Name: Introduction: Through the use of the apparatus known as a ballistic pendul

Question

Name: Introduction: Through the use of the apparatus known as a ballistic pendulum, we can analyze the essential aspects of inelastic collisions. In the past the ballistic pendulum consisted of a large block of wood which could swing like a pendulum. Bullets or pellets where shot into the block of wood. From the recoil swing of the block it was possible to determine the muzzle speed of the bullet. Sorry, but due to the present state of society our ballistic pendulum will not involve bullets or pellets, rather we will use a spring fired steel ball. Theory: For a one dimensional collision, when the condition that the sum of the external forces in the x direction equals zero is satisfied, then by Newton's 2d and 3 d Laws we discover that linear momentum is conserved. Applying this to the collision between the steel ball and the cage of the ballistic pendulum we get: (eq 1) where: mass of steel ball m M = mass of cage v- initial velocity of ball V velocity of ball plus cage just after impact. The instant after collision the ball and cage will possess a certain amount of kinetic energy. This kinetic energy will be transformed into gravitational potential energy as the pendulum swings up. If the ball and cage swing up through a vertical displacement equal to h, then we can equate the kinetic energy after impact to this increase in gravitational potential energy as follows (cq 2) (1/2)(m + M)V2 = (m+M)gh Note that: h=L-Lcose) From this equation we can solve for V (eq 3) From equations 1 and 3 we can solve for the theoretical initial velocity of the steel ball: m + M 2gh Equation 4 gives us the theoretical initial velocity of the ball as derived from Newton's Laws of motion as applied to an inelastic collision. However, we would like to determine v by a different method so that we may gauge the success of the theoretical calculations. This can be achieved by measuring the time it takes for the ball to pass through a photogate. Vespwhere D is the diameter of the ball and t is the average time through photogate

Explanation / Answer

1. The initial kinetic enery will be computed by the fomula as given:

KE= 1/2[{m}*v2] , U need to know that the velocity will be zero at the maximum height attained by the ball

2. The initial kinetic enery will be computed by the fomula as given:

KE=1/2(m+M)*V2, Here V corresponds to combined velocity of ball and cage

3. Since, it is the inelastic collision, there will be loss in energy, which can be calculated by conservation of energy

(KE1 - KE2)

4. The percentage of initial KE lost of steel ball is given as below:

(KE1 - KE2)/KE1

The lost Kinetic energy is converted to potential energy as it attains height (by conservation of energy)..

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