PROBLEM 5 A two-link robotic arm with a revolute and a prismatic (i.e., slider) joint is shown in the diagram below. The first link pivots at the origin of frame A and the second link can increase or decrease in length. a2 ai (a) Find the position of point P with respect to the frame A (P).
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- 1. Taking north as positive and south as negative for all reference frames, suppose Mayor Adams is riding a southbound train to New York City traveling at 40 m/s relative to the ground, while Governor Hochul is riding a northbound train to Albany at 33 m/s relative to the ground. A) What is the velocity of Mayor Adams in Governor Hochul's reference frame (i.e. in the reference frame where Governor Hochul isn't moving)? B) What is the velocity of Governor Hochul in Mayor Adams reference frame? C) To his surprise Mayor Adams observes a groundhog running along the aisle towards the back of the train with a speed of 2 m/s relative to the train. What is the velocity of the groundhog in Governor Hochul's reference frame? D) What is the groundhog's velocity in the reference frame of someone standing at the train station? E) What is its velocity in Mayor Adams's reference frame? F) What is its velocity in the groundhog's frame? 30 10 ft. 5 ft. 15 ft.The space and time coordinates for two events as measured in a frame S are as follows: Event 1: x1=x0 , t1=x0/c Event 2: x2=2x0, t2=x0/2c a. There exists a frame in which these events occur at the same time. Find the velocity of this frame with respect to S. b. What is the value of t at which both events occur in the new frame?q3
- that the axes get closer to one another. 2. Prove that the "interval", defined as x² +v² + =² – c²¢ is a conserved quantity across reference frame transformations. 3. Consider two events. Give an example of coordinates x,y,z,t and x',y',z',t and relativeA frame B shown below in Figure 1, is rotated 90° about the z-axis, then translated 3 and 5 units relative to the n- and o-axis respectively, then rotated another 90° about the n-axis, and finally, 90° about the y-axis. Find the new location and orientation of the frame. (1,1,2) {B} F y a Figure 1 11Please specify the reference frames and draw diagrams to illustrate the problem. show complete solution too
- A train, which is 200 m long, approaches a tunnel, which is 120 m long. The train is moving at a velocity of 0.89 c. a. What is the length of the train as seen be someone standing at the entrance to the tunnel? m b. Is the train ever entirely inside the tunnel as seen be the observer at the entrance to the tunnel? ONLY 1 ATTEMPT IS ALLOWED FOR THIS PART. ---Select--- v c. What is the length of the tunnel as seen be a passenger on the train? m d. Is the train ever entirely inside the tunnel as seen by the passenger on the train? ONLY 1 ATTEMPT IS ALLOWED FOR THIS PART. ---Select--- vfo 10. A square frame has sides that measure 2.00 m when it is at rest. What is the area of the frame when it moves parallel to one of its diagonal a speed of 0.72c as indicated in the figure? with m² ssf60 ssf60 ssf60 ssf60 s² sf60 ssf60 ssf60 ssf60 esf60 ssfor 50 ssf ss:60 ssi0 ssf603 js (9 08 09588 ssf60 ssf60 ssf60 ssi 60 ssf60 ssf60 ssf60 ssf60 ssf60 ssf60Problem 2 In terms of the xs, ŷ, 2s coordinates of a fixed space frame {s}, frame {a} has its x-axis pointing in the direction (0, 0, 1) and its ŷ₂-axis pointing in the direction (-1,0, 0), and frame {b} has its x-axis pointing in the direction (1, 0, 0) and its y-axis pointing in the direction (0, 0, -1). The origin of {a} is at (3, 0, 0) in {s} and the origin of {b} is at (0, 2, 0) in {s}. (a) Draw by hand a diagram showing {a} and {b} relative to {s}. (b) Write down the rotation matrices Rsa and Rsb and the transformation matrices Tsa and Tsb. (c Calculate the matrix exponential corresponding to the exponential coordi- nates of rigid-body motion S0 = (0, 1, 2, 3, 0, 0). Draw the corresponding frame relative to {s}, as well as the screw axis S.