A wooden block of mass M rests on a table over a large hole as in the figure bel

Question

A wooden block of mass M rests on a table over a large hole as in the figure below. A bullet of mass m with an initial velocity of v_i is fired upward into the bottom of the block and remains in the block after the collision. The block and bullet rise to a maximum height of h. (a) Describe how you would find the initial velocity of the bullet using ideas regarding linear momentum and collisions. Using the conservation of momentum, you can relate the speed of the block and bullet right after the collision to the initial speed of the bullet. Then, you can use the conservation of mechanical energy for the bullet-block-Earth system to relate the speed after the collision to the maximum height. Using the conservation of chemical energy you can relate the increased temperature of the block after the collision to the initial speed of the bullet. Then, you can use the conservation of mechanical energy for the bullet-block-Earth system to relate the speed after the collision to the maximum height. You can find the center of mass of the system based on how far the bullet stops inside the wooden block. Using the the work-energy theorem you can relate this the change in potential energy of the center of mass to the maximum height, U_g = Mgy_CM. Then, you can use the conservation of energy to relate this potential energy to the initial kinetic energy of the bullet. (b) Find an expression for the initial velocity of the bullet. (Use any variable or symbol stated above along with the following as necessary: g. Let up be the positive direction.) v_i =

Explanation / Answer

By conservation of momentum

M*0+m*Vi=(M+m)Vf

Vf=[m/(m+M)]Vi

By conservation of energy

(1/2)(m+M)Vf2=(m+M)gh

Vf=sqrt[2*g*h]

therfore initial velocity of the bullet is

Vi=[m/(m+M)]*sqrt(2gh)

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.