Question

we will look ar sa simple form or Niler with mass mois classic physics lab apparatus for measuring the speed of a projectile. Figure 8.13 of the apparatus, known as a ballistic pendulum, composed of a block and some string. is fired into a block of wood with mass mw suspended like a pendulum. The bullet lastic collision with the block, becoming embedded in it. After the impact of the bul- un to a maximum height h. Given values of h, me and my how can we find the initial hullet? What becomes of its initial kinetic energy? OW Video Tutor Solution es a completely inelastice the block swings up to or of the bulle SOLUTION STUP We analy Miller in the blockan strings. During the e quickly that the BEFORE COLLISION to its initial position in very nearly vertical served. In the ses analyze this event in two stages: first, the embedding of the Weck, and second, the subsequent swinging of the block on uring the first stage, the bullet embeds itself in the block that the block doesn't have time to swing appreciably away al position. So, during the impact, the supporting strings nearly vertical, there is negligible external horizontal force on the system, and the horizontal component of momentum is d. In the second stage, after the collision, the block and bullet unit. The only forces are the weight (a conservative force) the string tensions (which do no work). As the pendulum swings ward and to the right, mechanical energy is conserved. To keep the notation simple, we'll denote the x component of the Millet's velocity just before impact as v and the x component of the velocity of block plus bullet just after the impact as V. SOLVE Figure 8.13 shows the situation just before impact, the situa on just after impact, and the block (with the embedded bullet) at the Nghest point of its path. Conservation of momentum just before impact ind just after gives us mgu = (mg + mw)V, me mwy. тв The kinetic energy of the system just after the collision is K = img + mw)VThe pendulum comes to rest (for an instant) at a ght h, where its kinetic energy (mg + mwV has all become po- chergy (mg + mw)gh; then it swings back down. Energy con- mation gives }(mg + mw)V2 = (mp + mw)gh. TOP OF SWING AFTER COLLISION Mg + mw A FIGURE 8.13 Using a ballistic pendulum to find a bullet's speed. Assuming that h can be measured, we solve this equation for V: V = V2gh (velocity of block and bullet just after impact). CONTIN

Answer 1

monewtum will e Conduived just afth Coly meV=CMotma)V MB+MW MG nou afte that they move to heigld h eneyy Consvalio mpnv tmg V = motmw AJ