Bullet hitting block attached to spring

In summary, a 0.0125 kg bullet with a speed of 152.91 m/s strikes a 0.300-kg block attached to a fixed horizontal spring with a spring constant of 2.25 x 10^3 N/m. This sets the block into vibration with an amplitude of 12.4 cm. After the impact, both objects move together at a speed of 10.52 m/s, demonstrating conservation of momentum and energy.
  • #1
needhelp83
199
0
A 0.0125 kg bullet strikes a 0.300-kg block attached to a fixed horizontal spring whose spring constant is 2.25 x 103 N/m and sets it into vibration with an amplitude of 12.4 cm. What was the speed of the bullet if the two objects move together after impact?

E=(1/2)kA^2=(1/2)(2250 N/m)(0.124 m)2=17.30 J

m=0.0125 kg + 0.3 kg=0.3125 kg

K=(1/2)mv^2
17.30 J=(1/2)(0.3125 kg)v^2
v2=0.009
v=0.095 m/s

Conservation of momentum:
(.0125 kg)v=(0.3125 kg)(0.095 m/s)
v=2.375 m/s

Have I done this properly? The velocity doesn't seem right to me. Have I missed anything?
 
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  • #2
needhelp83 said:
K=(1/2)mv^2
17.30 J=(1/2)(0.3125 kg)v^2
v2=0.009
v=0.095 m/s
Redo this calculation.
 
  • #3
K=(1/2)mv2
17.30 J=(1/2)(0.3125 kg)v2
v2=110.72
v=10.52 m/s

Conservation of momentum:
(.0125 kg)v=(0.3125 kg)(10.52 m/s)
v=152.91 m/s

Yes, this looks better. Thanks for the help!
 

1. How does the bullet hitting the block affect the spring?

When the bullet hits the block attached to the spring, the spring will compress due to the force of the impact. This compression stores potential energy in the spring, causing it to stretch and release the energy when the force is removed.

2. What happens to the bullet after it hits the block?

After the bullet hits the block, it will either bounce off or become embedded in the block, depending on the force of impact and the properties of the materials involved.

3. Can the spring be damaged by the impact of the bullet?

Depending on the force and velocity of the bullet, the spring may experience some damage from the impact. However, most springs are designed to withstand high levels of force, so it is unlikely that a single bullet impact will cause significant damage.

4. How does the weight and speed of the bullet affect the spring's response?

The weight and speed of the bullet will determine the amount of force and energy transferred to the spring upon impact. A heavier and faster bullet will create a stronger impact and cause the spring to compress more, storing more potential energy.

5. What factors determine how far the spring will compress when the bullet hits the block?

The factors that determine how far the spring will compress include the force and velocity of the bullet, the properties of the materials involved, and the design and strength of the spring itself. These factors can vary and will affect the amount of potential energy stored in the spring.

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