training olimpiade fisika - problems 1 - 30
TRANSCRIPT
8/11/2019 Training Olimpiade Fisika - Problems 1 - 30
http://slidepdf.com/reader/full/training-olimpiade-fisika-problems-1-30 1/40
TrainingOlimpiade
Fisika
Zainal AbidinSMAN 3 Bandar Lampung
Jl. Khairil Anwar 30 Tanjung Karang Pusat
Kota Bandar Lampung, Indonesia 35115
Tel: +62-721-255600; Fax: +62-721-253287;
Email: [email protected]
8/11/2019 Training Olimpiade Fisika - Problems 1 - 30
http://slidepdf.com/reader/full/training-olimpiade-fisika-problems-1-30 2/40
8/11/2019 Training Olimpiade Fisika - Problems 1 - 30
http://slidepdf.com/reader/full/training-olimpiade-fisika-problems-1-30 3/40
I E Irodov
8/11/2019 Training Olimpiade Fisika - Problems 1 - 30
http://slidepdf.com/reader/full/training-olimpiade-fisika-problems-1-30 4/40
8/11/2019 Training Olimpiade Fisika - Problems 1 - 30
http://slidepdf.com/reader/full/training-olimpiade-fisika-problems-1-30 5/40
Problems:
1.1 – 1.388
8/11/2019 Training Olimpiade Fisika - Problems 1 - 30
http://slidepdf.com/reader/full/training-olimpiade-fisika-problems-1-30 6/40
Training 1:
Problems
1.1 – 1.30
2nd September, 2014
8/11/2019 Training Olimpiade Fisika - Problems 1 - 30
http://slidepdf.com/reader/full/training-olimpiade-fisika-problems-1-30 7/40
1.1. A motorboat going downstream overcame a
raft at a point A; σ = 60 min later it turned
back and after some time passed the raftat a distance l = 6.0 km from the point A.
Find the flow velocity assuming the duty of
the engine to be constant.
8/11/2019 Training Olimpiade Fisika - Problems 1 - 30
http://slidepdf.com/reader/full/training-olimpiade-fisika-problems-1-30 8/40
1.2. A point traversed half the distance with avelocity v o. The remaining part of the
distance was covered with velocity v for half
the time, and with velocity v for the other half
of the time. Find the mean velocity of the
point averaged over the whole time of
motion.
8/11/2019 Training Olimpiade Fisika - Problems 1 - 30
http://slidepdf.com/reader/full/training-olimpiade-fisika-problems-1-30 9/40
1.3. A car starts moving rectilinearly, first withacceleration ω = 5.0 m/s2 (the initial velocity
is equal to zero), then uniformly, and finally,
decelerating at the same rate w, comes to astop. The total time of motion equals σ = 25 s.
The average velocity during that time is
equal to <v> = 72 km per hour. How longdoes the car move uniformly?
8/11/2019 Training Olimpiade Fisika - Problems 1 - 30
http://slidepdf.com/reader/full/training-olimpiade-fisika-problems-1-30 10/40
1.4. A point moves rectilinearly in one direction.
Fig. 1.1 shows the distance s traversed bythe point as a function of the time t .
Using the plot find:
(a) the average velocity of the point during thetime of motion;
(b) the maximum velocity;
(c) the time moment t o at which the
instaneous velocity is equal to the mean
velocity averaged over the first t o
seconds.
8/11/2019 Training Olimpiade Fisika - Problems 1 - 30
http://slidepdf.com/reader/full/training-olimpiade-fisika-problems-1-30 11/40
8/11/2019 Training Olimpiade Fisika - Problems 1 - 30
http://slidepdf.com/reader/full/training-olimpiade-fisika-problems-1-30 12/40
1.5. Two particles, 1 and 2, move withconstant velocities v 1 and v 2. At the
initial moment their radius vectors are
equal to r 1 and r 2.
How must these four vectors be
interrelated for the particles to collide?
8/11/2019 Training Olimpiade Fisika - Problems 1 - 30
http://slidepdf.com/reader/full/training-olimpiade-fisika-problems-1-30 13/40
1.6. A ship moves along the equator to the eastwith velocity v o = 30 km/hour. The
southeastern wind blows at an angle φ = 600
to the equator with velocity v = 15 km/hour.Find the wind velocity v ' relative to the ship and
the angle φ' between the equator and the wind
direction in the reference frame fixed to the ship.
8/11/2019 Training Olimpiade Fisika - Problems 1 - 30
http://slidepdf.com/reader/full/training-olimpiade-fisika-problems-1-30 14/40
1.7. Two swimmers leave point A on one bank of
the river to reach point B lying right across on
the other bank. One of them crosses the riveralong the straight line AB while the other swims
at right angles to the stream and then walks the
distance that he has been carried away by thestream to get to point B. What was the velocity
u of his walking if both swimmers reached the
destination simultaneously? The stream velocityv o = - 2.0 km/hour and the velocity v ’ of each
swimmer with respect to water equals 2.5 km
per hour.
8/11/2019 Training Olimpiade Fisika - Problems 1 - 30
http://slidepdf.com/reader/full/training-olimpiade-fisika-problems-1-30 15/40
1.8. Two boats, A and B, move away from a buoy
anchored at the middle of a river along themutually perpendicular straight lines:
the boat A along the river, and the boat B
across the river. Having moved off an equaldistance from the buoy the boats returned.
Find the ratio of times of motion of boats σ A / σ B
if the velocity of each boat with respect to wateris η = 1.2 times greater than the stream
velocity.
8/11/2019 Training Olimpiade Fisika - Problems 1 - 30
http://slidepdf.com/reader/full/training-olimpiade-fisika-problems-1-30 16/40
1.9. A boat moves relative to water with a
velocity which is n = 2.0 times less than the
river flow velocity. At what angle to the
stream direction must the boat move to
minimize drifting?
8/11/2019 Training Olimpiade Fisika - Problems 1 - 30
http://slidepdf.com/reader/full/training-olimpiade-fisika-problems-1-30 17/40
1.10. Two bodies were thrown simultaneouslyfrom the same point: one, straight up, and
the other, at an angle of θ = 60 ° to the
horizontal. The initial velocity of each bodyis equal to V o = 25 m/s. Neglecting the air
drag, find the distance between the bodies
t = 1.70 s later.
8/11/2019 Training Olimpiade Fisika - Problems 1 - 30
http://slidepdf.com/reader/full/training-olimpiade-fisika-problems-1-30 18/40
1.11. Two particles move in a uniformgravitational field with an acceleration g .
At the initial moment the particles were
located at one point and moved with ,velocities v 1 = 3.0 m/s and v 2 = 4.0 m/s
horizontally in opposite directions.
Find the distance between the particles atthe moment when their velocity vectors
become mutually perpendicular.
8/11/2019 Training Olimpiade Fisika - Problems 1 - 30
http://slidepdf.com/reader/full/training-olimpiade-fisika-problems-1-30 19/40
1.12. Three points are located at the vertices ofan equilateral triangle whose side equals a.
They all start moving simultaneously with
velocity v constant in modulus, with the firstpoint heading continually for the second,
the second for the third, and the third for
the first. How soon will the pointsconverge?
8/11/2019 Training Olimpiade Fisika - Problems 1 - 30
http://slidepdf.com/reader/full/training-olimpiade-fisika-problems-1-30 20/40
1.13. Point A moves uniformly with velocity v so
that the vector v is continually "aimed" at
point B which in its turn moves rectilinearly
and uniformly with velocity u < v . At the
initial moment of time v ┴ u and the points
are separated by a distance l . How soon
will the points converge?
8/11/2019 Training Olimpiade Fisika - Problems 1 - 30
http://slidepdf.com/reader/full/training-olimpiade-fisika-problems-1-30 21/40
1.14. A train of length l = 350 m starts moving rectilinearlywith constant acceleration ω = 3.0•10-2 m/s2; t = 30 s
after the start the locomotive headlight is switched on
(event 1), and σ = 60 s after that event the tail signal
light is switched on (event 2). Find the distance
between these events in the reference frames fixed to
the train and to the Earth. How and at what constant
velocity V relative to the Earth must a certain referenceframe K move for the two events to occur in it at the
same point?
8/11/2019 Training Olimpiade Fisika - Problems 1 - 30
http://slidepdf.com/reader/full/training-olimpiade-fisika-problems-1-30 22/40
1.15. An elevator car whose floor-to-ceilingdistance is equal to 2.7 m starts ascending
with constant acceleration t = 1.2 m/s2; 2.0 s
after the start a bolt begins falling from theceiling of the car. Find:
(a) the bolt's free fall time;
(b) the displacement and the distance coveredby the bolt during the free fall in the
reference frame fixed to the elevator shaft.
8/11/2019 Training Olimpiade Fisika - Problems 1 - 30
http://slidepdf.com/reader/full/training-olimpiade-fisika-problems-1-30 23/40
1.16. Two particles, 1 and 2 , move with constantvelocities v 1 and v 2 along two mutually
perpendicular straight lines toward the
intersection point O. At the moment t = 0the particles were located at the distances l 1
and l 2 from the point O.
How soon will the distance between theparticles become the smallest? What is it
equal to?
8/11/2019 Training Olimpiade Fisika - Problems 1 - 30
http://slidepdf.com/reader/full/training-olimpiade-fisika-problems-1-30 24/40
1.17. From point A located on a highway (Fig. 1.2)one has to get by car as soon as possible to
point B located in the field at a distance l
from the highway. It is known that the carmoves in the field η times slower than on
the highway. At what distance from point D
one must turn off the highway?
8/11/2019 Training Olimpiade Fisika - Problems 1 - 30
http://slidepdf.com/reader/full/training-olimpiade-fisika-problems-1-30 25/40
8/11/2019 Training Olimpiade Fisika - Problems 1 - 30
http://slidepdf.com/reader/full/training-olimpiade-fisika-problems-1-30 26/40
1.18. A point travels along the x axis with avelocity whose projection v x is presented as
a function of time by the plot in Fig. 1.3.
Assuming the coordinate of the point x = 0at the moment t = 0, draw the approximate
time dependence plots for the acceleration
ωx, the x coordinate, and the distance
covered s.
8/11/2019 Training Olimpiade Fisika - Problems 1 - 30
http://slidepdf.com/reader/full/training-olimpiade-fisika-problems-1-30 27/40
8/11/2019 Training Olimpiade Fisika - Problems 1 - 30
http://slidepdf.com/reader/full/training-olimpiade-fisika-problems-1-30 28/40
1.19. A point traversed hall a circle of radius
R = 160 cm during time interval σ = 10.0 s.Calculate the following quantities averaged
over that time:
(a) the mean velocity (v );(b) the modulus of the mean velocity vector
I<v>l;
(c) the modulus of the mean vector of thetotal acceleration I<ω>I if the point moved
with constant tangent acceleration.
8/11/2019 Training Olimpiade Fisika - Problems 1 - 30
http://slidepdf.com/reader/full/training-olimpiade-fisika-problems-1-30 29/40
1.20. A radius vector of a particle varies with time t as r = at (1 - α t ), where a is a constant
vector and a is a positive factor.
Find:(a) the velocity v and the acceleration ω of
the particle as functions of time;
(b) the time interval Δt taken by the particle toreturn to the initial points, and the
distance s covered during that time.
8/11/2019 Training Olimpiade Fisika - Problems 1 - 30
http://slidepdf.com/reader/full/training-olimpiade-fisika-problems-1-30 30/40
8/11/2019 Training Olimpiade Fisika - Problems 1 - 30
http://slidepdf.com/reader/full/training-olimpiade-fisika-problems-1-30 31/40
8/11/2019 Training Olimpiade Fisika - Problems 1 - 30
http://slidepdf.com/reader/full/training-olimpiade-fisika-problems-1-30 32/40
8/11/2019 Training Olimpiade Fisika - Problems 1 - 30
http://slidepdf.com/reader/full/training-olimpiade-fisika-problems-1-30 33/40
8/11/2019 Training Olimpiade Fisika - Problems 1 - 30
http://slidepdf.com/reader/full/training-olimpiade-fisika-problems-1-30 34/40
8/11/2019 Training Olimpiade Fisika - Problems 1 - 30
http://slidepdf.com/reader/full/training-olimpiade-fisika-problems-1-30 35/40
8/11/2019 Training Olimpiade Fisika - Problems 1 - 30
http://slidepdf.com/reader/full/training-olimpiade-fisika-problems-1-30 36/40
8/11/2019 Training Olimpiade Fisika - Problems 1 - 30
http://slidepdf.com/reader/full/training-olimpiade-fisika-problems-1-30 37/40
8/11/2019 Training Olimpiade Fisika - Problems 1 - 30
http://slidepdf.com/reader/full/training-olimpiade-fisika-problems-1-30 38/40
8/11/2019 Training Olimpiade Fisika - Problems 1 - 30
http://slidepdf.com/reader/full/training-olimpiade-fisika-problems-1-30 39/40
8/11/2019 Training Olimpiade Fisika - Problems 1 - 30
http://slidepdf.com/reader/full/training-olimpiade-fisika-problems-1-30 40/40
An equilateral triangle is move in such a way that point A moves with velocity v 0
toward point B and point C moves from point B, as shown in the figure.
Determine the velocity of point B.
HW 1