A spring is compressed a distance of

x. When the spring is released, it shoots a marble of mass m vertically upward from ground level. The maximum height reached by the marble is h. The magnitude of the marble’s momentum at the highest point of the marble’s trajectory is equivalent to?

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To calculate the magnitude of the marble's momentum at the highest point of its trajectory, we need to use the concepts of conservation of energy and momentum. Here's how you can approach the problem:

1. Conservation of Energy: The potential energy stored in the compressed spring is converted into the kinetic energy of the marble as it is released and moves upwards. At the highest point, all of its kinetic energy is converted back into potential energy.

2. Potential Energy Calculation: The potential energy of a vertically raised object is given by the formula PE = mgh, where m is the mass of the object, g is the acceleration due to gravity (approximately 9.8 m/s^2), and h is the height.

3. Kinetic Energy Calculation: The kinetic energy of an object is given by the formula KE = (1/2)mv^2, where m is the mass of the object and v is its velocity.

4. Using Conservation of Energy: At the highest point, all of the marble's kinetic energy is converted back into potential energy. So we can set up the equation: KE = PE.

5. Kinetic Energy Calculation: Substitute the kinetic energy expression (KE = (1/2)mv^2) into the equation (KE = PE). Rearrange the equation to solve for v.

6. Magnitude of Momentum Calculation: Once you have the velocity at the highest point, you can calculate momentum using the formula momentum = mv. Since momentum is a vector quantity, we take its magnitude by considering the absolute value of velocity.

By following these steps, you should be able to calculate the magnitude of the marble's momentum at the highest point of its trajectory.