The x-and y-motions of guides A and B with right-angle slots control the curvilinear motion of the connecting pin P, which slides in both slots. For a short interval, the motions are governed by x= 12 +0.55t2 and y=16-0.57t³, where x and y are in millimeters and tis in seconds. Calculate the magnitudes of the velocity v and acceleration a of the pin for t = 2.5 s. Sketch the direction of the path and indicate its curvature for this instant. B Part 1 Calculate the x- and y-components of the velocity. Answers: Vx² mm/s Vy= mm/s i i

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
icon
Related questions
Question
### Analysis of Curvilinear Motion of a Connecting Pin

The x- and y-motions of guides **A** and **B** with right-angle slots control the curvilinear motion of the connecting pin **P**, which slides in both slots. For a short interval, the motions are governed by:
\[ x = 12 + 0.55t^2 \]
\[ y = 16 - 0.57t^3 \]
where \( x \) and \( y \) are in millimeters and \( t \) is in seconds. Calculate the magnitudes of the velocity \( v \) and acceleration \( a \) of the pin for \( t = 2.5 \, s \). Sketch the direction of the path and indicate its curvature for this instant.

Below is a diagram:
![Diagram](diagram_url)

**Explanation of the Diagram:**
- The diagram illustrates a mechanical setup where the guides **A** and **B** move in perpendicular directions.
- **A** moves horizontally along the x-axis, and **B** moves vertically along the y-axis, controlling the position of the pin **P**.
- The springs attached to the guides exert forces to control the motion of **P**.

### Part 1

#### Calculate the x- and y-components of the velocity.

The velocity components can be found by differentiating the position functions with respect to time.
1. For \( x = 12 + 0.55t^2 \):
\[ v_x = \frac{dx}{dt} = \frac{d}{dt}(12 + 0.55t^2) = 1.10t \]

2. For \( y = 16 - 0.57t^3 \):
\[ v_y = \frac{dy}{dt} = \frac{d}{dt}(16 - 0.57t^3) = -1.71t^2 \]

For \( t = 2.5 \, s \):
\[ v_x = 1.10 \times 2.5 = 2.75 \, \text{mm/s} \]
\[ v_y = -1.71 \times (2.5)^2 = -10.6875 \, \text{mm/s} \]

#### Answers
\[ v_x = \boxed{2.75} \, \text{mm/s} \]
\[ v_y =
Transcribed Image Text:### Analysis of Curvilinear Motion of a Connecting Pin The x- and y-motions of guides **A** and **B** with right-angle slots control the curvilinear motion of the connecting pin **P**, which slides in both slots. For a short interval, the motions are governed by: \[ x = 12 + 0.55t^2 \] \[ y = 16 - 0.57t^3 \] where \( x \) and \( y \) are in millimeters and \( t \) is in seconds. Calculate the magnitudes of the velocity \( v \) and acceleration \( a \) of the pin for \( t = 2.5 \, s \). Sketch the direction of the path and indicate its curvature for this instant. Below is a diagram: ![Diagram](diagram_url) **Explanation of the Diagram:** - The diagram illustrates a mechanical setup where the guides **A** and **B** move in perpendicular directions. - **A** moves horizontally along the x-axis, and **B** moves vertically along the y-axis, controlling the position of the pin **P**. - The springs attached to the guides exert forces to control the motion of **P**. ### Part 1 #### Calculate the x- and y-components of the velocity. The velocity components can be found by differentiating the position functions with respect to time. 1. For \( x = 12 + 0.55t^2 \): \[ v_x = \frac{dx}{dt} = \frac{d}{dt}(12 + 0.55t^2) = 1.10t \] 2. For \( y = 16 - 0.57t^3 \): \[ v_y = \frac{dy}{dt} = \frac{d}{dt}(16 - 0.57t^3) = -1.71t^2 \] For \( t = 2.5 \, s \): \[ v_x = 1.10 \times 2.5 = 2.75 \, \text{mm/s} \] \[ v_y = -1.71 \times (2.5)^2 = -10.6875 \, \text{mm/s} \] #### Answers \[ v_x = \boxed{2.75} \, \text{mm/s} \] \[ v_y =
Expert Solution
steps

Step by step

Solved in 2 steps with 2 images

Blurred answer
Knowledge Booster
Dynamics
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, mechanical-engineering and related others by exploring similar questions and additional content below.
Similar questions
  • SEE MORE QUESTIONS
Recommended textbooks for you
Elements Of Electromagnetics
Elements Of Electromagnetics
Mechanical Engineering
ISBN:
9780190698614
Author:
Sadiku, Matthew N. O.
Publisher:
Oxford University Press
Mechanics of Materials (10th Edition)
Mechanics of Materials (10th Edition)
Mechanical Engineering
ISBN:
9780134319650
Author:
Russell C. Hibbeler
Publisher:
PEARSON
Thermodynamics: An Engineering Approach
Thermodynamics: An Engineering Approach
Mechanical Engineering
ISBN:
9781259822674
Author:
Yunus A. Cengel Dr., Michael A. Boles
Publisher:
McGraw-Hill Education
Control Systems Engineering
Control Systems Engineering
Mechanical Engineering
ISBN:
9781118170519
Author:
Norman S. Nise
Publisher:
WILEY
Mechanics of Materials (MindTap Course List)
Mechanics of Materials (MindTap Course List)
Mechanical Engineering
ISBN:
9781337093347
Author:
Barry J. Goodno, James M. Gere
Publisher:
Cengage Learning
Engineering Mechanics: Statics
Engineering Mechanics: Statics
Mechanical Engineering
ISBN:
9781118807330
Author:
James L. Meriam, L. G. Kraige, J. N. Bolton
Publisher:
WILEY