{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

lecture+notes+5

# lecture+notes+5 - 14:440:222 Dynamics(Lecture Note#5...

This preview shows pages 1–5. Sign up to view the full content.

14:440:222 Dynamics (Lecture Note #5) Instructor: Prof. Peng Song Rutgers University Today’s Lecture Kinematic Analysis of Two-Particle Systems Dependent motion Relative motion

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
Applications The cable and pulley system shown can be used to modify the speed of the mine car, A, relative to the speed of the motor, M. It is important to establish the relationships between the various motions in order to determine the power requirements for the motor and the tension in the cable. For instance, if the speed of the cable (P) is known because we know the motor characteristics, how can we determine the speed of the mine car? Will the slope of the track have any impact on the answer? Rope and pulley arrangements are often used to assist in lifting heavy objects. The total lifting force required from the truck depends on both the weight and the acceleration of the cabinet. How can we determine the acceleration and velocity of the cabinet if the acceleration of the truck is known? Applications (cont’d)
Dependent Motion In many kinematics problems, the motion of one object will depend on the motion of another object. The motion of each block can be related mathematically by defining position coordinates, s A and s B . Each coordinate axis is defined from a fixed point or datum line, measured positive along each plane in the direction of motion of each block. The blocks in this figure are connected by an inextensible cord wrapped around a pulley. If block A moves downward along the inclined plane, block B will move up the other incline. In this example, position coordinates s A and s B can be defined from fixed datum lines extending from the center of the pulley along each incline to blocks A and B. If the cord has a fixed length, the position coordinates s A and s B are related mathematically by the equation s A + l CD + s B = l T Here l T is the total cord length and l CD is the length of cord passing over the arc CD on the pulley. Dependent Motion (cont’d)

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
The negative sign indicates that as A moves down the incline (positive s A direction), B moves up the incline (negative s B direction). Accelerations can be found by differentiating the velocity expression. Prove to yourself that a B = -a A .
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

### What students are saying

• As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

Kiran Temple University Fox School of Business ‘17, Course Hero Intern

• I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

Dana University of Pennsylvania ‘17, Course Hero Intern

• The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

Jill Tulane University ‘16, Course Hero Intern