Lab Motion on Incline_LAB

docx

School

University of Notre Dame *

*We aren’t endorsed by this school

Course

1 04

Subject

Physics

Date

Apr 3, 2024

Type

docx

Pages

Uploaded by CorporalElementKomodoDragon20

1-D Motion on Incline 1-D Motion on Incline1–Constant Acceleration OBJECTIVE The objective of this lab experiment is to make simultaneous experimental observations of the position, velocity, and acceleration of a uniformly accelerating object on an inclined plane. From these data, it will be possible to study the relationship between these three quantities, and make a measurement of the acceleration due to gravity. THEORY When an object is placed on a "frictionless" inclined plane, there are two forces acting on it : the force, mg , due to gravity and the normal force , N , exerted on it by the plane. Since the plane is assumed to be frictionless, there is no component of this contact force parallel to the plane. If the x- and y-axes of the system are chosen to be parallel and perpendicular to the incline of the plane respectively, then the weight, mg , can be resolved into its components as shown in Figure 1. Figure 1 Newton's second law of motion states that: ∑ F = m×a ( 1 ) Or ∑ F x = m×a x ∑ F y = m×a y where a y = 0 , since there is no motion perpendicular to the plane: F y = N − mg×cosθ = 0 F x = mg ×sinθ = m a x

1-D Motion on Incline Page 2 Then: a x = g×sinθ ( 2 ) Thus it is the component of the weight parallel to the incline that produces the acceleration down the plane. Since the plane in Figure 1 has length, L, and is inclined to a height, h , the value of sin θ is h/L . Substituting this into equation (2) yields an acceleration down the plane of: a x = gh L ( 3 ) The constant acceleration of the object on the incline can be determined with the equation of motion X ( t ) = X ( 0 ) + V x ( 0 ) + 1 2 a x t 2 If the object is released from a starting point, X (0) = 0 with V x (0) = 0 , then the acceleration of the object as it moves through a distance, X , in the time, t , is given by: a x = 2 X t 2 ( 4 ) Combining equations (3) and (4), an equation is obtained which can be used to determine the value of g with data acquired in this experiment: g = 2 XL ht 2 Thus g can be determined by measuring the quantities X , L , h , and t . Updated: Summer 2020

1-D Motion on Incline Page 3 1-D Motion on Incline– Lab Report Section: 7 Name: Sribhav Danthala GOAL: (briefly state what experiment(s) will be performed and with what purpose) Equipment You need the following items: 1. Ramp, 2. Meter Stick. 3. A small Ball or Empty tin can, 4. Electronic Stopwatch Figure 2.  For the ramp you can use any flat, level object such as a board or a cardboard box. It should be about 1.25 meters (4.0 ft.) long. It doesn't matter what the ramp is made of as long as it is flat and strong enough to support your tin can without bending (Be creative).  To raise one end of the ramp, use a pile of books. You may not be able to get the top of the ramp at exactly the height given in the instructions. Get it as close as you can and record the actual height in data tables A and B.  It is best to use a "starting gate" to avoid imparting to the can any uphill or downhill motion. The starting gate is a pencil or small ruler which holds the can in place, to be lifted when time starts. Think of how the gates at a parking garage operate. All of this is because we want to assure that the initial speed is zero (stationary).  A countdown of "5, 4, 3, 2, 1" is a good way to begin the timing whether there is one person or two involved in the experiment. Updated: Summer 2020

Your preview ends here

Eager to read complete document? Join bartleby learn and gain access to the full version

Access to all documents
Unlimited textbook solutions
24/7 expert homework help

1-D Motion on Incline Page 4  To stop the timing, it is best to use a flat object such as a ruler or the cover of a book as a physical stop. This allows you to use your sense of hearing along with sight to coordinate the stopwatch with the stopping point. In this experiment there are FOUR VARIABLES. 1. The distance along the ramp. 2. The steepness of the incline which is measured by the ratio of height to length of the ramp. 3. The height from which the object is released on the ramp. 4. The time required for the ball to roll a certain distance down the ramp. HYPOTHESIS A: Distance is directly proportional to the square of time if acceleration is uniform. In this part the distance d down the ramp is the variable while the angle  of slope is constant. 1. Set up the ramp with h= 0.10 m above the ground, (as shown in Figure 2.) 2. Starting with the cylinder at rest, use the stopwatch to measure the time to roll distance d = 1.0 meter down the ramp. 3. Take 6 time measurements, record in data Table A . Cross out the highest and lowest times and determine the average of the remaining four times. (Sum four times and divide by four to find the average.) 4. Repeat steps 2 and 3 for distances of 0.80 m , 0.60 , 0.40 m (see data Table A). HYPOTHESIS B: Rate of acceleration is proportional to incline of ramp. In this part the distance rolled down the ramp d and the angle  of slope are both variables. 1. The steepness of the incline can be measured by the ratio of height to length. Measure the total length of the ramp and record in data Table B as L. 2. Copy the data from the first set of measurements in hypothesis A into the data table for hypothesis B, unless you prefer to collect that data a second time. (Time to roll 1.0 m when h = 0.1 m) 3. Raise the top of the ramp to 0.15 m . 4. Starting with the cylinder at rest, use the stopwatch to measure the time to roll 1.0 meter down the ramp. 5. Take 6 time measurements, record in data. 6. Repeat steps 4 and 5 for heights of 0.20 m, 0.25 m. Updated: Summer 2020

1-D Motion on Incline Page 5 HYPOTHESIS C: Objects will reach the same speed from a given height regardless of incline. In this part the starting height is held constant while the distance rolled down the ramp and the angle of slope are varied. 1. With the top of the ramp at h = 0.25 m as in part B, find the point P on the ramp that is y = 0.10 m above the ground (see Fig 2). 2. Measure the length of the ramp from that point P to the BOTTOM of the ramp and record as d in data table (see Fig 2.) 3. Measure the time for the cylinder to roll from point P to the bottom of the ramp (start from rest as before). 4. Repeat steps 2 and 3 for ramp heights of h = 0.20 m, 0.15 m, and 0.10 m . * note that the distance d, the incline of the ramp, and point p will be different for each of the 4 trials while the height y remains constant. DATA TABLES A. Acceleration vs. Distance Calculate the average time for six trials. Discard the highest and lowest in each trial so you will average the middle four values. Enter the average time in the data table. In each case use t(avg) for the times to calculate t squared. Draw a graph of distance versus average time squared for your data. h (m) d (m) t1 t2 t3 t4 t5 t6 tavg 0 1 2 3 4 5 6 Acceleration vs Distance Series1 Series2 Series3 Series4 Updated: Summer 2020

1-D Motion on Incline Page 6 Table A d (m) t 1 t 2 t 3 t 4 t 5 t 6 t (avg) t 2 1.00 1.25 1.22 1.20 1.21 1.23 1.24 1.23 1.5129 0.80 1.05 1.08 1.07 1.06 1.09 1.07 1.07 1.1449 0.60 0.95 0.92 0.94 0.96 0.93 0.95 0.94 0.8836 0.40 0.82 0.84 0.80 0.81 0.83 0.82 0.82 0.6724 B. Acceleration vs. Slope L is the total length of the board, to be recorded below. Distance rolled (d) is 1.0 meter. "t 2 " means ‘t raised to the power of 2’ Height divided by length (h/L) is a measure of steepness of slope. Distance divided by time squared (d/t 2 ) is proportional to acceleration. The relationship will be linear if and only if acceleration is directly proportional to slope. h (m) t1 t2 t3 t4 t5 t6 tavg tavg2 (d/ t2)/ (h/L) 0 2 4 6 8 10 12 14 16 18 20 Acceleration vs Slope Series1 Series2 Series3 Series4 Table B L = 1.25m d = 1 m h (m) t 1 t 2 t 3 t 4 t 5 t 6 t avg t avg 2 (d/t 2 ) (h/L) 0.10 1.23 1.20 1.22 1.21 1.25 1.24 1.23 1.5129 0.6609 0.08 0.15 1.35 1.33 1.30 1.32 1.34 1.36 1.33 1.7689 0.5653 0.12 0.20 1.48 1.45 1.47 1.50 1.46 1.49 1.47 2.1609 0.4625 0.16 0.25 1.60 1.58 1.62 1.59 1.61 1.63 1.60 2.5600 0.3906 0.20 Updated: Summer 2020

Your preview ends here

Eager to read complete document? Join bartleby learn and gain access to the full version

Access to all documents
Unlimited textbook solutions
24/7 expert homework help

1-D Motion on Incline Page 7 From data table B above, calculate the average time, the square of the average time, ratio d/t avg 2 and the ratio h/L. For each of the four heights divide the two ratios from table B (divide d/t 2 by h/L) and enter the results in the table B1 below. Table B1 h (m) (d/t 2 )/(h/L) 0.10 8.26125 0.15 4.71083 0.20 2.89062 0.25 1.953 Examine the ratios and decide whether or not they are constant. Then plot a graph of ( d/t 2 ) vs. ( h/L ) with h/L on the horizontal axis. C. Speed vs. Height " y " is the constant height from which the object is rolled. " h " is the measurement to the top of the ramp as before, " d " is the distance from point P along the ramp to the bottom. See figure 2. Be sure you understand the meaning of the variables before you begin . You want the object to be rolled from the same height above the ground each time. The point of release and the distance rolled down the ramp will be different for each trial. h (m) d (m) t1 t2 t3 t4 t5 t6 tavg (d/t) 0 1 2 3 4 5 6 Speed vs Height Series1 Series2 Series3 Series4 Table C y = 0.10 m Updated: Summer 2020

1-D Motion on Incline Page 8 h (m) d (m) t 1 t 2 t 3 t 4 t 5 t 6 t avg 0.10 1.10 1.20 1.22 1.21 1.25 1.24 1.23 1.23 0.15 1.15 1.35 1.33 1.30 1.32 1.34 1.36 1.33 0.20 1.20 1.48 1.45 1.47 1.50 1.46 1.49 1.47 0.25 1.25 1.60 1.58 1.62 1.59 1.61 1.63 1.60 For each height, calculate the average speed at the bottom of the ramp, d/t and enter the results in the data table C1 below. If the speed is the "same" then the ratios d/t should be equal. Table C1 h (m) (d/t) 0.10 0.8943 0.15 0.8647 0.20 0.8163 0.25 0.7813 Comparing the ratios of d/t decide whether or not you think the speeds are the same, then draw a graph of d vs. t for each of the four slope angles. QUESTIONS QUESTIONS FOR HYPOTHESIS A . Using your data from part A, plot a graph of d (vertical axis) vs. t 2 (horizontal axis). Draw a "best fit" straight line through the points. 1. Is the graph linear? Yes 2. What does it mean if the graph is linear? A linear graph means that there is a relationship between distance and the square of time, suggesting that distance is proportional to the square of time 3. What does a linear graph indicate about the acceleration of rolling objects? The acceleration of rolling objects is constant. In this case, it would imply that the object is going under uniform acceleration down the incline 4. Does your data support hypothesis A? Briefly justify your answer. Updated: Summer 2020

1-D Motion on Incline Page 9 It supports Hypothesis A meaning that distance is directly proportional to the square of time, meaning there is uniform acceleration QUESTIONS FOR HYPOTHESIS B Using your data from part B calculate d/t 2 and h/L . Then plot a graph of d/t 2 vs. h/L with h/L on the horizontal axis. Draw a "best fit" straight line through the points. 1. Is the graph linear? Yes 2. What does it mean if the graph is linear? The acceleration is directly proportional to the steepness of the incline 3. Does your data support hypothesis B? Briefly justify your answer It supports Hypothesis B, meaning the acceleration is proportional to the steepness of the incline. QUESTIONS FOR HYPOTHESIS C The average speed of an object under constant acceleration is distance divided by time. Plot a graph of d vs. t with t on the horizontal axis. Draw a "best fit" straight line through the points. 1. Is the graph linear? Yes 2. What does it mean if the graph is linear? The speed remains constant over time 3. Does your data support hypothesis C? It supports Hypothesis C, meaning the speed remains constant regardless of the incline GENERAL QUESTIONS 1. What are the variables in this experiment? Distance, time, height, steepness of the incline and starting height of the object 2. How did you control the can to be sure it did not roll off the side of the board? Would this have any effect on the precision or accuracy of your measurements? The can was controlled using a starting gate to make sure it started from rest and a stop to halt its motion. This control makes it so there is very little sideways movement, which makes it more accurate. Updated: Summer 2020

Your preview ends here

Eager to read complete document? Join bartleby learn and gain access to the full version

Access to all documents
Unlimited textbook solutions
24/7 expert homework help

1-D Motion on Incline Page 10 3. How can you tell whether or not the points on the graph represent a linear relationship? Would you expect them to be perfectly linear? Why or why not? A linear relationship is indicated by the points aligning closely with a straight line. While perfect linear is unlikely, because of experimental differences and errors, close alignment suggests a linear relationship 4. Briefly discuss the problems encountered in making kinematic conclusions from experimental data. Don't confuse the process of collecting data with the process of drawing conclusions from it. Some problems I came across were measurement errors, and equipment problems. Note: Use Excel to plot all the graphs then copy and paste them to your report. Once you have completed the assignment, save your report as a PDF and upload using the blackboard submission on the lab course page (found under “Lab Online Submissions”) Updated: Summer 2020

Lab Motion on Incline_LAB

Related Documents