Oscillations, energy conservation

[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?

 

[OlderDan]

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.

 

[HallsofIvy]

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.)

 

[Dr.Brain]

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

 

[OlderDan]

?? 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.