Confused (simple harmonic motion problem)

In summary, when a bullet is fired at a block, the bullet's momentum is conserved, but the block's energy is dissipated into sound, block heating up/breaking and so forth.
  • #1
SnowOwl18
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0
Ok I've been trying this problem :

---A 21.0kg block at rest on a horizontal frictionless table is connected to the wall via a spring with a spring constant k=14.0N/m. A 2.10×10-2kg bullet traveling with a speed of 530m/s embeds itself in the block. What is the amplitude of the resulting simple harmonic motion? Recall that the amplitude is the maximum displacement from equilibrium.----


And I thought I could use the equation (1/2)mv^2 = (1/2)kA^2 ...but I got the answer wrong...and the hint says to first use conservation of momentum, and then conservation of energy. It seems like i couldn't do that, since it seems like I don't have enough information. Any help? Thanks :)
 
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  • #2
SnowOwl18 said:
Ok I've been trying this problem :
And I thought I could use the equation (1/2)mv^2 = (1/2)kA^2 ...but I got the answer wrong...and the hint says to first use conservation of momentum, and then conservation of energy.

That's right. In general, energy is not conserved in collisions, but momentum is.

It seems like i couldn't do that, since it seems like I don't have enough information. Any help? Thanks :)

You do have enough information. You know the mass of the bullet (m) and the mass of the block (M). You also know the initial velocity of the bullet (vi), and you want to know the final velocity of the bullet+block system (vf).

Can you write the law of conservation of momentum in terms of those symbols?
 
  • #3
Oh my bad...I wasn't thinking of the bullet block system. Thank you..I'll try that and see if it works.
 
  • #4
well, since the collision is not elastic (the bullet sticks), PE+KE energy is not conserved (dissipated into sound, block heating up/breaking and so forth). so you should calculate the velocity of the system after impact using conservation of momentum and then use this new velocity to determine the energy that must be equal to kA^2/2
 
  • #5
oh i got it, thanks!
 

FAQ: Confused (simple harmonic motion problem)

1. What is simple harmonic motion?

Simple harmonic motion is a type of periodic motion in which a system, such as a mass attached to a spring, oscillates back and forth with a constant amplitude and frequency. It follows a sinusoidal pattern and is characterized by a restoring force that is directly proportional to the displacement from equilibrium.

2. How do you solve a confused simple harmonic motion problem?

To solve a confused simple harmonic motion problem, first identify all the given variables, such as the mass, spring constant, amplitude, and initial conditions. Then, use the equations of motion for simple harmonic motion, such as F = -kx and a = -ω^2x, to find the missing variables. It may also be helpful to draw a diagram and use the appropriate units for each variable.

3. What is the difference between simple harmonic motion and regular oscillation?

The terms "simple harmonic motion" and "regular oscillation" are often used interchangeably, but there is a slight difference between them. Simple harmonic motion refers to a specific type of oscillation that follows a sinusoidal pattern and is characterized by a restoring force that is directly proportional to the displacement from equilibrium. Regular oscillation, on the other hand, is a more general term that describes any type of periodic motion, including simple harmonic motion.

4. Can simple harmonic motion occur in real-life systems?

Yes, simple harmonic motion can occur in many real-life systems, such as a pendulum, a mass attached to a spring, or the vibrations of a guitar string. These systems may not exhibit perfect simple harmonic motion due to external factors, but they can still be modeled using the equations of motion for simple harmonic motion.

5. How do you determine the period and frequency of a simple harmonic motion?

The period of a simple harmonic motion is the time it takes for one complete cycle of oscillation, while the frequency is the number of cycles per unit time. To determine the period, you can use the equation T = 2π/ω, where ω is the angular frequency. The frequency can be found using the equation f = 1/T. Alternatively, you can also use the period and frequency to find the angular frequency using ω = 2πf.

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