3) Before we introduce how to determine the value of the firing speed, a demonstration of the apparatus of our experiment is necessary to understand what is happening.
. We will be using a ballistic pendulum. There we have a small spring-loaded gun with the ball inside. As soon the gun fires the ball, it will make contact with a nylon block. The nylon block has a hole for the ball to enter. Behind the block is an angle indicator and the block will push the indicator as it reaches its maximum angle before it rebounds.4) Now that we have an idea what is going on in the problem, we will determine what mechanical values are included during the ballistic pendulum problem. We know the gun is parallel to the surface of the desk so there is no angle when the ball is fired out of the gun. Next the ball makes contact with the nylon block so we will write an equation for conservation of momentum. Lastly, the ball goes vertically by some angle and returns back down. We can determine that energy was conserved by the ball and the block. The work done by the mass is the potential energy and it will equal to the change of kinetic energy.
5) Here I summarized on how to solve the firing speed of the ball.
We used a weight scale for the ball and the nylon block. We next measured the length of the string. The moment the ball enters the nylon block, we will set up that point of the y-direction equal to zero. First we will solve for the velocity of the ball inside the block. At that point. Kinetic energy has a value greater than zero and the potential energy will be zero since that is the origin of y. When the mass reaches its maximum angle, the kinetic energy will be zero and the potential energy will equal to the initial kinetic energy. All we need to solve is the velocity of the ball and the block. Since the height is not vertical of the block, we know the block went up by some angle L-x. That x will equal to L cosine theta. So the height will equal L minus L cosine theta. Once we find the value of the speed of the ball and the block, we used the equation of conservation of momentum. The initial momentum will equal the mass of the ball and the unknown speed equal to the speed of the ball and block and mass. Our results came out as 4.96 +-0.677 meters per second.6)
7) By proving that energy is conserved by the mass of the ball and the block, here is our assumption of the graph of kinetic energy and potential energy. Since the potential energy is conserved, our assumption also proves that the momentum was conserved as well.
8) In order to prove our answer of the speed of the ball is correct, we will use another method using kinematics equations. We will shoot the ball on the edge of a table, measure the values of the height and the distance where the ball lands, and use our kinematics equations to see if our assumption is true.
Substituting time for the horizontal distance and velocity in the y-component, our answer came out as 4.9+-0.32 meters per second. So our answer of the speed of the ball is correct and we proved that energy was conserved in the ballistic pendulum.
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