Conservation of Energy With Air track

Conservation of Mechanical Energy
View the following video, which demonstrates and explains the experiment in which a glider accelerates along an airtrack due to the slight tilt of the track.
https://cuny907- my.sharepoint.com/:v:/g/personal/darya_krym87_login_cuny_edu/ERH9SHqxvytEmSsSKL3BOZ4BkXE
wTeVD00COKK1B8YMXXQ?e=eFZ9cB
Theoretical Principles
The motion of the glider can be analyzed in two different, equivalent ways. The first is using Newtons Law, i.e. the relationship between force and acceleration. The second is using energy conservation.
Compared to our previous discussions of forces causing acceleration, there is a small new subtlety here, which is that there is a force acting on the object in a direction, which is neither along the direction of motion, nor perpendicular to it, but at some arbitrary angle. To figure out the acceleration, we must
find the component of the force, which is along (i.e. parallel to) the direction of motion. The force which is at an angle to the direction of motion of the glider, is the gravitational force of the Earth. The part of the gravitational force which is parallel to the track is given by Fg=Mg sin where is the angle between
the track and the horizontal1. M is the gliders mass. If we assume there are no other forces along the direction of motion, we conclude that the acceleration is (g sin ). Note also, that we can express the sine in terms of the ratio of height change to position change. sin =(12)(x2x1)
The velocities of the glider at the two photogate locations are related by the familiar equation v22 v12=2a(x2x1)
where all these quantities are measured in the direction parallel to the track. v2 is the velocity at position x2 of the second (lower) photogate. v1 is the velocity at position x1 of the first (higher) photogate.
This equation can be used to get an alternative expression for the acceleration. =v22 v122(x2x1)
Going back to the previous equation, if we multiply it by M/2 and use the expression for sin , we get
12M v22 12M v12=Mg(12)
We can identify the following quantities in this equation.
Kinetic energy: K=12M v2
Gravitational potential energy: U=M g h
1 Look at your textbook, if you need a review https://openstax.org/books/college-physics/pages/4-5-
normal-tension-and-other-examples-of-forces
The equation can then be written as K2+U2=K1+ U1
The sum of the kinetic energy and the gravitational potential energy is sometimes referred to as mechanical energy. This last equation says that the mechanical energy is conserved i.e. it remains constant in time.
11/22/2021 Conservation of Energy With Air track • Student Homework Help
https://www.studenthomeworkhelp.com/conservation-of-energy-with-air-track/ 2/4
Note that we got this equation by assuming there were no forces other than gravity along the track. So, for example, the effect of friction is not taken into account here.
In the above discussion, reformulating the physics in terms of kinetic and potential energy is just a matter of algebraic manipulation. However, the equation is actually valid in more general situations. For example, the equation would still hold if the track was curved and if the track ascended and descended to several different heights between the initial and final points.
Assignment
The experiment is performed for three different masses, in two trials, corresponding to two different tilts of the track.
Use the data in the accompanying excel file and fill out the two tables. You are asked to show that the sum of the kinetic energy with the gravitational potential energy remains constant throughout the motion. You are also asked to find the acceleration of the glider from g and from the velocities.
Answer the questions below.
Questions
Watch the video and fill out the excel file first. Then look at questions.
1. How is the effect of friction counteracted in the experiment?
2. How is the speed of the glider measured in the experiment?
3. In principle, one could think about triggering the photogate on the glider itself, instead of using a flag, i.e. record the time it takes the entire glider to pass the photogate. Would this make the measurement of the speed more or less accurate? Hint: the glider is accelerating everywhere along the track,
including as it is passing through the photogate.
4. If two people choose two different levels as the 0 height i.e. one person chooses the lab floor and another the table top, would the potential energy values be different? Could this spoil agreement between the energy sums?
5. Comment on whether the experiment demonstrates conservation of mechanical energy.
6. Comment on whether the two different calculations of the acceleration agree.