Pen P of the flatbed plotter traces the curve - Path Coordinates

In summary, the problem involves a flatbed plotter tracing a curve using the equation y=x^3/80000. At a specific position, the speed of slider A is known and the question asks for the speed of point P and the normal component of its acceleration. The solution involves using the chain rule to find the derivative of y with respect to time in order to calculate the speed of P.
  • #1
Alexanddros81
177
4

Homework Statement


This is Pytels Dynamics 2nd edition problem 13.16

13.16. Pen P of the flatbed plotter traces the curve y=x3/80000, where x and y are
measured in mm. When x=200mm, the speed of slider A is 60 mm/s. For this position, calculate
(a) the speed of P; and (b) the normal component of the acceleration of P

Fig P13_16.jpg

Homework Equations

The Attempt at a Solution



Pytels_Dynamics 13_16.jpg


In part (a) I don't get 108.2 mm/s for the speed. what am I doing wrong?
 
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  • #2
##\dot y## is the derivative of ##y## with respect to time. You took the derivative of ##y## with respect to ##x##. Hint: chain rule.
 
  • #3
I guess this is correct. Right?

Pytels_Dynamics063.jpg
 
  • #4
That look's correct. Nice work.
 

Related to Pen P of the flatbed plotter traces the curve - Path Coordinates

1. What is a flatbed plotter?

A flatbed plotter is a type of computer-controlled drawing machine that uses a pen to create precise, detailed drawings and designs on a flat surface, such as paper or canvas.

2. What is the purpose of the Pen P in a flatbed plotter?

The Pen P is a component of the flatbed plotter that holds and controls the movement of the pen. It is responsible for creating the lines and curves that make up the final drawing.

3. How does the flatbed plotter trace a curve?

The flatbed plotter traces a curve by using a combination of precise movements and rotations of the Pen P. The computer controls these movements based on the specified path coordinates, resulting in a smooth and accurate curve.

4. What are path coordinates in the context of a flatbed plotter?

Path coordinates refer to the specific x and y coordinates on the flatbed where the Pen P will move to create a line or curve. These coordinates are programmed into the computer and dictate the path that the pen will follow.

5. Can a flatbed plotter only trace curves?

No, a flatbed plotter is capable of tracing both curves and straight lines. By controlling the movement and rotation of the Pen P, a flatbed plotter can create a wide range of intricate and precise designs.

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