PLEASE SEE ADDITIONAL QUESTION AT BOTTOM.
A pendulum was set up and measurements were made to enable the mechanical energy to be calculated at the start position S and the lowest point of the pendulums swing L.
The mass of the pendulum bob was determined on an electronic scale and its diamter was measured using calipers. The initial height was measured with a meter stick. At the lowest point of its swing, the pendulum bob broke a photogate light beam. The time interval that the light was interrupted was recorded on an electronic timer attached to the photogate.
Use the following data to complete a report.
MAss of pendulum bob = 240.3 g
Diameter of pendulum bob = 3.50 cm
Initial height of pendulum bob = 48.0 cm
Length of pendulum string = 2.14 m
Time interval of photogate light interruption = 11.8 ms
Your report should include the following:
(a) conclusion as to whether or not the pendulum demonstrated the law of conservation of energy
(b) calculations of the efficiency of the pendulum as a mechanical machine
I am really confused how to even start this question. I think that I should figure out the Emechanical = Ek + eg
=1/2(240.3)(0) + 240.3(9.8)(.48)
=1130.37J
but have no idea how to calculate the speed of when it hit. I don't know where to go from here at all, please help!
PHYSICS - Damon, Saturday, January 30, 2010 at 4:10pm
The clue is the diameter of the bob
it broke the beam for 11.8 *10^-3 seconds
it is .035 meters in diameter
so it went
.035 meters in 11.8^10^-3 seconds
which is about 2.97 meters/s
typo, left m out - Damon, Saturday, January 30, 2010 at 4:16pm
(1/2) 240.3 v^2 = mgh = 1130.37
v^2 = 9.407
v = 3.067 ideally but we only measured 2.97 m/s so some energy got lost along the way like air friction and stuff
DAMON: I understand how you got the 1130.37, but don't know how you got v^2. Can you please explain how you got there?...and what are you using for height in the second part of the question...
physics - Damon - bobpursley, Saturday, January 30, 2010 at 5:10pm
1/2 240.3 v^2=1130.37
120.1 v^2=1130.37
v^2= 1130.37/120.1= 9.407
DAMON; thanks for helping so much but I still need some clarification. So the speed when it hit the beam was 2.97 m/s, what does the 3.07 m/s speed represent?
When i subbed in the new speed of 3.07 into the Ek + Eg formula, i got this:
=1/2mv^2 + mgh
=1/2(240.3)(3.07)^2
=1132.4
i am not sure what the 1132.4 actually represents though..please help me more!
physics - Damon - bobpursley, Saturday, January 30, 2010 at 5:36pm
It represents the mechanical energy in joules at the speed gate, at the bottom.
Bob - but if this 1132.4 J is the mechanical energy at the bottom, and the mechanical energy at the top is 1130.37 J, then wouldn't that make is seem like energy was GAINED, rather than lost like DAMON first said?
also,what would percent efficiency equal?
physics - BOB - Damon, Saturday, January 30, 2010 at 6:29pm
The 3.07 is what it should have been if it had all the energy at the bottom that it started with at the top.
It ended up going slower, 2.97, with less energy. Some was lost.
physics - BOB - Damon, Saturday, January 30, 2010 at 6:45pm
(1/2) 240.3 v^2 = mgh = 1130.37
v^2 = 9.407
v = 3.067
this is simply saying that if there is no loss of energy due to friction, the kinetic energy at the bottom (1/2) m v^2 will be the same as the potenital energy at the top m g h
the actual speed measured was less so the actual energy at the bottom is
(1/2) 240.3 (2.97)^2 = 1059.83
so you lost
1130.37 - 1059.83 Joules to friction
and your efficiency is
100 (1130.37 - 1059.83)/1130.37
WOULD PERCENT EFFICIENCY NOT EQUAL:
KINETIC ENERGY GAINED/ENERGY AVAILABLE x 100
so that
1059.83/1130.37 X 100
=94%
because I thought the forumla that you used, Damon, was to calculate percent of energy lost...please clarify! Thanks so much!
percent efficiency: (final energy)/initial energy * 100
so I see about 1059/1130 * 100=93.7 percent
Now, on a: demonstrate the law of conservation of energy:
Does initial energy= final energy?
not exactly, some mechanical energy was lost, probably to friction.
Dude, you might want to convert your units before anything else .. M is always in kg not g. Your distance should always be in m not cm.
To start solving this problem, you need to understand the concept of mechanical energy and the law of conservation of energy. Mechanical energy is the sum of the kinetic energy (Ek) and the gravitational potential energy (eg). According to the law of conservation of energy, the total mechanical energy of a system remains constant as long as there is no external force doing work on the system.
In this case, you correctly calculated the gravitational potential energy at the starting position using the formula eg = mgh, where m is the mass, g is the acceleration due to gravity, and h is the height. The value you calculated, 1130.37J, represents the gravitational potential energy at the start.
Next, you want to calculate the kinetic energy (Ek) at the lowest point of the swing. Since the pendulum bob broke a photogate light beam, you can use the time interval of the interruption and the diameter of the bob to find the speed at the lowest point.
The diameter of the bob, 3.50cm, tells you the distance it traveled when it broke the beam. In this case, it moved approximately 0.035m in 11.8ms (0.0118s). To find the speed, you divide the distance by the time: v = d/t = 0.035m / 0.0118s ≈ 2.97m/s.
Now, you can use the speed to calculate the kinetic energy at the lowest point. Use the formula Ek = 1/2 mv^2, where m is the mass and v is the speed. Substituting the values, we get Ek = 1/2 (240.3g) (2.97m/s)^2. Evaluating this expression, you should get Ek ≈ 1059.83J.
This value represents the kinetic energy at the lowest point. Notice that it is less than the gravitational potential energy at the start. This means that some energy was lost, most likely due to factors like friction and air resistance.
To calculate the efficiency of the pendulum as a mechanical machine, you can use the formula: Efficiency = (Energy Gained / Energy Available) x 100. In this case, the energy gained is the kinetic energy at the lowest point (1059.83J), and the energy available is the initial gravitational potential energy (1130.37J).
Substituting these values into the formula, we get Efficiency = (1059.83J / 1130.37J) x 100 ≈ 93.96%.
Therefore, the percent efficiency is approximately 94%. This means that 94% of the initial energy was converted into useful work, while approximately 6% was lost due to factors like friction and air resistance.