![]() Ğstablish the x, y, z coordinate system.T2 ò m(vx)1 + Fx dt = m(vx)2 m(vy)1 + Fy dt = m(vy)2 m(vz)1 + Fz dt = m(vz)2 t1 t2 ò t1 t2 ò t1 IMPULSE AND MOMENTUM: SCALAR EQUATIONS Since the principle of linear impulse and momentum is a vector equation, it can be resolved into its x, y, z component scalar equations: The scalar equations provide a convenient means for applying the principle of linear impulse and momentum once the velocity and force vectors have been resolved into x, y, z components. The impulse diagram is similar to a free body diagram, but includes the time duration of the forces acting on the particle. PRINCIPLE OF LINEAR IMPULSE AND MOMENTUM (continued) mv1 + = mv2 The two momentum diagrams indicate direction and magnitude of the particle’s initial and final momentum, mv1 and mv2. The principle of linear impulse and momentum in vector form is written as t2 ò å F dt t1 The particle’s initial momentum plus the sum of all the impulses applied from t1 to t2 is equal to the particle’s final momentum. Graphically, it can be represented by the area under the force versus time curve. The impulse may be determined by direct integration. I acts in the samedirection as F and has units of N ![]() It is a vector quantity measuring the effect of a force during its time interval of action. Linear impulse: The integral F dt is the linear impulse, denoted I. The linear momentum vector has units of (kg PRINCIPLE OF LINEAR IMPULSE AND MOMENTUM (continued) Linear momentum: The vector mv is called the linear momentum, denoted as L. It relates the particle’s final velocity (v2) and initial velocity (v1) and the forces acting on the particle as a function of time. The equation of motion can be written F = m a = m (dv/dt) This equation represents the principle of linear impulse and momentum. Separating variables and integrating between the limits v = v1 at t = t1 and v = v2 at t = t2 results in t2 v2 ò ò å F dt dv = m = mv2 – mv1 t1 v1 PRINCIPLE OF LINEAR IMPULSE AND MOMENTUM (continued) The principle of linear impulse and momentum is obtained by integrating the equation of motion with respect to time. It can also be used to analyze the mechanics of impact (taken up in a later section). This principle is useful for solving problems that involve force, velocity, and time. ![]() It can be applied to problems involving both linear and angular motion. The result is referred to as the principle of impulse and momentum. PRINCIPLE OF LINEAR IMPULSE AND MOMENTUM (Section 15.1) The next method we will consider for solving particle kinetics problems is obtained by integrating the equation of motion with respect to time. 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? How can we determine the magnitude of the linear impulse applied to the fender? Could you analyze a carpenter’s hammer striking a nail in the same fashion? Sure!ĪPPLICATIONS (continued) When a stake is struck by a sledgehammer, a large impulse force is delivered to the stake and drives it into the ground. To do so the weight is gripped and jerked upwards, striking the stop ring. Which parameter is not involved in the linear impulse and momentum equation? A) Velocityě) Displacement C) Timeĝ) ForceĪPPLICATIONS A dent in an automotive fender can be removed using an impulse tool, which delivers a force over a very short time interval. A) friction forceě) equation of motion C) kinetic energyĝ) potential energy 2. The linear impulse and momentum equation is obtained by integrating the _ with respect to time. Principle of Linear Impulse and Momentum.Apply the principle of linear impulse and momentum. ![]() Calculate the linear momentum of a particle and linear impulse of a force.PRINCIPLE OF LINEAR IMPULSE AND MOMENTUM
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