lecture+notes+11 - 14:440:222 Dynamics(Lecture Note#11...

Info icon This preview shows pages 1–4. Sign up to view the full content.

View Full Document Right Arrow Icon
14:440:222 Dynamics (Lecture Note #11) Instructor: Prof. Peng Song Rutgers University Today’s Lecture Linear impulse Linear momentum
Image of page 1

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

View Full Document Right Arrow Icon
When a stake is struck by a sledgehammer, a large impulse force is delivered to the stake and drives it into the ground. If we know the initial speed of the sledgehammer and the duration of impact, how can we determine the magnitude of the impulsive force delivered to the stake? Linear Impulse: Applications This principle is useful for solving problems that involve force, velocity, and time. It can also be used to analyze the mechanics of impact (taken up in a later section). The result is referred to as the principle of impulse and momentum. It can be applied to problems involving both linear and angular motion. The next method we will consider for solving particle kinetics problems is obtained by integrating the equation of motion with respect to time. Principle of Linear Impulse and Momentum
Image of page 2
This equation represents the principle of linear impulse and momentum. It relates the particle’s final velocity ( v 2 ) and initial velocity ( v 1 ) and the forces acting on the particle as a function of time. The principle of linear impulse and momentum is obtained by integrating the equation of motion with respect to time. The equation of motion can be written F = m a = m (d v /dt) Separating variables and integrating between the limits v = v 1 at t = t 1 and v = v 2 at t = t 2 results in m v 2 – m v 1 d v m F dt v 2 v 1 t 2 t 1 = = Principle of Linear Impulse and Momentum (cont’d) Linear impulse: The integral F dt is the linear impulse, denoted I . It is a vector quantity measuring the effect of a force during its time interval of action. I acts in the same direction as F and has units of N·s or lb·s. Linear momentum: The vector m v is called the linear momentum, denoted as L . This vector has the same direction as v . The linear momentum vector has units of (kg·m)/s or (slug·ft)/s. The impulse may be determined by direct integration. Graphically, it can be represented by the area under the force versus time curve. If F is constant, then I = F (t 2 – t 1 ) .
Image of page 3

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

View Full Document Right Arrow Icon
Image of page 4
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

What students are saying

  • Left Quote Icon

    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.

    Student Picture

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

  • Left Quote Icon

    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.

    Student Picture

    Dana University of Pennsylvania ‘17, Course Hero Intern

  • Left Quote Icon

    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.

    Student Picture

    Jill Tulane University ‘16, Course Hero Intern