PS 115 Homework 91 Name Date

Question

Ps 115lhomework 91name Date Cleaned assignment instructions 1. Marble A is rolling towards Marble B and they undergo an elastic collision. Marble A has a mass twice that of Marble B. The initial velocity of Marble A is 30 m/s, and Marble B is initially stationary. Find the final velocity of Marble A, given that kinetic energy and momentum are conserved. Set up the equations correctly for full credit. 2. A car traveling east at 80 miles per hour collides with a swarm of mosquitoes with mass 5 kg. After the collision, the car and mosquito swarm move together at 79.85 miles per hour. If the mosquitoes' initial speed was negligible, determine the mass of the car. 3. A pool ball B1 with mass 30 kg rolls toward a stationary ball B2 with mass 50 kg. B1's initial velocity is 40 m/s, and after the collision, its velocity is 10 m/s. Find the final velocity of B2. 4. Write the general equations for an inelastic and an elastic collision. Indicate which type conserves momentum and which conserves kinetic energy.

Dr. Jack HW Helper · Accepted Answer

Understanding the principles of collisions is fundamental in physics, especially when analyzing momentum and kinetic energy conservation. This paper addresses three specific problems involving different types of collisions—elastic and inelastic—and explores the laws governing these interactions. Problem 1: Elastic Collision of Marbles In the first scenario, Marble A with mass $ m_A $ is moving towards Marble B, with mass $ m_B $. Given that $ m_A = 2m_B $, the initial velocity of Marble A is $ v_{A,i} = 30 \, \text{m/s} $, while Marble B is initially at rest ($ v_{B,i} = 0 $). Since the collision is elastic, both momentum and kinetic energy are conserved. Setting up the equations for these principles allows solving for the final velocity of Marble A, $ v_{A,f} $. The conservation of momentum is expressed as: $$ m_A v_{A,i} + m_B v_{B,i} = m_A v_{A,f} + m_B v_{B,f} $$ Substituting known values and the mass ratio, the equation becomes: $$ 2m_B \times 30 + m_B \times 0 = 2m_B \times v_{A,f} + m_B \times v_{B,f} $$ Dividing throughout by $ m_B $, simplifies to: $$ 60 = 2 v_{A,f} + v_{B,f} $$ For kinetic energy conservation: $$ \frac{1}{2} m_A v_{A,i}^2 + \frac{1}{2} m_B v_{B,i}^2 = \frac{1}{2} m_A v_{A,f}^2 + \frac{1}{2} m_B v_{B,f}^2 $$ Substituting known values, simplifying, and solving these equations simultaneously yields the final velocity of Marble A, approximately -10 m/s, indicating a change in direction post-collision. Problem 2: Car and Mosquito Swarm Collision This problem examines the conservation of momentum in a collision involving a large vehicle and a small mass particle—the mosquitoes. The initial momentum of the car is: $$ p_{car,i} = m_{car} \times 80 \, \text{mph} $$ The mosquitoes initially are stationary ($ p_{mosquitos,i} \approx 0 $). Post-collision, the combined system moves at 79.85 mph, so: $$ p_{total,f} = (m_{car} + m_{mosquitos}) \times 79.85 \, \text{mph} $$ Applying momentum conservation, we get: \[ m_{car} \times 80 = (m_

PS 115 Homework 91 Name Date

Ps 115lhomework 91name Date

Cleaned assignment instructions

Paper For Above instruction

Problem 1: Elastic Collision of Marbles

Problem 2: Car and Mosquito Swarm Collision

Problem 3: Pool Ball Collision

Inelastic vs. Elastic Collisions