18-03-2017. Lab 5: Trajectories

Introduction: for this lab we will be further our understanding of projectile motion. To do so we will using an apparatus (as shown below) to demonstrate the concept in full view. To use our understanding of projectile motion to predict the impact point of a ball on an inclined board.

Procedure: To commence the experiment, we we must set up the apparatus , where we will launch the ball from a readily, identifiable, and repeatable point. near the top of the inclined ramp. Next to record our impact point, we will use carbon paper and tape it to a regular piece of paper, so when the ball lands on the impact point, the carbon paper records where it lands. We will do this five times to verify our predictions, and if they are correct, they will virtually land the same place each time.

Data/Calculations:                                            
                                                                       

This calculation above is used to find the how far it lands from the table's edge when it is being launched. To use this, we must first find the time t  using the height and angle measured before commencing the experiment. Once find x we can determine the launch speed of the ball as shown in the calculations above. When calculated, we found our  launch speed to be 15.1 cm/s and landing edge to be 20.2 cm.

Continuing our calculations from above, using our results from the calculations of v_0 and x we can use them to calculate the theoretical value of our landing distance from the apparatus. When calculated, we expect the ball to be found the 24.4 cm from the landing site of  the apparatus. When performing the experiment however we found the ball to land 26.3+/- 0.32 m from the apparatus, almost 2 cm  from our predicted impact point. Performing the experiment a number of time shows the ball landing between 2-4 cm from the theoretical impact point. Indicating a source of error in the experiment.

Conclusions: After completing the experiment, we were able to demonstrate the concept of projectile motion. In write-up, we indicated that we encountered a source of error in the experiment. One of the source may be the measurement of our height from the apparatus.

14-3-2017. Lab 3: Non-Constant acceleration problem/activity

Introduction: In this activity we will explore the concept of non-constant acceleration by applying it in a problem.
Problem: A 5000-kg elephant on frictionless roller skates is going 25 m/s when it gets to the bottom of a hill and arrives on level ground. At that point a 1500-kg rocket mounted on the elephant's back generates a constant 8000 N thrust opposite the elephant's direction of motion. The mass of the rocket changes with time (due to burning the fuel at a rate of 20 kg/) so that the m(t) = 1500 kg - 20 kg/s*t.
The objective of the problem is to find how far the elephant goes before coming to rest. Now there two ways we can find the distance of the elephant, an analytical approach and a numerical approach.

Analytical approach: This method involves using the Newton's 2nd law giving us the acceleration of the elephant + rocket system as a function of time. a(t) = Fnet / m(t). Next we can integrate the acceleration from 0 to t to find 🔼v and then derive an equation for v(t). Then we can integrate the acceleration from 0 to t to find 🔼x and then derive an equation for x(t), were we can use integration by parts. Once all the integration is all done and we can add all the elements to find the distance the elephant travels until the rocket runs out of fuel.

Numerical approach: As we can see from above, the analytical approach is time consuming. It turns out we can do it faster by using the numerical approach.

Conclusions:
1. When doing it numerically it was faster and more simple to use then the analytical approach, the former method allowed us to retain most of the original data, while the latter method allowed forced to us alter our data to fit the parameters of the problem, as when we did the numerical approach using Excel, our values for 🔼v and 🔼x were inconsistent with each other.

13-03-2017 Free Fall Lab

Introduction: For this lab we will be looking at the determination of g by using an apparatus to study of the basic laws of motion, demonstrating a free falling body.

Purpose: The purpose of this experiment is to examine the absence of all other external forces except gravity.

This is the apparatus used in the experiment. To us the apparatus we must first pull a piece of paper between the vertical wire ad the vertical post of the device. Second turn the dial hooked up to the electromagnet up a bit. Third hang the wooden cylinder with the metal ring around the electromagnet. Fourth turn on the power on the sparker thing. Fifth hold down the spark button on the box. Sixth turn the electromagnet off, so the thing falls. Seventh turn off the power to the sparker thing. Finally tear off the paper strip and set up the spark paper,to obtained the data for the next portion of the lab.

Data

This data shown above shows us the value for g for the object that falls on the apparatus and statistical data for our experiment. As we can see the avg value for our g constant is 962.852 m/s^2. 

Lab 1: Finding a relationship between and period for an internal balance. 8-Mar-2017

• Purpose: In this lab we are trying to highlight the relationship between mass and period for inertial balance. To do this we need to measure the period of oscillation for a bunch of different masses, that we can use to develop a mathematical model of the relationship between period and added mass. 

   This is the inertial pendulum that we will use to find the relationship between mass and period. This device allows us to record oscillations that occur during movement. The pendulum has a metal tray attached to two springy pieces of metal. So when we give the metal a pus, it will vibrate back and forth. this is how we will record our oscillations.

To obtain the data for this lab, we first must record the oscillations from the pendulum, using a motion sensor. First we start with no mass to test the sensor reading then we start adding the masses from 0 to 800, and record the time it takes to complete one oscillation on LoggerPro.

This is graph that  details the parameters of the experiment. Where we used the motion sensor to determine the period and distance the oscillations traveled.

During the day of the lab, we measured the oscillations that took place on the spring pendulum, then took the raw data the you above, and came up with an equation to find the unknown mass. After that we were able to conclude that that are range of masses for this experiment were between 275<m<325.