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Welcome to the ME 274 blog. This blog is a complement to the lecture book for the course. Please review the resources that are available to you in the links on the left sidebar of the blog. Please use the discussion thread below to interact with your colleagues and friends in the course in learning the course material.

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Please start a discussion  thread between you and your colleagues on any topic of interest in the course. We will provide places on this page where you can discuss the homework assignments for the course. And, on every page for which you find links over on the left sidebar are accommodations for discussion threads on the topic of that page, such as exams, conceptual questions and lecture examples from the lecture book. Please take advantage of these discussion threads to learn what others in the course are thinking and to learn from them.

Homework 1.C

CORRECTION in problem statement:  All units for this problem should be in SI. Please use r = 0.5 m and v_P = 10 m/s.

 

Discussion and hints:

Using the path description, we know that there are two components of the acceleration vector:  one that is tangent to the path (the rate of change of speed), and one that is normal to the path and pointing inward toward the center of curvature (the centripetal component). The tangential component of acceleration will point:

  • in the direction of motion if the speed is increasing,
  • in the opposite direction of motion if the speed is decreasing, and
  • will be zero if the speed is constant.

All three situations are shown in the above animation - are you able to see these?


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Homework H1.A

Discussion and hints:

Note that the Cartesian components of for the position of P are both known explicitly in terms of time. Finding the Cartesian components of velocity and acceleration are found simply through differentiation with respect to time.

Provided above is an animated GIF of the motion for P.  Notice how you can observe from this motion the angles defining the directions of the velocity and acceleration. We see in the animation that the velocity is always tangent to the path, and the acceleration vector tends to point "inward" on the curved path. We will see in the next lecture that these characteristics of the velocity and acceleration vectors are valid regardless of the path.


We encourage you to interact with your colleagues here on conversations about this homework problem.

Homework H1.B

 

Discussion and hints:

Here the y-component of the position for P is known not as an explicit function of time, but rather as a function of the x-component of its position. For velocity and acceleration, you need derivatives with respect to time. Recall that you can use the chain rule of differentiation in order to effect the derivative of y with respect to time:  dy/dt = (dy/dx)*(dx/dt).

Provided above is an animated GIF of the motion for P.  Notice how the velocity vector for P is always tangent to the path of P. We will soon see why this is true, in general. If you carefully watch the motion of P, you will see that the horizontal component of the velocity vector is constant - WHY is that? Also, the acceleration of P always points vertically for this problem - WHY is that?


We encourage you to interact with your colleagues here on conversations about this homework problem.