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Student Exploration- 2D Collisions (answers)

Student Exploration- 2D Collisions (answers)

Author: Jack Bauer

Student Exploration: 2D Collisions

Vocabulary: center of mass, conservation of energy, conservation of momentum, elasticity, kinetic energy, momentum, speed, vector, velocity

Prior Knowledge Questions (Do these BEFORE using the Gizmo.)

A pool cue hits the white cue ball, which travels across the table and strikes the red ball, as shown at right. Draw a solid line to show the path you would expect the red ball to take..

Draw a dashed line to show how you think the white ball will move after it has struck the red ball.

Gizmo Warm-up

Objects collide all the time, but often with very different results. Sometimes colliding objects will stick together. Other times, they will bounce off each other at an angle. What determines how objects will behave in a collision? You can use the 2D Collisions Gizmo™ to find out.

Note the arrows, or vectors, on each puck. Click Play ().

How does the direction and length of its vector relate to the motion of a puck?

The velocity (speed and direction) of each puck is described by components in the i and j directions. The symbol for velocity is v. (Vector quantities are shown in bold.)

Which component represents movement in the east-west direction?

Which component represents movement in the north-south direction?

The speed (v) of a puck is equal to the length of its velocity vector. To calculate the speed of a puck with a velocity of ai + bj, use the Pythagorean theorem:

Set the velocity of the blue puck to 12.00i + 5.00j m/s. What is its speed?

Activity A:

Elastic collisions

Get the Gizmo ready:

Click Reset. Make sure Elasticity is set to 1.0.
Set the blue puck’s velocity to v = 4.00i + 3.00j and the gold puck’s velocity to v = 0.00i – 4.00j.

Introduction: An object’s elasticity describes how readily it returns to its original shape after it has collided with another object. In a perfectly elastic collision (in which elasticity equals 1), the two colliding objects return to their original shape immediately after the collision takes place.

Question: What is conserved during an elastic collision?

Calculate: The kinetic energy (KE) of an object is a measure of its energy of motion. The equation for kinetic energy is: KE = mv2 ÷ 2, and the unit for kinetic energy is the joule (J). In the equation, m represents an object’s mass and v represents its velocity.

Calculate the kinetic energy of each puck. (Note: The mass of the pucks can be found on the CONTROLS pane, and the magnitude of the pucks’ velocities (v) can be found at the bottom of the SIMULATION pane.)

Blue puck KE = Gold puck KE =

Add the kinetic energy of the blue puck to that of the gold puck to find the total kinetic energy for the system. Total system KE =

Compare: Turn on Velocity vectors during motion. Click Play and observe the pucks.

Calculate the final kinetic energy of the two pucks and the total system.

Blue puck KE = Gold puck KE = Total system KE =

Use the CALCULATION tab to check your work.

How did the kinetic energies of the two pucks change, and how can you explain these changes?.

How did the total system kinetic ener

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