A 4.10 g bullet is fired horizontally at two blocks resting on a smooth tabletop

Question

A 4.10 g bullet is fired horizontally at two blocks resting on a smooth tabletop, as shown in the top figure. The bullet passes through the first block, with mass 1.20 kg, and embeds itself in the second, with mass 1.80 kg. Speeds of 0.200 m/s and 1.19 m/s, respectively, are thereby imparted to the blocks, as shown in the bottom figure. Neglecting the mass removed from the first block by the bullet, find the speed of the bullet immediately after it emerges from the first block. Please show work and ans!

Explanation / Answer

This is a problem in conservation of momentum. The tabletop is "smooth" (no friction), so that means the total momentum "before" equals the total momentum "after". First, make variables for what you know and don't know: v1_bullet: bullet's speed before striking either block v2_bullet: bullet's speed after exiting first block v_block1: speed of block 1 after bullet exits (0.2 m/s) v_block2: speed of block 2 after bullet embeds (1.19 m/s)--this is also the bullet's final speed m_bullet: mass of bullet (0.041 kg) m_block1: mass of block 1 (1.2 kg) m_block2: mass of block 2 (1.8 kg) Total momentum before initial strike: (m_bullet)(v1_bullet) Total momentum after bullet exits block 1: (m_bullet)(v2_bullet) + (m_block1)(v_block1) Total momentum after bullet embeds in block2: (m_block1)(v_block1) + (m_bullet+m_block2)(v_block2) The conservation law says that all three of these are equal: (m_bullet)(v1_bullet) = (m_bullet)(v2_bullet) + (m_block1)(v_block1) = (m_block1)(v_block1) + (m_bullet+m_block2)(v_block2) You can rewrite the above as two separate equations: (m_bullet)(v1_bullet) = (m_bullet)(v2_bullet) + (m_block1)(v_block1) (m_bullet)(v1_bullet) = (m_block1)(v_block1) + (m_bullet+m_block2)(v_block2) You know the values of most of these variables, so what you're left with is two equations in two unknowns ("v1_bullet" and "v2_bullet"). Use the algebra of simultaneous equations to solve for the unknowns.

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

---

---

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