Concept explainers
(a)
To Prove:The experimental magnitude of the free-fall acceleration is given by
(a)
Explanation of Solution
Introduction:
The distance
Here,
The marble is dropped from a point at a negligible distance from the first light gate. Therefore, the distance travelled by the marble in the measured time interval
Therefore, substitute 0 for
Simplify for
Conclusion:
Thus, it is proved that the experimental value of the free fall acceleration is given by the expression,
(b)
The expected value of
(b)
Answer to Problem 113P
The expected value of the time
Explanation of Solution
Given:
The position of the first light gate (at the edge of the table)measured from the floor
The position of the second light gate when measured from the floor
The standard value of the free-fall acceleration
Formula used:
The time taken for the marble to fall between the two light gates is given from equation (2) and is written as
Where,
Calculation:
From equations (3) and (4)
Substitute the given values of variables in equation (5).
Conclusion:
Thus, the expected value of the time
(c)
The value of the
(c)
Answer to Problem 113P
The value of the free fall acceleration determined in the current experimental setup would be
Explanation of Solution
Given:
The height of the edge of the table from the floor
The position of the first light gate (at the edge of the table) measured from the table
The position of the second light gate when measured from the table
The standard value of the free-fall acceleration
Formula used:
The marble is dropped from the edge of the table with a velocity
Assume the origin to be located on the table and the initial velocity is zero.
The time
Here,
The value of the free fall acceleration that would be obtained from this experiment (with errors) is given by the following expression
The percentage difference between the calculated and the standard values of the free fall acceleration is given by
Calculation:
Calculate the speed of the marble when it passes through the first light gate by substituting the values of the variables in equation (6).
Calculate the distance between the light gates using equation (8).
Substitute the values of the variables (calculated and given) in equation (7) and write a quadratic equation in
Solve for
Taking the positive root alone
The person performing the experiment does not take into account the difference in the positioning of the light gates. Hence, the value of free fall acceleration
Substitute the values of variables in equation (9) and calculate the experimental value of the free fall acceleration.
Calculate the percentage difference between the measured value and the standard value is found using equation (10).
Conclusion:
Thus, the value of the free fall acceleration determined in the current experimental setup would be
Want to see more full solutions like this?
Chapter 2 Solutions
Physics for Scientists and Engineers
- For two decades, teams sought a connection between the Flint Ridge cave system and Mammoth cave in Kentucky. When the connection was finally discovered, the combined system was declared the world’s largest cave (more than 200 km long). The team that found the connection had to crawl, climb and squirm through countless passages, traveling a net 2.6 km westward, 3.9 km southward, and 25 km upward. What was their displacement from start to finish?arrow_forwardAs a city planner, you receive complaints from local residents about the safety of nearby roads and streets. One complaint concerns a stop sign at the corner of Pine Street and 1st Street. Residents complain that the speed limit in the area (55 mph) is too high to allow vehicles to stop in time. Under normal conditions this is not a problem, but when fog rolls in visibility can reduce to only 155 ft. Since fog is a common occurrence in this region, you decide to investigate. The state highway department states that the effective coefficient of friction between a rolling wheel and asphalt ranges between 0.536 and 0.599, whereas the effective coefficient of friction between a skidding (locked) wheel and asphalt ranges between 0.350 and 0.480. Vehicles of all types travel on the road, from small VW bugs weighing 1410 lb to large trucks weighing 8250 lb. Considering that some drivers will brake properly when slowing down and others will skid to stop, calculate the minimum and maximum…arrow_forwardAs a city planner, you receive complaints from local residents about the safety of nearby roads and streets. One complaint concerns a stop sign at the corner of Pine Street and 1st Street. Residents complain that the speed limit in the area (55 mph) is too high to allow vehicles to stop in time. Under normal conditions this is not a problem, but when fog rolls in visibility can reduce to only 155 ft. Since fog is a common occurrence in this region, you decide to investigate. The state highway department states that the effective coefficient of friction between a rolling wheel and asphalt ranges between 0.536 and 0.599, whereas the effective coefficient of friction between a skidding (locked) wheel and asphalt ranges between 0.350 and 0.480. Vehicles of all types travel on the road, from small VW bugs weighing 1310 lb to large trucks weighing 8.40 x 10° lb. Considering that some drivers will brake properly when slowing down and others will skid to stop, calculate the minimum and maximum…arrow_forward
- As a city planner, you receive complaints from local residents about the safety of nearby roads and streets. One complaint concerns a stop sign at the corner of Pine Street and 1st Street. Residents complain that the speed limit in the area (55 mph) is too high to allow vehicles to stop in time. Under normal conditions this is not a problem, but when fog rolls in visibility can reduce to only 155 ft. Since fog is a common occurrence in this region, you decide to investigate. The state highway department states that the effective coefficient of friction between a rolling wheel and asphalt ranges between 0.689 and 0.770, whereas the effective coefficient of friction between a skidding (locked) wheel and asphalt ranges between 0.450 and 0.617. Vehicles of all types travel on the road, from small VW bugs weighing 1210 lb to large trucks weighing 8640 lb. Considering that some drivers will brake properly when slowing down and others will skid to stop, calculate the minimum and maximum…arrow_forwardDanny takes his dog to the local dog park every morning, as well (dog-walking is very popular in this area). He walks with his dog 6 blocks east, 6 blocks north, and 6 west in order to get to the park. If each block is 50 meters, what distance did Danny travel in meters? Answer: marrow_forwardB (3,3) E (5,0) A (0,0) C (7,3) D (7,-6) Note: all coordinates in meters - not to scale! A robot has been designed and is tested on the course above (A-B-C-D-E). If the robot takes 3.4 minutes to complete the course, what is the robot's average speed? Answer: Om/s Xarrow_forward
- Suppose we are told that the acceleration a of a particle moving with uniform speed ν in a circle of radius r is proportional to some power of r, say rn, and some power of ν, say νm. Determine the values of n and m and write the simplest form of an equation for the acceleration.arrow_forwardA supersonic car (SSC) has a mass of 9615 kilograms on Earth. The SSC has a fuel consumption rate of 0.8 gallons per second and can store up to 300 gallons of fuel. Assuming the SSC begins with a maximum amount of fuel and constantly operates at the velocity of 763 miles per hour What is the maximum distance, in units of meters , the SSC can travel before running out of fuel?arrow_forwardA tortoise and a hare are competing in a 1200-meter race. The arrogant hare decides to let the tortoise have a 820-meter head start. When the start gun is fired the hare begins running at a constant speed of 8 meters per second and the tortoise begins crawling at a constant speed of 4.5 meters per second. Which of the following formulas expresses the distance between the tortoise and the hare in meters, d, in terms of the number of seconds, t, since the start gun was fired? Od = 820 - 8t Od = 820 + 3.5t Od = 820 - 3.5t Od = 1200 3.5t Od = 1200 - (8t + 4.5t)arrow_forward
- Your car is parked at the high school. After school you take off and travel for 27 km towards lowaCity. At this point, you realize you forget your wallet and travel back to Tipton for 15 km beforeyou find your wallet was just on the floor. You turn back and head towards lowa city for 36 km.What is your displacement?arrow_forwardA pumpkin is shot straight up with an initial speed of 5.9 m/s. What is the maximum height it can reach, in meters? Use g = 10 m/s2.Your answer needs to have 2 significant figures, including the negative sign in your answer if needed. Do not include the positive sign if the answer is positive. No unit is needed in your answer, it is already given in the question statement.arrow_forwardAs a city planner, you receive complaints from local residents about the safety of nearby roads and streets. One complaint concerns a stop sign at the corner of Pine Street and 1st Street. Residents complain that the speed limit in the area (89 km/h) is too high to allow vehicles to stop in time. Under normal conditions this is not a problem, but when fog rolls in visibility can reduce to only 47 meters. Because fog is a common occurrence in this region, you decide to investigate. The state highway department states that the effective coefficient of friction between a rolling wheel and asphalt ranges between 0.842 and 0.941, whereas the effective coefficient of friction between a skidding (locked) wheel and asphalt ranges between 0.550 and 0.754. Vehicles of all types travel on the road, from small cars with a mass of 531 kg to large trucks with a mass of 3463 kg. Considering that some drivers will brake properly when slowing down and others will skid to stop, calculate the minimum and…arrow_forward
- Principles of Physics: A Calculus-Based TextPhysicsISBN:9781133104261Author:Raymond A. Serway, John W. JewettPublisher:Cengage Learning