Οι ασκήσεις είναι στα αγγλικά αλλά μπορείτε να χρησιμοποιήσετε μετάφραση google.
Το επίπεδο δυσκολίας φαίνεται απο τα (*) δίπλα από τον αριθμό της άσκησης. (Τις αναλυτικές λύσεις θα τις αναρτήσω κάποια άλλη στιγμή)
Για πολλούς οι παρακάτω ασκήσεις μπορεί να είναι αρκετά δύσκολες, αλλά με λίγη προσπάθεια βγαίνουν.
καλή σας επιτυχία!
Κινηματική
1.*
A motorboat going downstream overcame a raft at a point A;
T = 60 min later it turned back and after some time passed the raft
at a distance l = 6.0 km from the point A. Find the flow velocity
assuming the duty of the engine to be constant. (3km/h)
2.**
A point traversed half the distance with a velocity v0. The
remaining part of the distance was covered with velocity vl for half
the time, and with velocity v2 for the other half of the time. Find
the mean velocity of the point averaged over the whole time of mo-
tion. 2v0(vl +v2)/[2v0 +vl +v2)]
3.*
A car starts moving rectilinearly, first with acceleration α=
5.0 m/s^2 (the initial velocity is equal to zero), then uniformly, and
finally, decelerating at the same rate α, comes to a stop. The total
time of motion equals t = 25 s. The average velocity during that
time is equal to <v> = 72 km per hour. How long does the car move
uniformly? (15sec)
4.
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 river along 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 the stream to get to point B. What was the velocity u
of his walking if both swimmers reached the destination simulta-
neously? The stream velocity v0 = 2.0 km/hour and the velocity if
of each swimmer with respect to water equals 2.5 km per hour.
(3km/h)
5.
Two boats, A and B, move away from a buoy anchored at the
middle of a river along the mutually perpendicular straight lines:
the boat A along the river, and the boat B across thg river. Having
moved off an equal distance from the buoy the boats returned.
Find the ratio of times of motion of boats TA /TB if the velocity of
each boat with respect to water is n= 1.2 times greater than the
stream velocity. (1.8)
6.
Two bodies were thrown simultaneously from the same point:
one, straight up, and the other, at an angle of θ = 60° to the hori-
zontal. The initial velocity of each body is equal to vo = 25 m/s.
Neglecting the air drag, find the distance between the bodies t =
= 1.70 s later. (22m)
7.
An elevator car whose floor-to-ceiling distance is equal to
2.7 m starts ascending with constant acceleration 1.2 m/s^2; 2.0 s
after the start a bolt begins falling from the ceiling of the car. Find:
(a) the bolt's free fall time; (0.7 sec)
(b) the displacement and the distance covered by the bolt during
the free fall in the reference frame fixed to the elevator shaft. (1.3m)
8.**
A point traversed half a circle of radius R = 160 cm during
time interval x = 10.0 s. Calculate the following quantities aver-
aged over that time:
(a) the mean velocity (v);
(b) the modulus of the mean velocity vector |(v)|;
(c) the modulus of the mean vector of the total acceleration | (w)|
if the point moved with constant tangent acceleration.
9.***
1.22. The velocity of a particle moving in the positive direction
of the x axis varies as v = a√x, where a is a positive constant.
Assuming that at the moment t = 0 the particle was located at the
point x = 0, find:
(a) the time dependence of the velocity and
(b) the acceleration of the particle.
10.
A body is thrown from the surface of the Earth at an angle θ
to the horizontal with the initial velocity v0 . Assuming the air drag
to be negligible, find:
(a) the time of motion;
(b) the maximum height of ascent and the horizontal range; at
what value of the angle a they will be equal to each other;
(c) the equation of trajectory y (x), where y and x are displacements
of the body along the vertical and the horizontal respectively.
11.**
A cannon and a target are 5.10 km apart and located at the
same level. How soon will the shell launched with the initial velocity
240 m/s reach the target in the absence of air drag?
(42.4sec για γωνία εκτόξευσης θ ή 22.5sec για γωνία 90-θ)
12.*
A cannon fires successively two shells with velocity vo =
= 250 m/s; the first at the angle θ = 60° and the second at the angle
φ = 45° to the horizontal, the azimuth being the same. Neglecting
the air drag, find the time interval between firings leading to the
collision of the shells.(~10sec)
Δυνάμεις
13.
An aerostat of mass m starts coming down with a constant
acceleration α. Determine the ballast mass to be dumped for the
aerostat to reach the upward acceleration of the same magnitude.
The air drag is to be neglected.
14.
A small body was launched up an inclined plane set at an
angle a = 15° against the horizontal. Find the coefficient of friction,
if the time of the ascent of the body is ν= 2.0 times less than the
time of its descent.
Το επίπεδο δυσκολίας φαίνεται απο τα (*) δίπλα από τον αριθμό της άσκησης. (Τις αναλυτικές λύσεις θα τις αναρτήσω κάποια άλλη στιγμή)
Για πολλούς οι παρακάτω ασκήσεις μπορεί να είναι αρκετά δύσκολες, αλλά με λίγη προσπάθεια βγαίνουν.
καλή σας επιτυχία!
Κινηματική
1.*
A motorboat going downstream overcame a raft at a point A;
T = 60 min later it turned back and after some time passed the raft
at a distance l = 6.0 km from the point A. Find the flow velocity
assuming the duty of the engine to be constant. (3km/h)
2.**
A point traversed half the distance with a velocity v0. The
remaining part of the distance was covered with velocity vl for half
the time, and with velocity v2 for the other half of the time. Find
the mean velocity of the point averaged over the whole time of mo-
tion. 2v0(vl +v2)/[2v0 +vl +v2)]
3.*
A car starts moving rectilinearly, first with acceleration α=
5.0 m/s^2 (the initial velocity is equal to zero), then uniformly, and
finally, decelerating at the same rate α, comes to a stop. The total
time of motion equals t = 25 s. The average velocity during that
time is equal to <v> = 72 km per hour. How long does the car move
uniformly? (15sec)
4.
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 river along 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 the stream to get to point B. What was the velocity u
of his walking if both swimmers reached the destination simulta-
neously? The stream velocity v0 = 2.0 km/hour and the velocity if
of each swimmer with respect to water equals 2.5 km per hour.
(3km/h)
5.
Two boats, A and B, move away from a buoy anchored at the
middle of a river along the mutually perpendicular straight lines:
the boat A along the river, and the boat B across thg river. Having
moved off an equal distance from the buoy the boats returned.
Find the ratio of times of motion of boats TA /TB if the velocity of
each boat with respect to water is n= 1.2 times greater than the
stream velocity. (1.8)
6.
Two bodies were thrown simultaneously from the same point:
one, straight up, and the other, at an angle of θ = 60° to the hori-
zontal. The initial velocity of each body is equal to vo = 25 m/s.
Neglecting the air drag, find the distance between the bodies t =
= 1.70 s later. (22m)
7.
An elevator car whose floor-to-ceiling distance is equal to
2.7 m starts ascending with constant acceleration 1.2 m/s^2; 2.0 s
after the start a bolt begins falling from the ceiling of the car. Find:
(a) the bolt's free fall time; (0.7 sec)
(b) the displacement and the distance covered by the bolt during
the free fall in the reference frame fixed to the elevator shaft. (1.3m)
8.**
A point traversed half a circle of radius R = 160 cm during
time interval x = 10.0 s. Calculate the following quantities aver-
aged over that time:
(a) the mean velocity (v);
(b) the modulus of the mean velocity vector |(v)|;
(c) the modulus of the mean vector of the total acceleration | (w)|
if the point moved with constant tangent acceleration.
9.***
1.22. The velocity of a particle moving in the positive direction
of the x axis varies as v = a√x, where a is a positive constant.
Assuming that at the moment t = 0 the particle was located at the
point x = 0, find:
(a) the time dependence of the velocity and
(b) the acceleration of the particle.
10.
A body is thrown from the surface of the Earth at an angle θ
to the horizontal with the initial velocity v0 . Assuming the air drag
to be negligible, find:
(a) the time of motion;
(b) the maximum height of ascent and the horizontal range; at
what value of the angle a they will be equal to each other;
(c) the equation of trajectory y (x), where y and x are displacements
of the body along the vertical and the horizontal respectively.
11.**
A cannon and a target are 5.10 km apart and located at the
same level. How soon will the shell launched with the initial velocity
240 m/s reach the target in the absence of air drag?
(42.4sec για γωνία εκτόξευσης θ ή 22.5sec για γωνία 90-θ)
12.*
A cannon fires successively two shells with velocity vo =
= 250 m/s; the first at the angle θ = 60° and the second at the angle
φ = 45° to the horizontal, the azimuth being the same. Neglecting
the air drag, find the time interval between firings leading to the
collision of the shells.(~10sec)
Δυνάμεις
13.
An aerostat of mass m starts coming down with a constant
acceleration α. Determine the ballast mass to be dumped for the
aerostat to reach the upward acceleration of the same magnitude.
The air drag is to be neglected.
14.
A small body was launched up an inclined plane set at an
angle a = 15° against the horizontal. Find the coefficient of friction,
if the time of the ascent of the body is ν= 2.0 times less than the
time of its descent.
