Collisions in 2-Dimensions (Lab Instruction) скачать в хорошем качестве

Collisions in 2-Dimensions (Lab Instruction)

The purpose of this lab is to test the conservation of momentum as well as the conservation of energy during a collision. If you allow two masses to collide and roll, you will have to factor in the rolling momentum (also known as the moment of inertia) and rolling energy into your calculations. That’s not so easy. So to simplify the set up, the collision will be observed-mid-air. Sounds crazy, but the set up is pretty easy. In fact, to simplify the set-up even more, the second mass will be at rest and the initial velocity of the first mass, as well as the velocities of the two masses after the collision will be determined by the distance that the masses fall compared to the time of fall from the edge of the table. Additionally, we can omit any influences due to gravity since it is in the vertical dimension. We will only focus on the x-dimension (the range) and the y-dimension (the deflection) from a sheet of paper below. You might ask, ‘Why is this set up easy?’ First, the time-of-fall is fixed for all drops. You’ll notice the ramp has a horizontal slope at the end of the run to ensure that the velocity in the vertical dimension is at zero. The first thing you should do is measure the height of this drop with a ruler. Ensure that you measure the drop from the base of the ball to the fall as this is the true drop in height. This provides three givens: viy = 0 m/s dy = 0.930 m ± 0.001 m ay = 9.81 m/s^2 ± 0.005 m By using the 3rd kinematics equation, this problem simplifies from Δd=viΔt + ½ aΔt^2 to Δd=½ aΔt^2. From the above givens, Δt = 0.4354 s ± 0.0008 s. Yes, the errors are reduced by half whenever you square root. This time is the definitive time for all 3 drops; this value should not change as long as viy = 0 m/s. Before you start the collision, first lay a sheet of paper on the ground. If you need to tape down two edges, please make sure that you remove the tape from the ground after the experiment is completed. Line the paper to the edge of the table, and use a pendulum bob to determine ground-zero, which is the position of mass2, which is at rest. If you drop the ball from this point, its displacement is at zero for both dimensions. Also, make sure you measure the mass of both the ball-bearing and the lighter plastic ball before you continue. The uncertainty of your measurement is always ½ of the least significant digit of the digital scale. From this particular scale, the uncertainty is ±0.005 g Make sure you slide the collision peg to the side before conducting your initial velocity drops. Make your first drop using the heavier mass. Centre the carbon paper at this location, and drop the heavier mass five more times. Circle and label this cluster as v1. Draw a line from ground-zero through the cluster of v1. This defines the x-dimension. The y-dimension is obviously 90° to this dimension. You can use a large protractor or a sheet of paper to draw in the y-dimension afterwards. Remove the carbon paper then place the lighter mass on top of the peg. Make sure that when the heavier mass collides with the lighter mass the velocity in the vertical dimension is at zero: • If you set the peg too high, the lighter mass will jump, and have a positive viy that you can’t easily measure. This will result in a time-of-flight longer than the calculated value above. • If you set the peg too low, the lighter mass will be pushed downwards and have a negative viy that you can’t easily measure. This will result in a time-of-flight shorter than the calculated value above. • Make sure the peg height levels both masses horizontally when they collide to ensure that viy is definitely zero so that you can faithfully rely on the time-of-drop of Δt = 0.4354 s ± 0.0008 s. • Make sure that you collide the moving heavier ball with the stationary lighter ball. If you do this experiment backwards the lighter ball will “bounce backwards” off the heavier ball and you won’t be able to attain any reliable data. After you have checked the above, perform one collision and centre two sheets of carbon paper over the two drop locations. Repeat the collisions 5 times, and circle and label the cluster of v1’ and v2’. Remove the tape from the ground and put all the equipment away.