1. Knight P11.15 A 150 g ball and a 250 g ball are held at rest with a horizontal compressed spring between them. When released the lighter ball shoots away with a speed of 8.00 m/s. What is the speed and direction of the heavier ball? Draw a "before" and "after" sketch of the situation. Be sure to label the masses, velocities, and the positive x-direction (the coordinate system).
1. Knight P11.15 A 150 g ball and a 250 g ball are held at rest with a horizontal compressed spring between them. When released the lighter ball shoots away with a speed of 8.00 m/s. What is the speed and direction of the heavier ball? Draw a "before" and "after" sketch of the situation. Be sure to label the masses, velocities, and the positive x-direction (the coordinate system).
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**Question 1:**
Two balls, one with a mass of 150 grams and the other with 250 grams, are held at rest with a horizontal compressed spring between them. When released, the lighter ball shoots away with a speed of 8.00 meters per second. What is the speed and direction of the heavier ball?
**Instructions:**
- Draw a "before" and "after" sketch of the situation.
- Be sure to label the masses, velocities, and the positive x-direction (coordinate system).
![**Useful Information**
**Conservation of Momentum**
\[
\Delta \vec{p} = 0, \text{ or } \vec{p_f} = \vec{p_i}
\]
**Simple Harmonic Motion**
- Displacement: \[ x(t) = A \cos(\omega t + \phi_0) \]
- Velocity: \[ v(t) = -A \omega \sin(\omega t + \phi_0) \]
- Acceleration: \[ a(t) = -A \omega^2 \cos(\omega t + \phi) \]
**Hooke's Law for a Linear Spring**
\[
F = -kx
\]
**Angular Frequency for an Oscillating Mass on a Spring**
\[
\omega = \sqrt{\frac{k}{m}}
\]
**Angular and Cyclical Frequency**
\[
\omega = 2\pi f
\]
**Total Mechanical Energy for an Oscillating Mass on a Spring**
\[
E_{mech} = \frac{1}{2} k A^2
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Transcribed Image Text:**Useful Information**
**Conservation of Momentum**
\[
\Delta \vec{p} = 0, \text{ or } \vec{p_f} = \vec{p_i}
\]
**Simple Harmonic Motion**
- Displacement: \[ x(t) = A \cos(\omega t + \phi_0) \]
- Velocity: \[ v(t) = -A \omega \sin(\omega t + \phi_0) \]
- Acceleration: \[ a(t) = -A \omega^2 \cos(\omega t + \phi) \]
**Hooke's Law for a Linear Spring**
\[
F = -kx
\]
**Angular Frequency for an Oscillating Mass on a Spring**
\[
\omega = \sqrt{\frac{k}{m}}
\]
**Angular and Cyclical Frequency**
\[
\omega = 2\pi f
\]
**Total Mechanical Energy for an Oscillating Mass on a Spring**
\[
E_{mech} = \frac{1}{2} k A^2
\]
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