A bullet with a mass m=12.5 g and speed v=85.4 m/s is fired into a wooden block with M=113 g which is initially at rest on a horizontal surface. The bullet is embedded into the block. The block-bullet combination slides across the surface for a distance d before stopping due to friction between the block and surface. The coefficients of friction are μs=0.753 and μk=0.659. What is the speed of the block-bullet combination immediately after the collision?
To find the speed of the block-bullet combination immediately after the collision, we need to apply the principle of conservation of momentum.
1. First, let's calculate the initial momentum of the bullet before the collision. Momentum (p) is calculated using the formula: p = mass (m) × velocity (v).
Initial momentum of the bullet (p_bullet) = m_bullet × v_bullet.
Given:
Mass of bullet (m_bullet) = 12.5 g = 0.0125 kg
Velocity of bullet (v_bullet) = 85.4 m/s
Therefore, p_bullet = 0.0125 kg × 85.4 m/s.
2. Next, let's calculate the initial momentum of the wooden block before the collision. Since the block is initially at rest, its initial momentum (p_block) is zero.
p_block = 0 kg × 0 m/s = 0
3. According to the principle of conservation of momentum, the total momentum before the collision is equal to the total momentum after the collision. Therefore, the total momentum before the collision (p_initial) is equal to the total momentum after the collision (p_final).
p_initial = p_bullet + p_block
p_final = (m_bullet + M_block) × v_combined
We want to find the velocity (v_combined) of the block-bullet combination after the collision.
4. Now, let's calculate the mass of the wooden block (M_block).
Given: Mass of block (M_block) = 113 g = 0.113 kg
5. Based on the given information, we can write the equation:
p_initial = p_final
(m_bullet × v_bullet) + (M_block × 0) = (m_bullet + M_block) × v_combined
(0.0125 kg × 85.4 m/s) + (0.113 kg × 0) = (0.0125 kg + 0.113 kg) × v_combined
6. Simplifying the equation:
(0.0125 kg × 85.4 m/s) = (0.0125 kg + 0.113 kg) × v_combined
7. Now, we can solve for v_combined:
v_combined = (0.0125 kg × 85.4 m/s) / (0.0125 kg + 0.113 kg)
Calculating this value will give us the speed of the block-bullet combination immediately after the collision.