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For the Scotch yoke
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Vector Mechanics for Engineers: Dynamics
- 3. a) The velocity of a platform in an amusement park which moves along the s-axis is given by v = 2– 4t + 5t²ª , where t is in seconds and v is in m/s. The platform is at the position S, = 3 'm when =0 Determine: (i) The position S, velocity v, and acceleration a when != 3s. (ii) The time at which the velocity of the platform is maximum. b) The race car A in Figure Q3 follows path a-a while race car B follows path b-b on the unbanked track. If each car has a constant speed limited to that corresponding to a lateral (normal) acceleration of 0.8g, determine the times a and 's for both cars to negotiate the turn as delimited by the line C-C. C a b 88 m 72 m b B a Aarrow_forwardA Scotch yoke is a mechanism that transforms the circular motion of a crank into the reciprocating motion of a shaft (or vice versa). It has been used in a number of different internal combustion engines and in control valves. In the Scotch yoke shown, the acceleration of Point A is defined by the relation a=-1.5sin(kt) , where a and t are expressed in m/s2 and seconds, respectively, and k=3 rad/s. Knowing that x=0 and v=0.6 m/s when t =0, determine the position of Point A when t=0.5 s.arrow_forwardThe acceleration of a particle is defined by the relation a = -k/ū where k is a constant knowing that a = 0 and v = 81 m/s at t = 0 and that v = determine the time required for the particle to come to rest. 36 m/s when a = 15 m a. 0.789 O b. 1.350 O c. 15.789 O d. 0.185arrow_forward
- Q6. As shown in the image below, two objects, A and B, are connected using the cable and pulley system. (The cable and pulley system is friction-less and weight-less.) If at this moment the acceleration of object Bis downward 2.3 m/s², determine the acceleration of object A (in m/s²2) at this moment. In this problem, downward motion is considered positive, and in your answer, negative sign must be included if the motion of A is upward. Please pay attention: the numbers may change since they are randomized. Your answer must include 1 place after the decimal point, and proper SI unit. A B VBarrow_forwarda 11.167 V To study the performance of a racecar, a high-speed camera is positioned at Point A. The camera is mounted on a mechanism which permits it to record the motion of the car as the car travels on straightway BC. Determine (a) the speed of the car in terms of b, 0, and 0 and (b) the magnitude of the acceleration in terms of b, 0, é , and ê. В C b Aarrow_forward2. A truck's speed increased uniformly from 20 km/hr to 70 km/hr in 30 sec. determine (a) the average speed (b) the acceleration and (C) the distance traveld.arrow_forward
- The angular position of a rotating object as a function of time is given below: e = 4t3-4.8t2 +4.3t+d Here 0 is in units of radians and t is in units of seconds and d is constant. Determine the instantaneous angular acceleration of the object at t=2s. Express your answer in units of rad/s2 using one decimal place.arrow_forward3) Link AB of a robotic arm is rotating at a constant speed of 4 rad/s, while link BC is rotating at 5 rad/s, a speed that is increasing at the rate of 2 rad/s². Find the magnitudes of the velocity and acceleration of point C when AB is vertical and BC is horizontal, as shown here. 2.0 ft 1.5 ft B WAB A WBC = 5 rad/s αBC = 2 rad/s² = 4 rad/s Carrow_forwardA brass (nonmagnetic) block A and a steel magnet B are in static equilibrium in a brass tube under the magnetic repelling force of another steel magnet, C. The magnet B is located a distance x =d, from C. If block A is suddenly removed, and the acceleration of block B is: k a =-g+ where g andk are known constants. Determine: a. the velocity, v, as a function of the position x and the known parameters (g,k,d,), and b. the position, x, when the velocity is maximum in terms of the known parameters (g,k,d,). Вarrow_forward
- PROBLEM 2.17 The position of an object as a function of time is given as x = 2.1t3 + t2 -4t + 3 where x is in meters and t is in seconds. 19. What is the velocity of the object at t = 10.0 s? c. 946 m d. 616 m а. 936 m b. 646 m 20. At what time is the object at rest? 0.654 s c. 0.454 s d. 0.754 s а. b. 0.554 s 21. What is the acceleration of the object at t = 0.50 s? с. 7.3 m/s2 d. 9.3 m/s² 6.3 m/s² 8.3 m/s2 а. b.arrow_forwardQ#7: Determine the smallest radius that should be used for a highway if the normal component of the acceleration of a car traveling at 62 km/h is not to exceed 0.8 m per 2arrow_forwardAn automobile travels along a straight road at 15.65 m/s through a 11.18 m/s speed zone. A police car observed the automobile. At the instant that the two vehicles are abreast of each other, the police car starts to pursue the automobile at a constant acceleration of 1.96 m/s . The motorist noticed the police car in his rearview mirror 12 s after the police car started the pursuit and applied his brakes and decelerates at 3.05 m/s . (Hint: The police will not go against the law.) a) Find the total time required for the police car to overtake the automobile. b) Find the total distance travelled by the police car while overtaking the automobile. c) Find the speed of the police car a the time it overtakes the automobile. d) Find the speed of theautomobile at the time it was overtaken by the police car.arrow_forward
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