A small wad of clay with a mass m is moving to the right at speed...

Transcribed Image Text:

A small wad of clay with a mass m is moving to the right at speed V,, as show in figure (a) below, when it strikes the edge of a thin rod. mo W M b The rod, which has a mass M and length d, is initially at rest and is free to pivot around a mostly frictionless axle through its center and perpendicular to the page at point O. The clay projectile sticks to the rod and the ro begins to rotate at an angular speed w, as shown in figure (b). (a) We wish to find the angular momentum and fractional change in kinetic energy after the collision. What is the appropriate analysis model to use in order to do this? isolated system O non-isolated system (For the following, use the following as necessary: m, v;, M, and d.) (b) What is the magnitude of the angular momentum of the system before the collision about an axis through O? total = (c) What is the moment of inertia of the system about an axis through O after the projectile sticks to the rod? I total = (d) What is the angular speed w after the collision (in terms of the given quantities)? @ = (e) What is the kinetic energy of the system before the collision? K = (f) What is the kinetic energy of the system after the collision? K = (g) What is the magnitude of the fractional change of kinetic energy of the system due to the collision? AK K (h) What If? What would the fractional change of kinetic energy of the system be if, instead of sticking to the end of the rod, the projectile continued its motion in the horizontal direction with a speed after the collision? (Assume m < M.) AK A small wad of clay with a mass m is moving to the right at speed V,, as show in figure (a) below, when it strikes the edge of a thin rod. mo W M b The rod, which has a mass M and length d, is initially at rest and is free to pivot around a mostly frictionless axle through its center and perpendicular to the page at point O. The clay projectile sticks to the rod and the ro begins to rotate at an angular speed w, as shown in figure (b). (a) We wish to find the angular momentum and fractional change in kinetic energy after the collision. What is the appropriate analysis model to use in order to do this? isolated system O non-isolated system (For the following, use the following as necessary: m, v;, M, and d.) (b) What is the magnitude of the angular momentum of the system before the collision about an axis through O? total = (c) What is the moment of inertia of the system about an axis through O after the projectile sticks to the rod? I total = (d) What is the angular speed w after the collision (in terms of the given quantities)? @ = (e) What is the kinetic energy of the system before the collision? K = (f) What is the kinetic energy of the system after the collision? K = (g) What is the magnitude of the fractional change of kinetic energy of the system due to the collision? AK K (h) What If? What would the fractional change of kinetic energy of the system be if, instead of sticking to the end of the rod, the projectile continued its motion in the horizontal direction with a speed after the collision? (Assume m < M.) AK