Calculate Speed of 50-g Bullet Impacting 2-kg Ballistic Pendulum Can

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In summary, a 50-g bullet is shot into the 2-kg can of a ballistic pendulum, causing the can to rise to a height of 1.3m. Using momentum and energy equations, the speed of the bullet just before the collision is determined to be 207 m/s.
  • #1
tandoorichicken
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A 50-g bullet is shot into the 2-kg can of a ballistic pendulum. The can rises to a height of 1.3m Determine the speed of the bullet just before the collision.

Don't know how to begin.
 
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  • #2
I know you say that you don't know how to begin, but I'm hoping you see that this is a momentum problem.

IMO momentum problems are best done by drawing a free body diagrams: one immediatly before an event, one immediatly after (or during) an event and one at the end of the event as felt be the whole system (ie a baseball just prior to being hit by a bat, a baseball while (or just after) being hit by the bat, and the final distance traveled by the baseball). Once you have a good set of FBD's analyze the energies at each point of the overall event.

That should get you going.
 
  • #3
Since the collision is completely inelastic, momentum is conserved.
 
  • #4
Conservation of energy. (You appear to be doing problems from a chapter on "conservation of energy!)

Initially, the bullet with mass 50 g= 0.05 kg has (unknown) speed v. It's kinetic energy is (1/2)(0.05)v2= 0.025v2. Taking the height of the bullet and block at the moment of impact to be 0 potential energy, since the block is not moving, the total energy of bullet and block is the kinetic energy of the bullet: 0.025v2.

The bullet and block together rise to a height 1.3 m above the base height, and have 0 speed there. Their potential energy is (0.05+2)(9.8)(1.3)= 26.117 Joules and is the total energy.

Solve 0.025v2= 26.117.
 
  • #5
I think if something hits and sticks, energy is not conserved.
 
  • #6
you'd need both momentum and energy equations for this question. letting

Mb = mass of bullet,
M = total mass of can and bullet,
Vb = velocity of bullet just before collision,
V = velocity of bullet+can immediately after collision,
h = height of rise,

we can write 2 equations:

(momentum) MbVb = MV

(energy) (1/2)MV^2 = Mgh

solving for Vb, we get

Vb = MV/Mb
Vb = (M/Mb) sqrt(2gh)
Vb = 2.05/0.05 rt(2x9.81x1.3)
Vb = 207 ms^-1
 
Last edited:

1. How do you calculate the speed of a 50-g bullet impacting a 2-kg ballistic pendulum?

To calculate the speed of a bullet impacting a ballistic pendulum, you can use the conservation of momentum equation, which states that the total momentum before a collision is equal to the total momentum after the collision. In this case, the momentum of the bullet before the collision is equal to its mass (in kg) multiplied by its velocity (in m/s). The momentum of the combined system after the collision is equal to the mass of the bullet and pendulum (in kg) multiplied by their shared velocity (in m/s). By setting these two equations equal to each other and solving for the velocity, you can calculate the speed of the bullet.

2. What is a ballistic pendulum and how does it work?

A ballistic pendulum is a device used to measure the speed of a projectile, such as a bullet. It consists of a pendulum suspended from a pivot point, with a bullet or other projectile placed at the end of the pendulum. When the projectile impacts the pendulum, the combined system moves upwards due to the transfer of momentum. The height the pendulum rises can then be used to calculate the speed of the projectile using the conservation of energy equation.

3. Can the speed of the bullet be accurately calculated using a ballistic pendulum?

Yes, the speed of a bullet can be accurately calculated using a ballistic pendulum, as long as certain assumptions are made. These assumptions include a perfectly elastic collision, no air resistance, and no energy lost to friction or other external forces. In real-world scenarios, these assumptions may not hold true and may lead to slight discrepancies in the calculated speed.

4. What factors can affect the accuracy of the calculated speed using a ballistic pendulum?

As mentioned before, the accuracy of the calculated speed using a ballistic pendulum can be affected by factors such as the elasticity of the collision, air resistance, and external forces. Additionally, the precision and accuracy of the measurements taken (such as the height the pendulum rises) can also impact the accuracy of the calculated speed.

5. Why is the mass of the bullet and pendulum important in calculating the speed?

The mass of the bullet and pendulum is important in calculating the speed because it affects the total momentum of the system after the collision. A higher mass will result in a lower velocity, while a lower mass will result in a higher velocity. This is why it is important to have accurate measurements of the mass in order to get an accurate calculation of the speed.

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