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UTPA STEM/CBI Courses/Physics (Calculus Based)/Linear Momentum and Collisions

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Course Title: Calculus Based Physics I

Lecture Topic:

Instructor: Liang Zeng

Institution: University of Texas-Pan American

Backwards Design

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Course Objectives

  • Primary Objectives- By the next class period students will be able to:
    • Know why we need to use the momentum vector (not able to solve final velocity after collision using kinematic equations, acceleration direction and magnitude changes)
    • Know how to express linear momentum and impulse mathematically
    • Know how why the time factor is meaningful in impulse
    • Know how to discern elastic versus inelastic collisions
    • Know when to apply conservation of linear momentum (conditions: isolated systems, net force=0)
    • Know to how to analyze 1-D collision problems
    • Know to how to analyze 2-D collision problems (decompose velocity)
    • Know the basic definition of kinetic energy associated with moving objects (Ek=1/2 mv2)
  • Sub Objectives- The objectives will require that students be able to:
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  • Difficulties- Students may have difficulty:
    • When does linear momentum conserve? (net force to the collision system equals 0)
    • Deep understanding of conservation of linear momentum for the entire system, not for each individual object involved in collision (schematic representation of the collision). For example, a ping pong ball bounds back off the wall (ball change direction of its velocity, wall does not move because it is subject to very small force that does not create noticeable acceleration. Elastic collision, linear momentum for the ball and wall system conserves. But for the ball only, its linear momentum changes).
    • Discerning what are inelastic and elastic collisions
    • Discerning along which direction the linear momentum conserves (reminder that total linear momentum in different dimensions can be analyzed independently)
    • Decomposing initial and final velocity
  • Real-World Contexts- There are many ways that students can use this material in the real-world, such as:
    • Car hit from the back (1-D collision), concussion, airbags (extend time during impulse)*
    • One car hits the other from the side*
    • Billiard ball games*
    • Shuffle board, curling
    • Cannon fires cannon ball, recoils; jump off a boat to the bank, boat recoils*
    • Ice skaters push each other by hands

Model of Knowledge

  • Concept Map
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  • Content Priorities
    • Enduring Understanding
      • Calculate linear momentum and total linear momentum of a system
      • Analyze impulse (time, force)
      • Apply and make good use of impulse knowledge (extending time to reduce force)
      • Difference between elastic and inelastic collisions and whether energy and linear momentum conservations apply
      • Solve 1-D collisions
      • Solve 2-D collisions (decompose velocities)
    • Important to Do and Know
      • Conservation of linear momentum also applies to collision with noncontact force, proton-proton collision, magnet strip pasted to carts examples
      • Change of kinetic energy for each individual collision object
      • 1-D special cases: (1) Two balls with equal masses in an elastic collision, one has initial velocity, the other one at rest. (2) Ping pong ball bounced back off the wall. (3) A ball with Velcro hits the wall with Velcro as well and sticks to the wall - analyze linear momentum for the ball and wall and kinetic energy change
    • Worth Being Familiar with
      • 1-D three-ball collisions (watch the simulation from the Exploration 8.5 in Physlet CD)

Assessment of Learning

  • Formative Assessment
    • In Class (groups)
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    • Homework (individual)
      • Pay attention to the following new units: p/impulse (kg m/s = N s), K.E. (kg m2/s2 = J)
      • Self-reading Chapter 9: Sections 9.1 - 9.4 in the textbook
        • (Impulse: Serway 7th edition page 260 #6). A friend claims that as long as he has his seat belt on, he can hold on to a 12.0-kg child in a 60.0 mi/h head-on collision with a brick wall in which the car passenger compartment comes to a stop in 0.050 0 s. Is his claim true? Explain why he will experience a violent force during the collision, tearing the child from his arms. Evaluate the size of this force. (A child should always be in a toddler seat secured with a seat belt in the back seat of a car).
        • (1-D elastic collision: Serway 7th edition page 262 #20). A tennis ball of mass 57.0 g is held just above a basketball of mass 590 g as shown in the figure (insert figure). With their centers vertically aligned, both are released from rest at the same moment, to fall through a distance of 1.20 m, as shown in the figure (insert figure).
          • Find the magnitude of the downward velocity with which the basketball reaches the ground. Assume an elastic collision with the ground instantaneously reverses the velocity of the basketball while the tennis ball is still moving down. Next, the two balls meet in an elastic collision
          • To what height does the tennis ball rebound?
        • (1-D inelastic collision: Serway 7th edition page 261 #15). A 10.0-g bullet is fired into a stationary block of wood (m = 5.00 kg). The bullet imbeds into the block. The speed of the bullet-plus-wood combination immediately after the collision is 0.600 m/s. What was the original speed of the bullet?
        • (2-D elastic collision: Serway 7th edition page 262 #27). A billiard ball moving at 5.00 m/s strikes a stationary ball of the same mass. After the collision, the first ball moves, at 4.33 m/s, at an angle of 30.0° with respect to the original line of motion. Assuming an elastic collision (and ignoring friction and rotational motion), find the struck ball’s velocity after the collision.
        • (2-D inelastic collision: Serway 7th edition page 262 #28). Two automobiles of equal mass approach an intersection. One vehicle is traveling with velocity 13.0 m/s toward the east, and the other is traveling north with speed v2i. Neither driver sees the other. The vehicles collide in the intersection and stick together, leaving parallel skid marks at an angle of 55.0° north of east. The speed limit for both roads is 35 mi/h, and the driver of the northward-moving vehicle claims he was within the speed limit when the collision occurred. Is he telling the truth? Explain your reasoning.
        • (Kinetic energy: Serway 7th edition page 261 #16). A railroad car of mass 2.50 x 104 kg is moving with a speed of 4.00 m/s. It collides and couples with three other coupled railroad cars, each of the same mass as the single car and moving in the same direction with an initial speed of 2.00 m/s.
          • What is the speed of the four cars immediately after the collision?
          • How much energy is transformed into internal energy in the collision?
  • Summative Assessment
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Legacy Cycle

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OBJECTIVE

By the next class period, students will be able to:

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The objectives will require that students be able to:

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THE CHALLENGE

(adapted from Exploration 8.5: Two and Three Ball Collisions in Physlet CD). Two balls can freely and smoothly move on a horizontal air track 40-meters long as shown in the figure below.


Figure 1: Red ball placed in middle in track with green ball .5m to its right, both travelling with a speed of 5 m/s to the left.

We can ignore the effect of gravity so as to make the physics as clear as possible. The mass ratio between the red ball and the green ball is 10 to 1. The center of mass of the red ball is originally located in the middle of the track, and the green ball is originally located 0.5 m to the right of the red ball. They both head left at the same constant speed of 5.0 m/s. Assume all collisions are elastic. Predict the velocities and positions of the red ball and the green ball immediately after the second collision between the two balls. You can ignore the sizes of the balls. Show all your work.

GENERATE IDEAS

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MULTIPLE PERSPECTIVES

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RESEARCH & REVISE

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TEST YOUR METTLE

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GO PUBLIC

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Pre-Lesson Quiz

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Test Your Mettle Quiz

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