A projectile of mass m moves to the right with a speed v_i. The projectile strik
ID: 1624409 • Letter: A
Question
A projectile of mass m moves to the right with a speed v_i. The projectile strikes and sticks to the end of a stationary rod of mass M, length d, pivoted about a frictionless axle perpendicular to the page through O. We wish to find the fractional change of kinetic energy in the system due to the collision. (Use any variable or symbol stated above as necessary.) (a) Which properties are conserved during the collision? Select all that apply. angular momentum total energy linear momentum (b) What is the magnitude of the angular momentum of the system before the collision about an axis through O? L_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) Find the angular speed after the collision in terms of the given quantities. omega = (e) Determine the fractional change of kinetic energy due to the collision. |delta K/K| = (f) The collision resolves over a very short interval of time tau. What is the magnitude of the average force exerted on the projectile during the collision? F_ovc =Explanation / Answer
B. L = r x p. Notice the radius from the axis of rotation end of the rod is d/2. the initial momentum is the mass of the ball times the initial velocity. L = mv(d/2). v initial that is
C. I of a rod is (1/12)ML^2. I of a ball is mr^2. L = d and r = d/2, so you can substitute those in. The moments of inertia can be added so Itotal = (1/12)Md^2 + m(d/2)^2
D. L = Iw. I was determined in C so just multiply by omega.
So we get w = 6m(v - d /2) / M
5. K = Energy loss
Ki =1/2 m v^2
Kf =1/2 I ^2 = 1/ 2 *1/3 * m L^2( 3 v/ 2 L) ^2
Kf = 3 /8 m v^2
Kf Ki = K = 1/8 m v^2