Math Problem Statement

Mass 1 (0.311 kg) is moving at +30.3 m/s. Mass 2 (0.0570 kg) is moving at -19.2 m/s. After an elastic collision of the two masses, what would the velocity of the mass 1 be?

Solution

The image you've provided involves an elastic collision between two masses, with the goal of determining the final velocity of mass 1 after the collision.

The formula given is:

v1f=(m1m2m1+m2)v1i+(2m2m1+m2)v2iv_1f = \left( \frac{m_1 - m_2}{m_1 + m_2} \right) v_1i + \left( \frac{2m_2}{m_1 + m_2} \right) v_2i

Where:

  • m1=0.311kgm_1 = 0.311 \, \text{kg} (mass 1),
  • m2=0.0570kgm_2 = 0.0570 \, \text{kg} (mass 2),
  • v1i=+30.3m/sv_1i = +30.3 \, \text{m/s} (initial velocity of mass 1),
  • v2i=19.2m/sv_2i = -19.2 \, \text{m/s} (initial velocity of mass 2).

Step 1: Substituting values into the equation:

v1f=(0.3110.05700.311+0.0570)×30.3+(2×0.05700.311+0.0570)×(19.2)v_1f = \left( \frac{0.311 - 0.0570}{0.311 + 0.0570} \right) \times 30.3 + \left( \frac{2 \times 0.0570}{0.311 + 0.0570} \right) \times (-19.2)

Step 2: Perform the calculation.

Let me compute this value for you. Given values m1 = 0.311 # kg m2 = 0.0570 # kg v1i = 30.3 # m/s v2i = -19.2 # m/s

Calculate final velocity of mass 1 using the given formula

v1f = ((m1 - m2) / (m1 + m2)) * v1i + ((2 * m2) / (m1 + m2)) * v2i v1fThe final velocity of mass 1 after the elastic collision is approximately 14.97m/s14.97 \, \text{m/s}.

Would you like any further details or clarifications?

Here are 5 related questions:

  1. How do you calculate the final velocity of mass 2 in an elastic collision?
  2. What is the principle of conservation of momentum, and how does it relate to elastic collisions?
  3. How do mass and velocity affect the outcome of an elastic collision?
  4. What are some real-world examples of elastic collisions?
  5. How does energy conservation apply in elastic collisions?

Tip: When solving problems with elastic collisions, always ensure that both momentum and kinetic energy are conserved!

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Math Problem Analysis

Mathematical Concepts

Elastic Collision
Momentum Conservation
Kinematics

Formulas

v_1f = ((m_1 - m_2) / (m_1 + m_2)) * v_1i + ((2 * m_2) / (m_1 + m_2)) * v_2i

Theorems

Conservation of Momentum
Elastic Collision Theorem

Suitable Grade Level

Grades 10-12