What is the initial speed of the bullet that hits the pendulum?

In summary, a bullet weighing 10g hits a 2kg pendulum, causing the center of mass to rise 12cm. Assuming the bullet embeds itself in the pendulum, the bullet's initial speed can be calculated using the conservation of energy and momentum equations. The final result is 308m/s, which is higher than the initial estimation of 21.7m/s.
  • #1
joex444
44
0
A bullet, 10g, hits a pendulum, 2kg. The center of mass of the pendulum rises a vertical distance of 12cm. Assuming the bullet embeds itself in the pendulum, calculate the bullet's initial speed.

What I did was assume that at 12cm vertical distance the pendulum and bullet are momentarily at 0m/s velocity, and all their energy is gravitational potential, so mgh = 2*9.8*0.12 = 2.36J. The bullet's inital speed could be found by assuming the pendulum was at rest before being shot, and its GPE was 0. So, 2.36J came from the bullet, and 1/2mv^2 shows that v^2=472m^2/s^2. Taking the square root, v=21.7m/s.

Now, my professor says the answer is 308m/s. 21.7m/s is quite slow for a bullet...
 
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  • #2
the speed you have of 21.7m/s is the speed of the pendulum/bullet system. Energy is conserved.

you still have one more step to find the initial speed of the bullet, where energy is not conserved.
 
  • #3
I think I got it. Momentum during the collision is conserved, so Velocity of the block+bullet = m(bullet)*v(bullet)/(m(bullet)+M(block)). Then I use that V in the KE and GPE conservation equation, and I did get 308m/s.
 

1. How does a bullet affect the motion of a pendulum?

When a bullet hits a pendulum, it transfers its momentum to the pendulum, causing it to swing in the direction of the bullet's motion. This can change the amplitude and period of the pendulum's swing, depending on the force and angle of the bullet's impact.

2. Can a pendulum continue swinging after being hit by a bullet?

Yes, a pendulum can continue swinging after being hit by a bullet, but the bullet's impact will likely disrupt its normal motion and cause it to eventually come to a stop due to friction and air resistance. The pendulum's material and design can also affect its ability to continue swinging.

3. What factors affect the impact of a bullet on a pendulum?

The impact of a bullet on a pendulum is affected by several factors, including the mass and velocity of the bullet, the mass and length of the pendulum, and the angle and location of the bullet's impact on the pendulum. The environment, such as air resistance and friction, can also play a role.

4. Can a pendulum's motion be predicted after being hit by a bullet?

The motion of a pendulum after being hit by a bullet can be predicted to some extent using physics principles and equations. However, the exact motion will depend on the specific circumstances of the pendulum and bullet impact, making it difficult to predict with complete accuracy.

5. How does the speed of the pendulum affect the impact of a bullet?

The speed of the pendulum can affect the impact of a bullet in several ways. A faster pendulum may be more difficult for a bullet to hit accurately, making the impact less predictable. Additionally, a faster pendulum may have more momentum to transfer to the bullet, potentially causing it to deflect or ricochet in a different direction.

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