ChemPhys 173/273

Unit 12: Momentum and Collisions

Problem Set A

Overview:

Problem Set A targets your ability to use the momentum equation and the impulse-momentumchange theorem in order to analyze physical situations involving collisions and impulses. You will need to have a solid grasp of at least four skills or conceptual understandings to be successful on Problem Set A. These skills include:

1. Momentum Equation: An object which is moving has momentum. The amount of momentum possessed by the moving object is the product of mass and velocity.
p = m • v

2. Impulse-Momentum Change Equation: In a collision, a force acts upon an object for a given amount of time to change the object's velocity. The product of force and time is known as impulse. The product of mass and velocity change is known as momentum change. In a collision the impulse encountered by an object is equal to the momentum change it experiences.

It will be crucial to understand the above relationship in this problem set. In many of the problems, a piece of extraneous information is provided. Without an understanding of the above relationships, you will be tempted to force such information into your calculations. Physics is about conceptual ideas and relationships; and problem sets test your mathematical understanding of these relationships. If you treat this problem set as a mere exercise in the algebraic manipulation of physics equations, then you are likely to become frustrated quickly. As you proceed through this problem set, be concepts-minded. Do not strip physics of its conceptual meaning.

3. Using an Equation as a Guide to Thinking: An equation can be treated as an algebraic recipe for problem-solving. But it also can be treated as a statement which describes qualitatively how one variable depends upon another. Two quantities in an equation could be thought of as being either directly proportional or inversely proportional. Thinking and reasoning proportionally about quantities allows you to predict how an alteration in one variable would effect another variable. You will need to use your proportional reasoning skills in Problem 9 of this set.

4. Calculation of Velocity Change: You will need to be able to calculate the velocity change of an object, particularly for a rebound situation. Velocity is a vector and is distinguished from speed in that it has a direction associated with it. This direction is often expressed in mathematics as a + or - sign. In a collision, an object expreieinces a force which causes a velocity change. The velocity change is computed by subtracting the initial velocity value from the final velocity value. If an object is moving in one direction before a collision and rebound or somehow changes direction, then its velocity after the collision has the opposite direction as before. Mathematically, the before-collision velocity would be + and the after-collision velocity would be - in sign. Ignoring this principle will result in great difficulty when analyzing any collision involving the rebounding of an object.

To be successful on this problem set, you will have to:

• use the two equations stated above with comfort and confidence.
• recognize that impulse can be calculated as the product of F and t or as the product of m and delta v.
• distinguish between the force acting on an object and the impulse delivered to an object.
• recognize that a change in a quantity is calculated as the final value of the quantity minus the initial value of the quantity.
• recognize that resistive forces reduce the momentum of an object and forces in the same direction of motion increase the momentum of objects.
• practice the habits of a good problem solver.

Additional Readings/Study Aids:

The following pages from The Physics Classroom tutorial may serve to be useful in assisting you in the understanding of the concepts and mathematics associated with these problems.

Momentum | Impulse-Momentum Change Equation | Real World Applications

View Sample Problem Set.

 Problem Description Audio Link 1 Routine use of the equation for momentum 2 Use of the impulse-momentum change equation to determine an impulse. 3 Use of the impulse-momentum change equation in a physical situation involving direction change 4 Use of the impulse-momentum change equation in a rebounding situation 5 Complex analysis which relies on the impulse-momentum change equation to determine a velocity change and then a final velocity value. 6 Use of the impulse-momentum change equation to determine a force. 7 Routine use of the equation for momentum 8 Use of the impulse-momentum change equation to determine a momentum change. 9 Use of the impulse-momentum change equation as a guide to thinking qualitatively 10 Use of the impulse-momentum change equation to determine an impulse. 11 Referring to the previous problem; determination of the force. 12 Use of the impulse-momentum change equation to analyze a complex motion involving multiple impulses. 13 Use of the impulse-momentum change equation to analyze a complex motion involving multiple impulses. 14 Use of the impulse-momentum change equation to analyze a complex motion involving multiple impulses. 15 Use of the impulse-momentum change equation to analyze a complex motion involving multiple impulses.

Audio Help for Problem: 1 || 2 || 3 || 4 || 5 || 6 || 7 || 8 || 9 || 10 || 11 || 12 || 13 || 14 || 15 ||

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