MECE 102Engineering Mechanics Lab

A First Year Course in Newtonian Mechanics, Experimentation,

and Computer Tools

Created by the Faculty of the Mechanical Engineering Department in the Kate Gleason College of Engineering at RIT

Week 12 Lecture

Circular Motion• This week we will:• Study the response of a system subjected to

uniform circular motion Problem A: Theoretical analysis of motion of a body in uniform circular motion

Problem B: Experimental analysis of uniform circular motion

• Use a video capture system to acquire data and Matlab to simulate system

iCLICKER: Which assumption is incorrect when analyzing this week’s system?

• Select your Answer: A. Mass of rod = 0B. Mass of bob = constantC. Acceleration = 0D. Friction force = 0

iCLICKER: Which assumption is incorrect when analyzing this week’s system?

• Select your Answer: A. Mass of rod = 0B. Mass of bob = constantC. Acceleration = 0D. Friction force = 0

FORMULATE: Problem A: State the Known and Desired Information

FORMULATE: Identify Assumptions

iCLICKER: Which of the following statements is CORRECT with respect to the Bob mass?

• Select your Answer: A. The velocity is directed radially inwardB. The velocity is directed radially outwardC. The acceleration is directed radially inwardD. The acceleration is directed radially outward

iCLICKER: Which of the following statements is CORRECT with respect to the Bob mass?

• Select your Answer: A. The velocity is directed radially inwardB. The velocity is directed radially outwardC. The acceleration is directed radially inwardD. The acceleration is directed radially outward

CHART: Schematic Diagram

CHART: Schematic Diagram

CHART: Velocity Vector Diagram

CHART: Acceleration Vector Diagram

EXECUTE: Calculate the Acceleration Components

By taking the first derivative of the Velocity components with respect to time we determine the acceleration components.

iCLICKER: Which of the following statements is CORRECT with respect to the centripetal acceleration?

• Select your Answer: A. It is directly related to the distance RB. It is inversely related to the distance RC. It is directly related to the velocity vD. It is inversely related to the velocity v

iCLICKER: Which of the following statements is CORRECT with respect to the centripetal acceleration?

• Select your Answer: A. It is directly related to the distance RB. It is inversely related to the distance RC. It is directly related to the velocity vD. It is inversely related to the velocity v

EXECUTE: Calculate the “Centripetal” Acceleration

Note that the acceleration is constant with respect to time since x2(t) + y2(t) = R2 !

This acceleration is a result of the changing direction of motion, and is referenced as the “Centripetal Acceleration”.

FORMULATE: Problem B: State the Known and Desired Information

FORMULATE: Identify Assumptions

Also neglect all Frictional effects associated with the bearing in the armature and pendulum.

B.

CHART: Picture of Test Set-Up – Side View

CHART: Picture of Test Set-Up – Top View

CHART: Schematic Diagram – Side View with Parameters Identified

CHART: Schematic Diagram – Side View with Displacement Angle

CHART: Schematic Diagram – Top View with Displacement Angle

We need to make sure we account for “perceived” side view distances of the Armature length and the pendulum rod length!

CHART: Lab Set-Up with Parameters Identified

iCLICKER: When analyzing the FBD of the Bob mass, how many forces are acting on it?

• Select your Answer: A. 1B. 2C. 3D. 4

iCLICKER: When analyzing the FBD of the Bob mass, how many forces are acting on it?

• Select your Answer: A. 1B. 2C. 3D. 4

CHART: Free Body Diagram of the Bob

The Bob mass has 2 Forces acting on it - The Weight and the Tension force in the pendulum rod.

The system achieves a form of Equilibrium when subjected to a uniform circular motion.

Execute: Derive Equations

Using Newton’s 2nd Law we sum forces in both the “radial” and “z” directions:

We observe that the angular displacement q is a constant when the armature is revolved at a constant angular speed. This implies that there is no acceleration in the z direction.

Execute: Derive Equations

Substituting the relationship for “T” from our analysis in the z-direction gives:

Equation 12.45 provides us with a convenient experimental means to measure the centripetal acceleration of our system.

Test: Comparing Theoretical to Experimental Acceleration Values

Equations 12.24 and 12.45 provide us with relationships to determine the theoretical and experimental centripetal acceleration values.

Recall that the distance from the orign to the center of the mass of the Bob is given by:

Test: Comparing Theoretical to Experimental Acceleration Values

In-Class problem ……• A 3 [kg] rock is attached to a massless rope and swings in

a circle of diameter 10 [m]. The rope can withstand a tensile force up to 40 [N] before breaking.

If the rock has a constant speed of 8 m/s, calculate the

A) Centripetal acceleration [m/s2]

B) Corresponding centripetal force [N] in the rope

C) Will the rope break?

In-Class problem ……• A 3 [kg] rock is attached to a massless rope and swings in

a circle of diameter 10 [m]. The rope can withstand a tensile force up to 40 [N] before breaking.

If the rock has a constant speed of 8 m/s, calculate the

A) Centripetal acceleration = 12.8 [m/s2]

B) Corresponding centripetal force = 38.4 [N] in the rope

C) Will the rope break? No since Fcent < Fmax

Homework• Pendulum Lab Report due tonight! • Prior to LAB tomorrow• Read section 12.2 of the textbook• Watch LAB Videos• Complete the on-line LAB quiz in myCourses

• Attempt to solve all assigned Homework problems in your logbook before RECITATION.

• WEEK 12 Problem Set: • From Section 12.5: Problems 1, 2, 4