Determining Velocity of Ball Fired Horizontally from Ballistic Pendulum

In summary, the conversation is about using the Work-Kinetic Energy Theorem to determine the velocity and range of a ball fired horizontally from a ballistic pendulum. The data given includes the masses of the ball, spring, and rod, as well as the length of the spring and its initial and compressed lengths. The equation used is Kbo + Kro + Kso = Kb + Kr + Ks, and the final equation for velocity is v_oball = (kx^2 /m_ball)^.5. The second part of the conversation involves determining the range of the ball when fired from a height of 101.05 cm above ground, using the equation R = v^2 /g sin2t, but with the
  • #1
lip1993
1
0
I am trying to determine the velocity of a ball fired horizontally from ballistic pendulum. The data is as follows:
ball mass: 62.2 g
spring mass: 14.7 g
rod mass: 89.3 g
length of spring: 126.1 mm
initial spring length: 5 cm
compressed spring length: 1 cm
k: 2.05 N/m calculated from previous experiment

Using the Work-Kinetic Energy Theorem
Kbo + Kro + Kso = Kb + Kr + Ks
.5mv^2oball + .5mv^2orod + .5kx^2 = .5mv^2ball + .5mv^2rod - .5kx^2
I took all the terms to 0 and got v_oball = (kx^2 /m_ball)^.5.

this doesn't seem correct, shouldn't the mass and lengths of the spring and rod be used?

2nd part is to determine the range it should travel from a height of 101.05 cm above ground fired horizontally.
I used the R = v^2 /g sin2t but since angle t= 0 I am getting 0 for the range.
 
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  • #2
welcome to pf!

hi lip1993! welcome to pf! :smile:

(try using the X2 button just above the Reply box :wink:)
lip1993 said:
I am trying to determine the velocity of a ball fired horizontally from ballistic pendulum.

i don't understand the set-up :redface:

do you mean a ball fired horizontally at a ballistic pendulum (from a spring)? :confused:
 

1. How does a ballistic pendulum work?

The ballistic pendulum works by using the principles of conservation of momentum and conservation of energy. When a projectile (in this case, a ball fired horizontally) hits a pendulum, it transfers some of its momentum and energy to the pendulum. The pendulum then swings upward, and by measuring the height of the swing, we can calculate the initial velocity of the projectile.

2. What equipment is needed to determine the velocity of a ball fired horizontally using a ballistic pendulum?

The equipment needed includes a ballistic pendulum apparatus, a projectile (such as a ball), a meter stick or ruler to measure the height of the pendulum swing, and a scale to measure the mass of the projectile and the pendulum.

3. What are the steps to determine the velocity of a ball fired horizontally using a ballistic pendulum?

The steps include setting up the ballistic pendulum apparatus, firing the projectile horizontally into the pendulum, measuring the height of the pendulum swing, measuring the mass of the projectile and pendulum, and then using the equations for conservation of momentum and energy to calculate the initial velocity of the projectile.

4. How accurate is the ballistic pendulum method for determining velocity?

The accuracy of the ballistic pendulum method depends on several factors, such as the precision of the equipment and the skill of the person conducting the experiment. However, with proper setup and measurements, the method can provide relatively accurate results, typically within a few percentage points of the actual velocity.

5. What are some sources of error when using a ballistic pendulum to determine velocity?

Some sources of error include friction in the pendulum's pivot point, air resistance on the projectile, and imprecise measurements of the height and mass. Additionally, the accuracy of the results can be affected by the angle at which the projectile hits the pendulum and the elasticity of the materials used in the apparatus.

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