1 Problem Let I = {0,11,12,13} be an inertial reference frame from which the position of a particle is measured. At initial time to = 0 a particle is at rest in the x - y plane at coordinates (xo, yo) (6,0) in units of inches (where x is the component along the 2₁ direction and y is the component along the 12 direction). If the particle is then subjected to the acceleration components ax(t) 0.5-0.35t in/sec² and ay = 0.15 0.02t2 in/sec². What is the vector describing the particle's position when t = 6? = =

1 Problem Let I = {0,11,12,13} be an inertial reference frame from which the position of a particle is measured. At initial time to = 0 a particle is at rest in the x - y plane at coordinates (xo, yo) (6,0) in units of inches (where x is the component along the 2₁ direction and y is the component along the 12 direction). If the particle is then subjected to the acceleration components ax(t) 0.5-0.35t in/sec² and ay = 0.15 0.02t2 in/sec². What is the vector describing the particle's position when t = 6? = =

Elements Of Electromagnetics

7th Edition

ISBN:9780190698614

Author:Sadiku, Matthew N. O.

Publisher:Sadiku, Matthew N. O.

ChapterMA: Math Assessment

Section: Chapter Questions

Problem 1.1MA

See similar textbooks

Similar questions

Problem Statement: A car drives on a circular track with radius 270 m. Initially, the displacement s=0 and the speed is 24 m/s. The car then begins to accelerate at At 0.3s (given in m/s? where s is in meters). After 3.4 seconds has passed, determine: (To get this answer you may need to use a table of integrals and/or a numerical equation solver.) The distance traveled: ûn The velocity vector: un The acceleration vector: Be sure to include units with your answers.
A mechanic changing a tire rolls a wheel along the ground towards the car. The radius of the wheel is 42cm, and the speed of the wheel as it rolls is 2 revolutions per second. Height Above Ground (m) radiu HIDE wheel spet Time The diagram above illustrates the vertical motion of a point on the tire over time. It is possible to model the height of this point using a sinusoidal function of the form h(t)=-a sin[b(t-c)]+d. a) Determine the length of time required for one revolution of the tire. b) State the numerical value for each of the parameters a, b, c & d. And write a function representing the motion of the point in the form h(t)= -a sin[b(t−c)]+d.
You are the mechatronics engineer of a manufacturing plant. You decide to perform an analysis on a robot arm of the assembly line with the objective of optimizing its performance. After taking several readings of the speed of the arm’s end effector, you approximate its velocity to the function given below. v(t) = -t4 + 5t3 - 7t2 + 3t + 0.22 0 =< t =< 3 where the velocity is in ms-1 d) Knowing that the distance travelled by an object is the area under its velocity-time graph, determine the distance travelled by the end effector on the interval 0 =< t =< 1 by using the mid-ordinate rule. Simpson’s rule correct to 3 decimal places using four intervals. e) Calculate the same distance as in (d) above by using the appropriate definite integral. f) Compare the distances you calculated in (d) and (e) above and comment on the accuracy of the two methods you used in (d)
You are the mechatronics engineer of a manufacturing plant. You decide to perform an analysis on a robot arm of the assembly line with the objective of optimizing its performance. After taking several readings of the speed of the arm’s end effector, you approximate its velocity to the function given below. v(t) = -t4 + 5t3 - 7t2 + 3t + 0.22 0 =< t =< 3 where the velocity is in ms-1 Use your knowledge of differentiation to sketch the velocity-time graph, clearly marking the critical points. Using the graph sketched in (a) above, estimate the velocity when t = 1.5 s Calculate the velocity of the function when t = 1.5 s by substituting to the velocity function. Compare this value to the value you estimated in b above.
For the Following question Graph all 4 : [I just need all 4 graphs and please explain and make clean solution] Position vs time Velocity vs time Acceleration vs time Force vs time [For your convenience, I have solved the numerical solutions for the problem] (Please Look at the picture since it is much cleaner) Question : A 550 kilogram mass initially at rest acted upon by a force of F(t) = 50et Newtons. What are the acceleration, speed, and displacement of the mass at t = 4 second ? a =(50 e^t)/(550 ) [N/kg] v = ∫_0^t▒(50 e^t )dt/(550 )= v_0 +(50 e^t-50)/550=((e^t- 1))/11 x = ∫_0^t▒(e^t- 1)dt/(11 )= x_0 +(e^t- t - 1)/(11 ) a(4s)=(50*54.6)/550= 4.96[m/s^2 ] v(4s)=((e^4-1))/11= 4.87[m/s] x(4s)=((e^4- 4 - 1))/11= 4.51 [m]
rad The rod OA rotates clockwise at a constant angular velocity of 0 = (3) Two pin-connected slider block, located at B, move freely on OA. The curved rod is described by the equation r (300 (3-cos)) m. Hint: 1. Remember clockwise rotation is negative velocity. OA Variable 0₁ d₁ d₂ d3 0₁ d2 d3 Values for the figure are given in the following table. Note the figure may not be to scale. Value 110 degrees 0.45 m 0.1 m 0.275 m Using cylindrical components, a. Determine the cylinders's radial and transverse components of velocity at the instant shown, u, and vg. b. Determine the cylinders's radial and transverse components of acceleration at the instant shown, ar and ag. c. Determine the cylinder's magnitude of the velocity at the instant shown, ·M. d. Determine the cylinder's magnitude of the acceleration at the instant shown, |a1. Round your final answers to 3 significant digits/figures. 7= fr + a= M-C Hr+ m S M 82 He) Fe) m S m
V-axis X-axis A Figure 1. An object (yellow point) travels from point A to point B along the arc of a circle that is centered at point O (red point). velocity of an object, either due to a change in speed or direction, means the object is accelerating. According to Newton's second law, an object will accelerate only if there is a non-zero total force acting on the object. For uniform circular motion, it turns out that this force must always be pointing towards the center of the circle that the object is travelling around and we say that there is a centripetal force present. You can use Newton's second law and a little bit of geometry to understand why an object undergoing uniform circular motion must be experiencing a force that is pointing towards the center of the circle the object is travelling on. If the acceleration vector pointed above or below the plane of the circle, the velocity vector would also end up pointing out of the plane that the circle is on. Since the velocity vector…
R(S) XIS K 1 s+5 s+ 2 S+3 Y(s)
2- find the center of mass, the velocity of the center of mass, the momentum, and the kinetic energy of the following system: do f(xd) xaf] m₁ = 1 kg T₁=1+2j+3 k v₁ = 2î+3ĵ m₂ = 1 kg T₂ = 1-j+ k v₂ = 2) + 3k
2. Try to write the motion equations of the system under the following conditions, and judge whether it is acceleration, deceleration or uniform speed(The arrows in the figure show the actual direction of torque). TX-IL IN CIL IW TW TL TO TL (4) IL TV TL TH= TL (1) Judge whether the intersection in the figure below is a stable working point? "Tx. Iz K
You walk along the beach towards a dock while your friend rows a boat towards the same dock on a flat lake. Your friend's boat approaches the dock on a straight course, but also rotates about its center-of-mass since your friend is not pulling evenly on the oars. If you knew your own velocity (vwalker), the magnitude of boat's angular velocity (thetaboat), and radius vector from yourself to your friend in the boat (rfriend) at any given time, you could use the following equation to calculate the your friend's velocity: vfriend = vwalker + (thetaboat)k x rfriend where k is a unit vector in the vertical direction. True False
3. Use the second method of frame assignment, and find the Jacobian of the following robot using the velocity propagation method (Ignore all theta related offsets): 03 02 L2 01 Please answer the question precisely and completely to use the second method of frame assignment to find the D-H table [alpha (i-1) , a (i-1) , d (i) , theta (i)], and find the jacobian matrix using the velocity propagation method