Question

A pellet gun is discharged at a cardboard box of mass m₂ = 0.55 kg on a frictionless surface. The pellet has a mass of m₁ = 0.0105 kg and travels at a velocity of v₁ = 74 m/s. It is observed that the box is moving at a velocity of v₂ = 0.21 m/s after the pellet passes through it.

Write an expression for the magnitude of the pellet's velocity as it exits the box v

Answer 1

The pellet's exit velocity after passing through the box can be calculated using the conservation of momentum principle. The formula m1 * v1 = m1 * v + m2 * v2 allows us to solve for v by rearranging it to v = (m1 * v1 - m2 * v2) / m1 and then inserting the given values.

Step-by-step explanation:

The question involves finding the velocity of a pellet after it passes through a cardboard box. Conservation of momentum must be used to solve for the pellet's exit velocity, v. According to the law of conservation of momentum, in a closed system with no external forces, the total momentum before and after an event must be the same.

Initial momentum is the product of mass and velocity of the pellet before impact. Final momentum is the sum of the momenta of the box and the pellet after the pellet has passed through the box. The formula to calculate the final velocity v of the pellet is: m1 * v1 = m1 * v + m2 * v2, where:

m1 = 0.0105 kg (mass of the pellet)

v1 = 74 m/s (initial velocity of the pellet)

m2 = 0.55 kg (mass of the box)

v2 = 0.21 m/s (velocity of the box after impact)

To solve for v, rearrange the equation: v = (m1 * v1 - m2 * v2) / m1. Plug in the known values to find v.