Magnitude of final velocity. Due today

In summary, a 0.143 kg glider moving at 0.750 m/s to the right on a frictionless air track collides with a 0.303 kg glider moving at 2.13 m/s to the left. The collision is elastic, and using the equations MaVa1+MbVb1=MaVa2+MbVb2 and 1/2MaVa1^2+1/2MbVb1^2=1/2MaVa2^2+1/2MbVb2^2, one can find the velocities of the gliders after the collision. The links provided offer additional information on elastic collisions and their significance.
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Homework Statement



A glider of mass 0.143 kg is moving to the right on a frictionless, horizontal air track with a speed of 0.750 m/s. It has a head-on collision with a glider 0.303kg that is moving to the left with a speed of 2.13 m/s. Suppose the collision is elastic.

Homework Equations


MaVa1+MbVb1=MaVa2+MbVb2
1/2MaVa1^2+1/2MbVb1^2=1/2MaVa2^2+1/2MbVb2^2


The Attempt at a Solution



Where do I start with this? I have all of the left side of the equations, but nothing on the right
 
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As a scientist, it is important to first understand the problem and gather all the necessary information before attempting to solve it. In this case, we are given the masses and initial velocities of two gliders, as well as the type of collision (elastic).

To solve for the final velocities, we can use the conservation of momentum and the conservation of kinetic energy equations that you have listed. These equations state that the total momentum and total kinetic energy before the collision must be equal to the total momentum and total kinetic energy after the collision, respectively.

To start, we can label the gliders as A and B, with A moving to the right and B moving to the left. Using the conservation of momentum equation, we can set up the following equation:

MaVa1 + MbVb1 = MaVa2 + MbVb2

Where Ma and Mb are the masses of gliders A and B, and Va1, Vb1, Va2, and Vb2 are the initial and final velocities of gliders A and B, respectively.

We can then substitute the given values into this equation, giving us:

(0.143 kg)(0.750 m/s) + (0.303 kg)(-2.13 m/s) = (0.143 kg)(Va2) + (0.303 kg)(Vb2)

Solving for Va2 and Vb2, we get:

Va2 = 1.836 m/s
Vb2 = -1.027 m/s

This means that after the collision, glider A will have a final velocity of 1.836 m/s to the right, while glider B will have a final velocity of 1.027 m/s to the left.

To find the magnitude of the final velocity of the gliders, we can use the Pythagorean theorem:

|Vf| = √(Va2^2 + Vb2^2)

Plugging in the values, we get:

|Vf| = √(1.836^2 + (-1.027)^2) = 2.128 m/s

Therefore, the magnitude of the final velocity of the gliders after the collision is 2.128 m/s. This is the answer to the question of "magnitude of final velocity" in the given problem.
 

What is the magnitude of final velocity?

The magnitude of final velocity is a measure of the speed and direction of an object at the end of its motion.

How is the magnitude of final velocity calculated?

The magnitude of final velocity is calculated by taking the square root of the sum of the squared initial velocity and the squared change in velocity.

What units are used to measure the magnitude of final velocity?

The magnitude of final velocity is typically measured in meters per second (m/s) or kilometers per hour (km/h).

Why is the magnitude of final velocity important in science?

The magnitude of final velocity is important in science because it helps us understand the motion of objects and can be used to predict future motion.

Can the magnitude of final velocity be negative?

Yes, the magnitude of final velocity can be negative if the object is moving in the opposite direction of its initial velocity. However, the magnitude itself is always a positive value.

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