Physics > QUESTIONS & ANSWERS > PHYS 1405 Lab 3. Virtual Lab: Velocity and Acceleration on a Frictionless Inclined Plane, and Free F (All)

Virtual Lab: Velocity and Acceleration on a Frictionless Inclined Plane, and Free Fall Theory: The Italian scientist Galileo Galilei (1564-1642) discovered mathematical relationships that describe... the motion of falling objects, and the motion of objects rolling down inclined planes. These equations paved the way for the subsequent development of the field of classical mechanics (the science of forces and motion) by the English physicist, Sir Isaac Newton, who was born the same year Galileo died. This short PBS video describes Galileo’s groundbreaking work on inclined planes: In this lab, we will explore the motion of objects on inclined planes just like Galileo did, some 400 years ago. Definitions: Speed: a measure of how fast an object moves, or how much distance it covers in a given amount of time. The units for speed are m/s. Velocity (v): the quantity that describes the speed of an object as well as the direction in which it is traveling. The units for velocity are m/s. Acceleration (a): a measure of how much the velocity of an object changes in a given amount of time (or how fast its velocity is changing). The change in velocity may be due to change(s) in the object’s speed, or due to change(s) in the object’s direction. The units for acceleration are m/s2. Free fall: motion of an object that falls under the influence of the force of gravity alone, with other forces such as air resistance being so small that they can be ignored. In the absence of air resistance all objects, heavy or light, fall at the same speed and with the same acceleration, whose value is g = 9.80 m/s2. This acceleration experienced by all objects on our planet is called the acceleration due to gravity, and it can be rounded off to: g = 10.0 m/s2. To study an object’s motion, we measure quantities such as the height it falls through, its velocity, the time it takes, and so on. The height through which an object falls is denoted by the symbols h or d, and is measured in meters. In free fall, the above three quantities are related through the equation: v2 = 2gh … Equation [1] Taking the square root of both sides, this equation can also be written as: v=√2 gh (remember, this is only for free fall, where we can ignore air resistance. An equation that describes the motion of an object falling under the influence of gravity alone is (this equation was discovered by Galileo): h=1 2 gt2 … Equation [2] Here, t is the time taken to travel a height h. Another equation that describes the motion of an object that has a steady (or non-changing) acceleration, as it would have when moving on an inclined plane or in free fall (this equation was also discovered by Galileo): velocity = acceleration x time Which, in symbols, can be written as: v=at ,∨v=¿ … Equation [3] where the acceleration of the object is denoted by the letter a, or g (g, if it is falling under the influence of the force of gravity). Purpose: to study the motion of an object on an inclined plane. Example: Let us see how we can use equation [1] to solve a problem: Problem: A ball of mass 1.0 kg was dropped from a height of 2.0 m. What is final velocity of the ball? (that is the velocity of the ball just before it touches the ground.) Solution: Known quantities: h = 2.0 m, g = 10 m/s2, m = 1.0 kg Formula: v2 = 2gh Substitution and calculations: v2 = 2 * 10 m/s2 * 2.0 m We multiply all these numbers and their units v2 = 40.0 m2 / s2 Find the square root of this number and its units: v = 6.32 m/s (A number with its units in physics is called a physical quantity - velocity in this case.) Note: the motion on a frictionless inclined plane is the same as that in free fall with no air resistance, with the velocity at the bottom of the inclined plane depending only on g and h, allowing us to use the same formula (v2 = 2gh). However, if there was friction between the surface of the inclined plane and the object, or significant air resistance, then this formula would not apply. Figure 1 Procedure: Getting started: 1. Check that you have Adobe Flash Player installed on your computer and the pop-up blocker is disabled. 2. Ctrl + Click on the link below to open the animation: The URL for the animation is: 3. Click on “How to use,” and read the “Description” and “Instructions.” No fricton v2 = 2gh v2 = 2gh No air resistance h Part 1: Analyzing velocity In this part of the lab we will find the velocity of the ball at the bottom of the inclined plane, using two methods, the experimental method and the theoretical method. 1. Adjust the “Angle of Incline” slider to 15 degrees. Click on “play” and observe the graph of Velocity vs. Time. Record the magnitude of the height h and velocity v for this angle in the table below. The height (h) is given at the top left of the graph, and the velocity (v) is shown on the speedometer. The velocity on the speedometer is the experimental value of the ball’s velocity when it reaches the bottom of the incline. 2. Click “Reset,” and change the angle to the next angle listed in the table. Record your observations in the next row of the table. Repeat the above steps to complete the table. Please round off all numbers to two places after the decimal. Use: acceleration due to gravity = g = 10.0 m/s2 Table 1 Angle (degrees) h (height in meters (m)) vexp (experimental velocity in m/s read from the speedometer) Calculation v2 = 2gh (calculate the right hand side of this equation substituting g = 10 m/s2 and h from the animation) vtheory (theoretical velocity is the square root of the column on the left, that is the fourth column) Percent error The vertcal bars mean to take the absolute value or ignore any negatve signs that result from the subtracton % The last column (Percent error) is a measure of how close an experimentally-measured value is to the theoretical value. The smaller the percent error, the closer the measurement is to the theoretical value. A percent error of less than 10% generally indicates a good experimental measurement. Part 2: Analyzing acceleration: In this part of the lab we will find the acceleration of the ball, and see how it changes as we change the angle of the inclined plane. 1. Adjust the angle of the incline to the different values listed in Table 2 below. 2. Record the final velocity of the ball in column 3. 3. Calculate the acceleration of the ball in column 5. The first row has been completed as an example. Note: the acceleration of the ball is also equal to the slope (or steepness) of the lines in the Velocity vs. Time graph in the animation. Table 2 Angle (degrees) vi (initial velocity of the ball in m/s, before it is released from the top – it is always zero m/s in this experiment) vf (final velocity of the ball in m/s, as it reaches the bottom of the incline– this is displayed on the speedometer) time (t) (time in seconds taken by the ball to reach the bottom of the incline – it is always 3 seconds in this experiment) acceleration (a) a= (vf -vi) t Take the difference between the final and inital velocites, and divide that by the tme. This equaton is another form of equaton 3, on page 2 of this document. 15⁰ 0 m/s 7.61 m/s 3 s a = (7.61 - 0)/3 = 2.54 m/s2 30⁰ 0 14.70 m/s 3 s 4.9 m/s2 45⁰ 0 20.70 m/s 3 s 6.9 m/s2 60⁰ 0 25.46 m/s 3 s 8.49 m/s2 75⁰ 0 28.40 m/s 3 s 9.47 m/s2 90⁰ 0 29.4 m/s 3 s 9.8 m/s2 Questions: Please select (highlight in a different color) the best answer from the choices provided. (3 points each) 1. In this experiment we see that as the angle of the incline is increased from 15 to 90 a) the lines on the Velocity vs Time graph become less steep. b) the lines on the Velocity vs Time graph become more steep. c) the lines on the Velocity vs Time graph do not change their steepness. d) the lines on the Velocity vs Time graph start to curve downwards. 2. In this experiment, if we turn the “Strobe” on and run the animation at different angles, we will see that the time the ball takes to reach the bottom of the incline is a) 1 second b) 2 seconds. c) 3 seconds. d) 4 seconds. 3. If we turn the “Strobe” on, run the animation at different angles, and look at the distance covered by the ball between 2.5 seconds and 3 seconds, we see that a) this distance decreases as the angle increases. b) this distance does not change as the angle increases. c) this distance increases sometimes and decreases sometimes with no definite pattern. d) this distance increases as the angle increases. 4. In this experiment, we see that the velocity of the ball at the bottom of the incline a) is 100 m/s for all angles. b) decreases with angle. c) does not change with the angle of incline. d) increases with angle. 5. If we carefully observe the speedometer and the graph of Velocity vs. Time (for a 15 angle for example), we see that as the ball moves down the incline, a) its velocity keeps decreasing at a steady rate. b) its velocity keeps increasing at a steady rate. c) its velocity neither increases or decreases. d) its velocity increases initially, but then starts to decrease until if finally reaching 0 m/s at the end. 6. If we apply Equation 2, on page 1 of this lab document (h =1/2 gt2), to the motion of the ball when the angle is 90, and use time (t = 3 seconds), and the acceleration due to gravity (g = 9.8 m/s2) we find that the height (h) is: a) 1 m b) 10 m c) 44.1 m d) 100 m 7. In this experiment, if we divide the change in velocity (final velocity of the ball minus the initial velocity, which is 0 m/s) by the time it takes to travel the incline (3 seconds), we get values that a) increase with increasing angle. b) decrease with increasing angle. c) do not change with angle. d) increase steadily till 45 and then decrease steadily till 90. 8. From question 7 above, we can conclude that, since the rate of change of velocity increases with angle, a) the acceleration of the ball decreases with angle. b) the acceleration of the ball increases with angle. c) the deceleration of the ball increases with angle. d) the weight of the ball increases with angle. 9. From this experiment we can conclude that at the angle of 90 a) the ball experiences free fall, and accelerates at 9.8 m/s2. b) the ball does not fall. c) the ball moves with a constant velocity of 1 m/s. d) the ball moves upwards. 10. If we could have made the angle 0, then we would have seen that a) the ball would fall down at 1 m/s. b) the ball would fall down at a rate of 1 m/s2 c) the ball would move upwards at a speed of 10 m/s. d) the ball would stay still and not fall at all. 11. In this experiment, if we divide the units of the y-axis (m/s) by the units of the x-axis (s), we get a) ms/s, which are the units of acceleration. b) s/ms, which are the units of acceleration. c) m/s2 which are the units of acceleration. d) m, which is the unit for distance. Please enter the names of all group members at the top of this document. Each member of the group is required to submit an individual copy of the lab report through eCampus. [Show More]

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