# Oscillations, energy conservation

• Lalasushi
In summary, the conversation discusses a physics problem involving a bullet embedding itself in a block attached to a spring. The question asks for the initial speed of the bullet and the time for the bullet-block system to come to rest. The hint suggests using conservation of momentum for the collision and then treating the rest of the problem as energy conservation for a harmonic oscillator. However, since the bullet embeds itself in the block, conservation of energy is not possible and the system will never come to a complete rest.
Lalasushi
A 10g bullet embeds itself in a 0.5kg block which is attached to a spring of force constant 36N/m. If the maximum compression of the spring is 1.5cm, find a)the initial speed of the bullet and b)the time for the bullet-block system to come to rest.

can someone give me some help with the above question? I am not sure how to start it, anyone got any hints to start me off?

Lalasushi said:
A 10g bullet embeds itself in a 0.5kg block which is attached to a spring of force constant 36N/m. If the maximum compression of the spring is 1.5cm, find a)the initial speed of the bullet and b)the time for the bullet-block system to come to rest.

can someone give me some help with the above question? I am not sure how to start it, anyone got any hints to start me off?

Hint: Treat the capture of the bullet by the block as a conservation of momentum problem; ignore the spring. Once you have the final momentum, find the velocity; treat the rest of the problem as energy conservation for a harmonic oscillator.

b)the time for the bullet-block system to come to rest.
?? If there is no friction and energy really is conserved, the bullet-block will NEVER come to rest.

(By the way, you do NOT have conservation of energy in the original bullet-block collision. Because the bullet embeds itself in the block that is a completely inelastic collision. Conservation of momentum, as Older Dan said, and the fact that the bullet and block have the same speed after the collision will give you that speed.)

Use conservation momentum in inelastic collission.Kinetic energy conservation is not possible since some of the energy will be lost in other forms . After you find out the final velocity of the system of both blocks (M). Before you apply conservation of momentum,first claculate the initial expansion of spring due to the mass hanging from it . Then use conservation of energy such that KINETIC ENERGY of single block is converted into compression of spring and kinetic energy of the combined system formed through inelastic collision.

BJ

HallsofIvy said:
?? If there is no friction and energy really is conserved, the bullet-block will NEVER come to rest.

It's worded a bit obscurely, but I assume they are looking for the time when the system is momentarily at rest at maximum displacement rather than some final rest condition, which, as you have noted, will never be achieved if energy is conserved.

## 1. What is an oscillation?

An oscillation is a repetitive back-and-forth movement or vibration around a central equilibrium point. It can occur in various systems, such as a pendulum, a mass on a spring, or a sound wave.

## 2. How is energy conserved in an oscillating system?

In an oscillating system, energy is converted between kinetic energy (energy of motion) and potential energy (stored energy). As the object moves towards the equilibrium point, potential energy decreases and kinetic energy increases. As it moves away from the equilibrium point, the opposite occurs. The total energy remains constant, thus conserving energy.

## 3. What factors affect the frequency of an oscillation?

The frequency of an oscillation depends on the system's mass and its restoring force. For example, a heavier object will oscillate at a lower frequency than a lighter object. A stronger restoring force will result in a higher frequency of oscillation.

## 4. How does damping affect an oscillating system?

Damping refers to the gradual decrease in the amplitude (size) of an oscillation over time. This can occur due to friction or other dissipative forces. Damping reduces the energy of the system and can eventually cause it to come to a complete stop.

## 5. Can the energy of an oscillating system be changed?

Yes, the energy of an oscillating system can be changed by applying an external force. For example, a person pushing a swing can increase its amplitude and thus increase its energy. However, the total energy of the system will still be conserved.

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