Math Problem Statement

The figure below shows a bullet of mass 120 g traveling horizontally towards the east with speed 400 m/s, which strikes a block of mass 2.5 kg that is initially at rest on a frictionless table.

A drawing of a block on a table, and a bullet headed toward it.

After striking the block, the bullet is embedded in the block and the block and the bullet move together as one unit.

What is the speed of the block/bullet combination immediately after the impact? Hints The speed of the combination is m/s. What is the magnitude and direction of the impulse by the block on the bullet? Hints The block exerts an impulse of N·s on the bullet Select an answer . What is the magnitude and direction of the impulse from the bullet on the block? The bullet exerts an impulse of N·s on the block Select an answer . If it took 5 ms for the bullet to change the speed from 400 m/s to the final speed after impact, what is the average force between the block and the bullet during this time? Hints The magnitude of the average force is N. Of the kinetic energy initially present in the bullet, what percentage still remains as kinetic energy of the block/bullet? Hints Of the original kinetic energy, % remains as kinetic energy of the block/bullet.

Solution

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Math Problem Analysis

Mathematical Concepts

Conservation of Momentum
Impulse-Momentum Theorem
Kinetic Energy
Average Force

Formulas

m1*v1 + m2*v2 = (m1 + m2)*v_final
Impulse = Δp = m*(v_final - v_initial)
F_avg = J / Δt
KE = 0.5 * m * v^2

Theorems

Conservation of Linear Momentum
Newton's Third Law
Work-Energy Principle

Suitable Grade Level

Grades 10-12