Momentum p can be decomposed into and Momentum is a vector pointing in the same direction as the object’s velocity. Momentum The product of a particle’s mass and velocity is called the momentum of the particle: u We need some new tools to help us make sense of Equation 11.2. The velocity changes from vix to vfx during the collision thus m 3 dvx = mvfx - mvix = 3 Fx 1t2 dt (11.2) vf The force is nonzero only during an interval of time from ti to tf = ti + ∆t, so let’s integrate Equation 11.1 over this interval. Acceleration in one dimension is ax = dvx /dt, so the second law is dvx max = m = Fx 1t2 dt After multiplying both sides by dt, we can write the second law as m dvx = Fx 1t2 dt (11.1) We can use Newton’s second law to find how the object’s velocity changes as a result of the collision. Note Both vx and Fx are components of vectors and thus have signs indicating Because an impulsive force is a function of time, we will write it as Fx1t2. The force is zero before contact begins and after contact ends. The graph of Figure 11.1 shows how a typical impulsive force behaves, rapidly growing to a maximum at the instant of maximum compression, then decreasing back to zero. A large force exerted for a small interval of time is called an impulsive force. The force of a collision is usually very large in comparison to other forces exerted on the object. We’ll examine the energy issues of collisions later in this chapter. Indeed, that’s exactly what happens during a collision at the microscopic level: Molecular bonds compress, store elastic potential energy, then transform some or all of that potential energy back into the kinetic energy of the rebounding object. Instead, we model a colliding object as an elastic object that compresses and then expands, much like a spring. A particle cannot be deformed, so we cannot model colliding objects as particles.
Notice that the object, as in the photo above, deforms during the collision. The object approaches with an initial horizontal velocity vix, experiences a force of duration ∆t, and leaves with final velocity vfx. FIGURE 11.1 shows an object colliding with a wall. A collision between two steel balls lasts less than 200 microseconds. The harder the objects, the shorter the contact time. This is the time during which the two objects are in contact with each other. The duration of a collision depends on the materials from which the objects are made, but 1 to 10 ms (0.001 to 0.010 s) is fairly typical. It takes time to compress the ball, and more time for the ball to re-expand as it leaves the racket or bat. A high-speed photograph reveals that the side of the ball is significantly flattened during the collision. The collision between a tennis ball and a racket, or a baseball and a bat, may seem instantaneous to your eye, but that is a limitation of your perception. Notice that the left side of the ball is flattened.Ī collision is a short-duration interaction between two objects. Rocket propulsion the object’s mass is changing continuously.Ī tennis ball collides with a racket. Where else is momentum used? This chapter looks at two other important applications of momentum conservation:Įxplosion is a short interaction that drives two or more objects apart. ■ In a perfectly elastic collision, the objects bounce apart. a totally inelastic collision, the objects stick together. How does momentum apply to collisions? One important application of momentum conservation is the study of collisions. ❮❮ LOOKING BACK Section 9.1 Energy overview The momentum principle says that a system’s momentum changes when an impulse is delivered: ∆px = Jx A momentum bar chart, similar to an energy bar chart, shows this principle graphically. It’s important to clearly define the system. How are impulse and momentum related? Working with momentum is similar to working with energy. For timedependent forces, impulse and momentum are often more useful than Newton’s laws. The impulse Jx that this forceĭelivers to an object is the area under the force-versus-time graph. What is impulse? A force of short duration is an impulsive force. ❮❮ LOOKING BACK Section 10.4 Energy conservation Regardless of how intense the interactions are, the final momentum equals the initial momentum. The particles of an isolated system interact with each other but not with the environment. The total momentum of an isolated system is conserved. Momentum is a vector, and it is especially important to pay attention to the signs of the components of momentum. An object can have a large momentum by having a large mass or a large velocity. What is momentum?Īn object’s momentum is the product of its mass and velocity. IN THIS CHAPTER, you will learn to use the concepts of impulse and momentum. Nonetheless, the explosion obeys some simple laws of physics.
11 Impulse and Momentum An exploding firework is a dramatic event.
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