A large crate is suspended by a light string. A bullet is firedhorizontally into the crate and becomes firmly lodged inside it.After being struck by the bullet, the crate swings upward to amaximm height and then swings back up.
Just before the collision (time t1), the crate is at rest andthe bullet moves horizontally with speed v0. Immediately after thebullet becomes lodged inside the crate (time t2) the bullet andcrate move together with speed v. The crate reaches its maximumheight at time t3.
1. Consider the time interval between times t1 and t2 (i.e., thecollision between the bullet and crate).
A) During the collision, how does the force exerted on thecrate by the bullet compare to the force exerted on thebullet by the crate? Discuss both magnitude and direction.Explain?
B) Is the total momentum of the bullet-and-crate systemconserved during the collision? Explain how you can tell.
C) Is the total kinetic energy of the system conserved duringthe collision? Explain how you can tell.
2. Now consider the time interval from t2 to time t3 for thesituation described (when the bullet and crate move together to amaximum height after the collision).
A) Draw a free body diagram for the bullet-crate system for aninstant between times t2 and t3. Clearly label all forces.
Is the total momentum of the system conserved from tme t2 totime t3? Explain.
B) For each force you indicated on your free body diagram inpart a, indicate whether the work done by that force on thebullet-crate system is positive, negative, or zero. Explain yourreasoning.
Is the total mechanical energy (kinetic + potential) of thebullet-crat system conserved from time t2 to time t3? Explain.
3. Is it incorrect to say that the total mechanical energy ofthe bullet-crate system remains conserved for the entire motion.Explain why this is so, and indicate other types of energy intowhich the initial energy of the bullet could have beentransformed.
