Download Experimental Verification of Work Energy Theorem

Dier Yassin Secondary School
Lebanon, Tyre, Al Buss Camp
Scholastic Year 2010 - 2011
Mid Year Exam in Physics
Name: .........................................................
Grade 11 (Sc)
Date: 7 / 2 / 2011
Duration: 120 mints.
First Question: (Parts A and B are independent) (10pts)
A. Phase Difference between Two Signals-Speed of Sound
(4pts)
A speaker (H) emits a sinusoidal sound of frequency f. the sound is captured by two microphones M1 and
M2.the microphones are connected to the channels of the oscilloscope.
1. The microphones are placed together at a point O in front of the speaker.
Why are the signals visualized on the screen of the oscilloscope are in phase?
2. We fix M1 and move M2 away from the speaker, along the axis Ox of the speaker, to a point A of abscissa
d=66mm (d<λ). We obtain the oscillograms on the figure below.
(A)
(H)
d
O
(B)
A
M1
a.
b.
c.
d.
e.
x
M2
Calculate the frequency of sound f. the horizontal sensitivity of the oscilloscope is Sh=0.2ms/div
Correspond, with justification, to each microphone its oscillogram.
Calculate, using the oscilloscope, the time taken by the sound wave to move from M1 to M2.
Deduce the value of the speed of sound in air.
Calculate the wavelength of wave A and that of B. Conclude
B. Studying the Interference on the Surface of the Water
(6pts)
A fork carrying two ends S1 and S2, 5cm apart, is tied to a vibrator. The points slightly touch the horizontal
surface of a water tank. The vibrator functions with a frequency 25Hz and amplitude 4mm. Waves produced on
the surface of the water with a speed of 0.5m/s
1. Name the conditions of interference.
2. What are the frequencies of S1 and S2 and their amplitudes?
3. Describe the fringes between S1 and S2.
4. a. Calculate the numbers of bright and dark fringes between S1 and S2.
b. What is the amplitude of a point on bright fringe and that of point on a dark fringe?
5. What is the amplitude of the point I on the surface of water such that: S1I=15cm and S2I=25cm?
6. We illuminate the pattern between S1 and S2 with a stroboscope of frequency fe=101 flashes/s. What do
you observe?
Second Question: (Parts A and B are dependent) (8pts)
A. Center of Mass
(3pts)
A uniform homogenous rod AB of mass M=250gm and length L=32cm is bent at O in the form as shown in
L
the adjacent figure such that OB  .
A
O
4
 
Show that the position of the center of mass is: OG  (9i  j ) in cm.
B

Where i is a unit vector along OA and j along OB .
B. Newton’s Second law of Rotational Dynamics
(5pts)
The above bent rod is allowed to rotate around a frictional vertical axis (Δ) passing through O. To do this, a
string is enrolled about a light pulley coupled with the bent rod and drawn with a horizontal constant moment force
M=4N.m.The rod starts rotation from rest at t=0s and undergoes 500turns during t1=5s just before the sting
release the sphere.
1
Given the moment of inertia of the uniform rod about an axis passing at its extremity: I  ml 2
3
A. Before the string is released
1. Calculate the angular acceleration of the sphere and its angular velocity at t1.
2. Determine the magnitude of the moment of frictional force.
O
B. After the string is released
A
1. Determine the nature of motion.
2. Find the number of rotations of the rod before it stops.
B
Third Question: Experimental Verification of Work Energy Theorem
(10pts)
A puck of mass m=0.5kg is left without initial velocity from a point A0 on an inclined plane makes an angle α
with the horizontal. The puck starts registrations at the same instant τ=50ms.
1. Determine the speed of a puck at A4 and A6.
2. Determine the kinetic energy at A4 and A6.
A0

Deduce the variation of the kinetic energy ΔEk.
3. Calculate the acceleration of motion of a puck.
4. Calculate  Fex on a puck during motion.
α
5. Determine ƩWex of the external forces between A4 and A6.
6. Compare ΔEk with ƩWex .
7. Calculate the angle α.
8. Determine the variation of gravitational potential energy ΔEpg between A4 and A6.
9. Compare ΔEpg with ΔEk. Is there resistive forces? Justify.
0
A1
1
cm
A2
2
3
A3
4
5
A4
6
7
A5
8
9
10
A6
11
12
13
A7
Fourth Question: Non Conservation of Mechanical Energy
(12pts)
A solid (S) of mass m=0.6kg, launched
with a speed V0 along the line of greatest slope
of a plane inclined by an angle α with respect to
the horizontal as shown in figure (a).
In figure (b) we represent the mechanical
energy Em and the gravitational potential energy
Epg of the system [(S);Earth] as shown of the
position x of (S).
(S)
x
Vo
o
α
Epg=0
Fig (a)
The zero level of the gravitational potential energy is the horizontal plane passing through O.
Given g=10m/s2.
E (J)
1. The graph shows that the mechanical energy of the
system is not conserved. Justify.
2. What is graphically the values of the potential and
kinetic energy of the system for x=3m?
3
3. Deduce the value of α.
Em
4. Calculate the initial value of the kinetic energy.
2
Deduce the value of V0 .
5. The non-conservation of mechanical energy is due
E pg
to the force of friction between (S) and the support.
1
Calculate the value of friction supposed constant.
6. Determine graphically the value of x and of Em for
0
which Ek=Epg.
1
2
3
0
Deduce again the value of α.
7. Exploit from the graph a relation between Em and x.
Fig (b)
What does the slope represent? Justify.
8. Determine the average power done by friction until (S) covers x=3m.
Good work
Mr. I. Hanafi
x (m)