Download Conservation of mechanical energy

Kingdom Saudi Arabia, Riyadh
Imam Mohammed bin Saud University
College of science
Physics department
281 physics – section 292
2nd term – 2011
3rd lecture – 3rd experiments
Tr.Muneerah Alaqeel
Conservation of mechanical energy
 Aim
To find the final velocity of an object sliding an incline with constant
acceleration using:
1. Energy conservation law.
2. Kinematics equations.
Verify conservation of mechanical energy.
 Theory
Energy is the ability to do work and is measured by Jouls.
Mechanical energy has two different forms:
Potential energy is the energy an object stores due to its
position.
The gravitational potential energy is given by:
PE = m g h
(1)
Where m is the mass of the object, g is the gravitational
acceleration and h is the height of the object.
Kinetic energy is the energy of motion.
The kinetic energy is given by:
KE = (1/2) m v2
(2)
An object held at some height h above the floor has no
kinetic energy (v=0). If the object is dropped, it falls to the floor; as
it falls, its speed and thus its kinetic energy increase, while the
potential energy of the system decreases. In other words, the sum
of the kinetic K and potential energies U – the total mechanical
energy E – remains constant. This is an example of the principle of
conservation of mechanical energy.
The total mechanical energy E, of any isolated system of
objects that interact only through conservative forces, is
defined as the sum of the kinetic and potential energies, we can
write
E  K U
(3)
We can state the principle of conservation of energy as Ei  E f , and
so we have
Ki  U i  K f  U f
(4)
Trolley
xB  xA  d
A
hA
Track
B
hB
Figure1. The incline makes the trolley to move down with a
constant acceleration
If we apply the equation (4) to figure 1, we can write it as:
K A U A  KB UB
(5)
The velocity deduced from the principle of conservation of energy:
vc  2 g hA  hB 
(6)
Where:
g is acceleration of the gravity, hA initial height, hB final height.
The velocity from the kinematics equations:
vk 
2d
tB
(7)
Where:
d is distance (m), tB the time needs to travel distance (s)
 Equipment
Track – trolley – holding magnet – electronic stop clock – light
barrier – cables.
 Procedure
1. Make the track inclined.
2. use the holding magnet to hold the trolley.
3. Connect the stop clock with a light barrier and put the light
barrier at a certain distance and record the distance that the
trolley should travel.
4. Measure the height at the beginning (hA) and at the end of
the motion of the trolley (hB).
5. Release the trolley by pressing the START/STOP key at the
electronic stop clock and find the time it needs to travel the
distance three times and find the average time of traveling.
6. Reset the stopclock to zero by pressing the RESET key.
7. Move the light barrier to change the distance & height for 4
times then calculate the time in each distance as in step 5.
(make the differences between each distance 10 cm at least)
8. Use the equations to find the final velocity. The two values
should be equal.
9. Plot a graph between
v k versus v c . ( v k is the y-axis and v c
is the x-axis) Each axis should be labeled and appropriate
units indicated. The graph should have a title.
10.
11.
Determine the slope from the graph
Find percentage error.
12.
Verify conservation of mechanical energy by
calculating potential energy & kinetic energy.
13.
Remember to write your data in table.
Table1
d
(m)
hA
hB
(m)
(m)
(m)
t1
t2
(s)
(s)
t3
(s)
t avr
(s)
vk
(m/s)
vc
(m/s)
(m/s)2
Table2
PEi (J)
KEi (J)
Ei (J)
PEf (J)
KEf (J)
Ef (J)
Ei = Ef (J)
Homework
Q1: what is potential energy? (Definition & equation)
Q2: what is kinetic energy? (Definition & equation)
Q3: what is mechanical energy? (Definition & equation)
Q4: what is principle of conservation of mechanical energy?
(Definition & equation)
Q5: proof equation 6 & 7.
Q6: Calculate the potential energy, kinetic energy, mechanical
energy, velocity, and height of the skater at the various locations.
Answer:
1.
0 J; 1.92 kJ; 1.92 kJ
2.
588 J; 1.33 kJ; 1.92 kJ; 6.66 m/s
3.
1.92 kJ; 0 J; 1.92 kJ; 0 m/s ; 3.27 m