KadeVeillon_W10104428_Lab2

Lab 2 — One Dimensional Motion Date Submitted — 9/7/22 Student — Kade Veillon USM ID - W10104428

Purpose To help to understand the relation ship between the velocity and acceleration of an object as it rolls down at an angle. Using experimentation to learn how to determine the velocity and acceleration of an item. Measuring the time (t) it takes a ball to roll down a ramp. The distance (x) of the roll is also measured. Using these numbers to determine the acceleration (a) and velocity (v). Introduction To figure out a and v, you fist need to get the measure for x and t. Measuring for x is simple. Using a tape measure you can get the length of the ramp. Rolling and measuring the time the ball takes to go to the end will give you the t needed. By using a series of formulas v=2x/t and a=2x/t%. Using this method to understand the relationship of velocity and acceleration as an object moves.

Part #1: Experiments with constant acceleration Procure the following equipment: A small steel ball (or marble or other hard small sphere) A grooved board to serve as a ramp (or a long board, rail etc.) A meter stick or ruler Wooden blocks (or something else to lift one end of the grooved track) Stopwatch (or use the stopwatch function on a cell phone) Masking tape We are going to roll the steel balls down the rail in order to investigate motion. We could simply drop balls, but that would be too quick for us to study in detail, so we will use the grooved board (ramp) to slow the balls. If a grooved ramp is not available, any long, straight board will do, as long as you can rolls balls down it and it doesn’t bend. 1. Place the ramp on a smooth, horizontal surface such as a table or countertop. Use a piece of masking tape (or something similar) to mark the middle of the ramp (Figure 2-1). Place the tape on the side of the ramp, so that the ball won’t roll over the tape. Then prop up one end so that a ball, released from rest, will take several seconds to roll to the bottom of the ramp. (Something as thin as a magazine may be enough for this to work) Make sure the ball continues to pick up speed as it rolls. 2. Measure the distance from the starting position of the ball to the middle mark, and measure the distance from the starting position to the end of the ramp. Record both values in Table 2-1 in units of meters. Start Middle End Figure 2-1. Marked positions on the ramp. 3. Next, prop up one end of the ramp so that a ball, released from rest, will take several seconds to roll to the bottom of the ramp (Figure 2-2). Something as thin as a magazine may be enough for this to work. Test your setup to ensure the ball continuously picks up speed as it rolls. The ramp needs to be straight (i.e. it can’t bend). S Figure 2-2. The ramp propped up at one end.

10. Measure the horizontal distance that the rail is propped up (“Ax”) and the vertical distance (height) of the block (“Ay”) and record them below: Horizontal distance Ax = 3b O cm Vertical distance Ay = C’/ - cm . These distances subtend a right triangle. The tangent function related the vertical to the horizontal distance: A 1 (A tand = 2 or 6 = tan 1{_3/} Ax Ax Where the angle is symbolized by the Greek letter 0 (“theta”). To determine the angle, calculate the ratio of the distances and take the inverse tangent using your scientific calculator (if you don’t have a separate calculator, there’s a good chance your cell phone does). Make sure the calculator is reporting angles in units of degrees. Record your result below: 6.% Angle = %’ degrees Practice using a stopwatch to measure the time needed for the ball to roll down the ramp. Release the ball from rest at the starting position. Use a stopwatch to measure the time needed to pass the middle mark. Do this a total of 5 times and record the results in Table 2-1. Release the ball from rest at the starting position. Measure the time needed to reach the end of the ramp. Do this a total of 5 times and record the results in Table 2-1. Calculate the average times for each distance and record the results in Table 2-1. Graph distance (vertical axis) vs. average time (horizontal axis). Draw a smooth curve through the points. Does this resemble any of the graphs from the simulations? If so, which one(s)?

Table 2-2. Velocities and Accelerations of the Ball down the Rail Distance Average Final Acceleration (m) Time (s) Velocity (cm/s) (cm/s?) Mid: - |78 .79 45./ 57.0 End: . 359 //8/ éOZ/ Sl o 13. What happens to the velocity of the ball as it rolls down the ramp? (Does it change much as the ball rolls?) ,’L-l— ynovuves ‘Cc‘s-(-e(‘, ~\-\m¢ —Quf*\'\er \<ep Sc)es \‘Bdwr\ ‘\-\(\c (‘o\N\P 14. What happens to the acceleration of the ball as it rolls down the ramp? (Does it change much as the ball rolls?) T~ s\dws ‘r‘nc ‘Fur*\/\cr ‘\-\— SSO(S bowfl 1~"\<- oy b 2( .17;§' Increase the height of the raised end of the ramp. How do the velocity and acceleration ni ve —g 9 appear to behave ngw, cqmpared to the original experiment? (Take measurements again 2(, 355 i : :z.‘ _2 y:,:727'" 4 if needgb“ v: 22 Vc loc\vyY ‘gn f j::: b( e ;%:;T:a\:ra . “bcf as _2._._.———<'1:‘) ’.502 v 28(7325) h\(gp\alo X ‘A‘w\.cvl L‘ll ,‘ "I-Tfflt%z 677 ST bosr. TG g1 23— | 1ofmk 16. Turn the concept of the experiment around: how does the total distance increase as time passes? (Or, does distance increase at a constant rate, does the rate of distance increasing itself increase, or does the rate of increase of distance slow down?) ?\ ckemce —\—ro»\)c\-r> MoVes &t 4 he Sarme fat= \ 05 Veloan®/

Summary 1. This is a rough way to find the acceleration due to the Earth’s gravity. But because objects fall so fast, it is hard to measure the time it takes an object to fall with a stopwatch. So we allowed a ball to roll down an inclined plane instead. Calculate the value of the Earth’s acceleration due to gravity (“g”) using the following formula.! Show your work and include the units: ¢ b é‘n Q> m . 7a 7( E(M/St\) = Z g = - 52 e s 7.5 k") Ssing S(S5\nGb) 5 (sin 6.5) - (.03 mls" 4 b. 79" 3 - 603, /52 2. The real (“accepted”) answer is g = 9.81 m/s? (in Hattiesburg, MS). How close is your result? Express your answer as a percentage error: |calculated answer — accepted answer| % error = x 100 .y accepted answer 603 - % ~- — X100 9.%1 - 3%.5% % error = 38"770 3. The average velocity of a moving object is given by Ax U=E Where Ax is the total distance traveled and Ar is the total time. How is this similar to our formula for final velocity? How is it different? S‘\Mu\ar Set wp D—'\b Measule ments ‘PV\‘\\ Ve \05"'\7 bGVb\"b +he B‘\S'\'O\V\Cc. \ ! The factor of 7/5 accounts for the fact that we are using a rolling solid ball. If this were (for example) a piece of ice sliding down the incline with no friction, then the 7/5 would not be there.

7. Suppose the initial velocity of the ball is zero. The ball rolls 30 centimeters (0.30 meters) in 2.0 seconds. Refer to the equations above to solve the following: (a) What is the final velocity (i.e. the velocity of the ball after traveling 30 cm) of the ball? \/ V £V, + G4 - 04+ (19)(2.0) - 0.30m / S (b) What is the acceleration of the ball? CL: 2 ( ¢ 3(‘)j 2 2.0 anZ, ls—m/ia 8. Suppose the initial velocity of the ball is zero. The acceleration of the ball is 0.25 meters per second squared and the final velocity of the ball is 0.50 meters per second. Refer to the equations above to solve the following: (a) How far did the ball roll down the ramp? QY= (., 50ml5) 2 (b) How much time did it take for the ball to roll down the ramp? Ve sV +at) 1 -(ni~ @) Ve ::5257(.507W 9. Suppose you are standing at the edge of a cliff overlooking water. You have a rock in your hand and a stopwatch. What could you do to determine the height of the cliff? @co (‘Oc\c RO 4+ e Loom (‘e\caSc, 40 Con tact o\t Loatel Lse 6(61‘8lm/sz) Cot cucCeleranion (LSe AX:(V&‘)(%&?) ‘o Bc-& c(w\r'\c ‘\'\«e. ke‘\ +t o Ll

Results Upon completing the measurements and math It was determined that at the halfway point the v was 0.451 m/s with an a of 0.570m/s?. At the end of the ramp v was 0.602 m/s and an a of 0.510 m/s2. Conclusion As an object moves down a ramp the speed will increase the further it goes down and the acceleration will gradually lower as it continues down the ramp.