1 gt. AP Physics 1 Lab: ACCELERATION DUE TO GRAVITY. Purpose. Theory. LAB#02-2: Free Fall & Acceleration (g)

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1 LAB#0-: Free Fall & Acceleration (g) AP Physics 1 McNutt Name: Date: Period: AP Physics 1 Lab: ACCELERATION DUE TO GRAVITY Purpose To determine the value of the gravitational acceleration Theory When we use the word acceleration we mean the rate at which the velocity of a moving object changes with time. Acceleration is always caused by force gravitational force as one of the fundamental forces of nature. This is the essence of Newton s first law. In today s lab we will measure the acceleration due to the gravitational force exerted by the earth on two different types of objects, a tennis ball, baseball and a ping-pong or golf ball. An object falling near the surface of the earth experiences constant gravitational acceleration. If we drop the object from the certain distance on a free fall, the distance traveled by an object in a free fall after t seconds is: d y v i t + 1 gt = = (1) The velocity of an object in free fall after t seconds is: v= vi+ gt () Here, the parameters v i and g are, respectively, the initial velocity and the acceleration. Galileo first demonstrated this result when he dropped cannonballs of different masses from the Leaning Tower of Pisa to show that although they had different masses, when dropped together, they landed together. This happened in this manner because they both experienced the same acceleration. A similar experiment can be done by dropping a coin and a feather. When dropped in air, the coin always lands first, but when they are dropped in a vacuum, an environment where there is no air, they land together! In the coin and feather case, the different velocities are due to the presence of a force, the frictional force on the coin and the feather due to the presence of air. In this experiment, you will be dropping an object from rest, so that vi = 0. We will assume that the only acceleration present is due to the force of gravity. We then obtain the relation that describes the distance the object falls as a function of time 1 gt d =. (3)

2 Equation (3) can be used to measure g. All we need to do is to drop an object through a known distance y and then measure the time t it takes to hit. If we know both y and t, we can solve equation (3) for g, d g = (4) t By measuring the travel distance y and the travel time t for an object falling from rest, gravitational acceleration can be determined. Procedure Each group will drop three types of objects: small wiffle ball, tennis ball, and baseball. 1. One student from the group will stand on the laboratory desk and drop a wiffle ball, tennis, and a baseball from the same height of d = 1.5 m from the floor. During the lab you will measure the time it takes each ball to hit the floor. You also need to measure very accurately distance from which each ball is dropped.. Each lab group should select 1 wiffle ball, 1 tennis ball and 1 baseball. In order to measure the distance, use a meter stick. 3. Time it takes each ball to hit the floor is measured using a stopwatch. 4. The balls should each first be dropped from rest from the height of 1.5 m above the floor. Measure the time it takes the ball to hit the floor. Record this number in seconds, in the data table. Perform 4 drops for each ball. 5. Lab partners should take turns dropping the balls so that everyone has dropped all balls four times each. 6. Using the meter stick, measure the drop distance, in units of meters, from the dropping point to the floor. Record this value in your data table as y. 7. Find the second dropping point of.5 m above the floor. 8. Drop and time all balls four times each. Record the drop times in the tables below. 9. Lab partners should alternate positions so that everyone has dropped both balls four times each from the height of.5 m from the floor. 10. Calculate the value of gravitational acceleration g. 11. Determine the percentage difference between the calculated value of g and the actual value near the surface of the earth, which is 1 m/s. ( x The percentage difference is found using the following equation: ) 100% 1. Calculate the velocity of an object just : v vo + gt =. Page

3 Data Table Part I: wiffle ball Objects: Ball with mass: m = kg, distance dropped d = 1.5 m Objects: Ball with mass: m = kg, distance dropped d =.5 m Part II: Tennis Ball Objects: with mass: m = kg, distance dropped d = 1.5 m Page 3

4 Objects: with mass: m = kg, distance dropped d =.5 m Part III: the Objects: with mass: m = kg, distance dropped d = 1.5 m Objects: with mass: m = kg, distance dropped d =.5 m Page 4

5 Questions 1. Do travel times vary with the mass of the ball? Why?. Which ball has the largest velocity just before they hit the floor and why? 3. What is the gravity at h = 1000 km above? 4. What happened to the value of gravitational acceleration as you move closer to the center of the Earth? 6. At what point on the Earth is the gravitational acceleration at maximum? Value of "g" Acceleration due to gravity at different locations Place Latitude Altitude "g" in m/s North Pole 90 o 0m 3 Green Land 70 o 0m 5 Stockholm 59 o 45m 18 Brussels 51 o 10m 11 New York 41 o 38m 03 Chicago 4 o 18m 03 Denver 40 o 1638m San Francisco 38 o 114m 00 Page 5