinder rolls without slipping between two moving plates C and D. The radius of the cylinder is r=4.0m. The velocity of the plate C is VC=6.0 m/s to the right. The velocity of the plate D is VD=2.0 m/s to the left. Using the instantaneous center of zero velocity (IC) to determine (2) The distance between point B and IC point, rB/IC=_____ marrow_forwardA cylinder rolls without slipping between two moving plates C and D. The radius of the cylinder is r=4.0m. The velocity of the plate C is VC=6.0 m/s to the right. The velocity of the plate D is VD=2.0 m/s to the left. Using the instantaneous center of zero velocity (IC) to determine (1) The distance between point A and IC point, rA/IC=_____ marrow_forward
- An aircraft carrier is transiting out to sea with acceleration ag = -1 m/s² and speed VG = -5 m/s (i.e., both to the left) when its onboard radar detects a UFO. At the instant shown, the radar is pointed at angle = π/4, has angular velocity = 0.5 rad/s (CCW), and has angular acceleration α = 0.02 rad/s² (CCW). The radar uses a body reference frame that is moving and rotating with the radar: B = {O', 6₁, 62, 63} to report measurements. The radar reports the relative position (x, y) = (100, 150) meters in the radar's body frame along with the body-frame velocities (x, y) = (Vx, Vy) = (-30, 30) m/s a body-frame acceleration (x, y) = (ax, ay) = (0.1,0.3) m/s² of the UFO. 1. Determine the inertial velocity vector of the UFO expressed in terms of unit vectors of the inertial frame I = {0, 11, 12, 13} located at the base. 2. Determine the inertial acceleration vector in terms of the unit vectors of the radar body frame B. aG VG X RADAR UFO Y j = Ω Ö = d i3 BASEarrow_forwardAt the instant shown, the arm OA of the conveyor belt is rotating about the z axis with a constant angular velocity w₁ = 6.1 rad/s, while at the same instant the arm is rotating upward at a constant rate w2 = 3.5 rad/s. (Figure 1) Figure 0₂₁ 6032 r = 6 ft 8=45° 1 of 1 Part If the conveyor is running at a rate r = 5 ft/s, which is increasing at * = 8 ft/s², determine the velocity of the package P at the instant shown. Neglect the size of the package. Enter the x, y, and z components of the velocity in feeet per second to three significant figures separated by commas. vp = Submit Part B ap = — ΑΣΦ Submit Request Answer ↓↑ — ΑΣΦ Determine the acceleration of the package P at the instant shown. Enter the x, y, and z components of the acceleration in feet per second squared to three significant figures separated by commas. Request Answer < Return to Assignment vec vec www. Provide Feedback ? ft/s ? ft/s²arrow_forwardIt is known that an airplane B is flying at a constant speed v, and at a constant altitude h as shown in Figure 3. The radar station at A tracks the plane by measuring the distance r between it and the plane, the rate at which r is changing, the antenna orientation 0, and the angular velocity of the antenna. Detemine the relationships between those quantities that can be found by the tracking station and the speed, and height of the airplane. Figure 3: A radar sta tion tracking a plane in flight.arrow_forward
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