collision lab with ball and pendulum

Purpose: the purpose of this laboratory is to calculate the velocity of the ball using conservation of momentum and energy. And show that the values calculated are within reasonable error by calculating the propagated uncertainty.

The purpose of this apparatus is to measure the angle that the block rises after the ball is shot into it so that we can calculate the initial velocity of the ball .

Procedure:
In this experiment we used the apparatus to launch a ball into block and saw the angle in degrees that the block rose. Measuring the length of the string that the block is hanging from, and measuring the mass of the ball and the mass of the block, we will use conservation of momentum and conservation of energy to find the initial velocity. We will see if our value calculated for the initial velocity is allowed within the uncertainty of our instruments.

The first thing that we had to do was find a relationship to calculate the velocity initial. To do this we see that momentum is conserved before the collision and an instant after the collision before the block rises. So we use the equation for conservation of momentum.

The problem is that we are going to have two variables V initial and V final. Because there is kinetic energy in the beginning of the collision and potential energy at the end and energy is conserved we could use conservation of energy equation.

The V initial in the conservation of energy equation is equal to the V final in the conservation of momentum equation so we solve for V initial in the conservation of energy equation and we get the expression:

Where h is:

where L is the measured length of the string holding the block, and theta is the angle the block elevates. so the final expression we get is.

We measured everything we needed to measure and got:

m1 (mass of the ball) : .00763 kg
m2 (mass of the block) : .0809 kg
L (length of the string) : .2 m
theta (angle of elevation) : 16.5 degrees

plugging the measurements into the equation and solving for the initial velocity we get:

The initial velocity that we get is 4.66 m/s +/- the uncertainty.

Next, we have to find the propagated uncertainty to see if our value is within the allowed error. To do this we take partial derivatives for each variable measured and multiply them with their respective uncertainty in measurement and add them all up. The propagated uncertainty was calculated for this lab:

The data suggests that the initial velocity of the ball before the collision was 4.66 m/s with a uncertainty ranging from +/- 1.204 from the instruments we used to measure.