---
Facebook page : https://www.facebook.com/MrSherifYehiaAlMaraghy
Mr . Sherif Yehia Al Maraghy https://twitter.com/Mr_Sherif_yehia
01009988836 – 01009988826 Email : [email protected]
rd -72
-
Three bodies, two of them is horizontal and the other is vertical connected by 2 strings Case 2If resistance F appears plane is rou
Three bodies, one of them is horizontal and two are vertical connected by 2 strings Case 3If resistance F appears plane is rough
* Bo
Facebook page : https://www.facebook.com/MrSherifYehiaAlMaraghy
Assume the acceleration is moving in the direction of body B Before cutting: to find the acceleration
Three bodies, one of them is horizontal and two are vertical connected by 2 strings Case 4A body of mass 600 gm rests on a smooth horizontal table and tied to a string passing over a smooth pulley fixed at the edge of the table and its other end hangs vertically from it, a scale
pan of mass 100 gm, a body of mass 50 gm is placed on the pan, find the magnitude of pressure on each of the pulley and the pan.
To find the pressure on the panT m g a 50 980 196 39200 dyne 40 gm.wt
Facebook page : https://www.facebook.com/MrSherifYehiaAlMaraghy
A body of mass 350 gm is placed on a smooth horizontal table, then it is connected by a light string passing over a smooth pulley at the edge of the table whose other end holds a body of mass 140 gm, find the magnitude of the acceleration of the system and the magnitude of the tension in the string. If the string is cut after just one second from the begining of the motion,
find the distance that each 1
of the two bodies will cut after second from the moment of cutting 2
order to find the distance done by each body
after cutting the string, we have to find the final velocity just before cutting Before cutting: Get the final velocity just before cutting
So V u a t 0 280 1 2
Facebook page : https://www.facebook.com/MrSherifYehiaAlMaraghy
Two bodies of masses 125 gm and 175 gm are placed on a smooth horizontal table and connected by a light string, then the greatest mass is tied to another string passing over a smooth pulley at the edge of the table, and a body of mass m is hanged from the other end of the string, if the
motion of the system starts from rest and the magnitude of the tension in the string that connects the two bodies on
the table is 50 gm.wt, find the magnitude of the acceleration of the system and the magnitude of the tension of the string, also find the value of m .
125
Facebook page : https://www.facebook.com/MrSherifYehiaAlMaraghy
Mr . Sherif Yehia Al Maraghy https://twitter.com/Mr_Sherif_yehia
01009988836 – 01009988826 Email : [email protected]
rd -76
-A body of mass 700 gm is placed on a smooth horizontal table and tied by a string passing over a smooth pulley fixed at the edge of the table and holds at its end a body of mass 280 gm hangs vertically from it, and it is connected by another string below it to hang another body of mass m
gm. , if the magnitude of the pressure on the pulley equals 300 2 gm.wt, then find the magnitude of the acceleration of the system and the magnitude of the tension in both strings, also find m .
T2
T2
a
280 700
m gA
m gC
A
B
T1
C m
a
T1
T2
P
2 2 2
2 A
2
C 1 C
B 1 2 B
C B
Pressure on the pulley is P 2 T 2 T 300 2 T 300 gm.wt To find the acceleration * Body at A: T m a
300 980 700 a a 420 cm/sec
* Body at C: m g T m a 1
* Body at B: m g T T m a 2 By adding: m g m
2 B C
C 1 C
1
1
g T m a m a
980 m 280 980 300 980 280 420 420m
560 m 137200 m 245
From 1 : m g T m a 245 980 T 245 420
T 137200 dyne 140 gm.wt
Example (4)
Answer
Facebook page : https://www.facebook.com/MrSherifYehiaAlMaraghy
Mr . Sherif Yehia Al Maraghy https://twitter.com/Mr_Sherif_yehia
01009988836 – 01009988826 Email : [email protected]
rd -77
-T T
T a
a
48 344
m gA
m gB
A
B
A & B are two bodies of masses 344 , 48 gm respectively, the body A is placed on a horizontal table whose height is 60 cm at a distance 180 cm from the edge of the table, it is connected by a light string of length 180 cm, while the body B is connected by the other end of the string that is passing over a smooth pulley that is fixed at the edge of the table, if the body B is moved softly so that it is dropped from the edge of the table, find the time taken to hit the ground, and the time that the body A will take after that to reach the edge of the table
180 cm
60 cm
floor
B B A
B A B B A B
B 2
A B
To find the acceleration * Body at B: m g T m a 1 * Body at A: T m a 2
By adding: m g m a m a m g a m m
m g 48 980
a a 120 cm / sec
m m 344 48
To find the time taken by B to hit the ground:
u 0
2 2
2
S 60 a 120
1 1
S u t a t 60 120 t
2 2
t 120 1 t 1 sec
120
When body B reached the ground, body A have made a distance 60 cm, after that body A moves uniformly a 0 , so we need to know
the final velocity done.
So, V u at 120 1 120 cm / sec
u 120 a 0 S 180 60 120 cm
S u t 120 120 t t 1 sec
Example (5)
Answer
---
Facebook page : https://www.facebook.com/MrSherifYehiaAlMaraghy
After cutting the string connected between AC, there are two parts separated fro
st
First : we have to find the final velocity just before cutting:
u 0 a 49 t 2 V u a t 49 2 98 cm / sec 1 part 2
m each other
nd part
Two bodies of masses 1300 gm and 600 gm are placed on a smooth horizontal plane and connected together by a tight string of length 50 cm, the body of mass 600 gm is then tied by another string on the same level of the first and passing over a smooth pulley fixed at the edge of the plane that is near to the second mass, and another body of mass 100 gm is hanged to the other end of the string, find the magnitude of the acceleration of the system and the magnitude of the tension in each of the two strings. And if the string that connects the first two bodies is cut after two seconds from the begining of the motion, what is the distance between the two bodies after 1 second from cutting the string.
1300
Facebook page : https://www.facebook.com/MrSherifYehiaAlMaraghy
Assume the acceleration is moving in the direction of body B Before cutting: to find the acceleration
a 140 cm/sec then our assumption is true
150 300 250
After cutting the string connected between AB, The bodies separated and new
First : we have to find the final velocity just before cutting:
u 0 a 140 t 3 V u a t 140 3 420 cm / sec
a' cm/sec The bodies change their directions
150 300 3
A body of mass 300 gm is placed on a smooth horizontal table and connected by two light strings each of them is passing over a smooth pulley where the two pulleys are fixed at the table's
opposite edges, so that the two pulleys on the table are collinear, the first string holds a body of mass 250 gm and the second string holds a body of mass 150 gm and both bodies are hanged vertically, find the magnitude of the common acceleration of the system, and if the string which holds the greatest mass is cut after 3 seconds from the begining of the motion, prove that the rest of the system will move a distance of 270 cm before it comes to rest instantaneously.
T1
Facebook page : https://www.facebook.com/MrSherifYehiaAlMaraghy
Assume the acceleration is moving in the direction of body B
Before cutting: to find the acceleration * Body at B: m g T m a 1
After cutting the string connected between AB, The bodies separated an
First : we have to find the final velocity just before cutting:
u 0 a 140 t 1 V u a t 140 1 140 cm / sec
a' -196 cm/sec The bodies change their directions 200 800
Then the total time done from cutting the string is 1 3 sec.
7 7
A body of mass 800 gm is placed on a smooth horizontal plane and is tied to two threads, the first passes over a smooth pulley at the edge of the table 150 cm from the body, and a body of mass 400 gm hangs vertically downwards, the second string passes over a smooth pulley at the opposite edge of the table 80 cm from the body and hangs vertically a body of mass 200 gm, the two pulleys and the body between them are collinear and the system starts its motion from rest for one second then the string that holds the 400 gm mass is cut, calculate when the 800 gm mass will arrive to the edge of the table.
Facebook page : https://www.facebook.com/MrSherifYehiaAlMaraghy
Mr . Sherif Yehia Al Maraghy https://twitter.com/Mr_Sherif_yehia
01009988836 – 01009988826 Email : [email protected]
rd -81
-A body of mass 90 kg is placed on a rough horizontal table far from the table's edge 80 cm, it is then tied to a string passing over a smooth pulley that's fixed at the edge of the table, and hangs vertically from the other end of the string a body of mass 50 kg, if the magnitude of the resistances to the motion of the body that's placed on the table equals 1 of its weight, and the system starts
5
moti 1
on from rest, then the string is cut after a second from the begining of the motion. Find the 2
distance that the body on the table will move to come to rest from the begining of the motion.
T T
when we are dealing with rough planes, then we use either Resistance force or F R
1 1
First , we have to find the resistance: R W 90 980 17640 dyne
5 5
Before cutting the string, we have to find the final velocity u 0 a 224 t 0.5
After cutting the string, body A is moving under the action of resistance only
So, T R m a' - R m a' -17640 90 a' a' -196 cm/sec
Facebook page : https://www.facebook.com/MrSherifYehiaAlMaraghy
Mr . Sherif Yehia Al Maraghy https://twitter.com/Mr_Sherif_yehia
01009988836 – 01009988826 Email : [email protected]
rd -82
-A body of mass 126 gm is placed on a rough horizontal table and it is connected by a horizontal string passing over a smooth pulley fixed at the edge of the table, at the other end of the string a body of mass 70 gm is hanged and at a height of 70 cm over the floor, if the coefficient of friction is , find the magnitude of the acceleration of the system and the velocity when the mass hanged1
3
arrives to the floor, then determine the distance that will be covered by the body on the table until it stops.
when we are dealing with rough planes, then we use either Resistance force or F R
F R , where R 126 980 123480 dyne F 1 123480 41160 dyne
The final velocity of body B when reached the floor u 0 a 140 S 70 The distance done by body A till it stops
When body B reached the ground, then body A moves under the action of resistance F only
So, T F m a' - F m a' - 41160 126 a' a' -980
ThenThen the total distance is S 70 30 100 cm
Facebook page : https://www.facebook.com/MrSherifYehiaAlMaraghy
Mr . Sherif Yehia Al Maraghy https://twitter.com/Mr_Sherif_yehia
01009988836 – 01009988826 Email : [email protected]
rd -83
-A body of mass 500 gm is placed on a rough horizontal table and it is connected by a horizontal string passing over a small smooth pulley fixed at the edge of the table, hanged at its other end a scale pan of mass 80 gm, it is noticed that if we placed on the pan a body of mass 70 gm, the body on the table is about to move. Find the coefficient of friction. And if we increase the mass of the body on the pan to 120 gm, and the system moved with a uniform. Find the magnitude of the system's velocity after 5 seconds from the begining of motion.
T T
when we are dealing with rough planes, then we use either Resistance force or F R The body is about to move then the body is in equilibrium position a 0 and F R where R 500 980 490000 dyne
When increasing the mass on the pan to 120 gm Then the body is moving with a uniform
of the system after 5 seconds u 0 a 70 t 5
Facebook page : https://www.facebook.com/MrSherifYehiaAlMaraghy
Then the pressure on the pulley before cutting is P 106400 2 dyne 4
First : we have to find the final velocity just before cutting:
280 280
g connected between AC, there are two parts separated from each other
1 part
2
1 C
2 2 2
the action of resistance only as T 0
T 50 980 m a' 0 49000 210 a' a' -700 cm / sec
Two bodies of masses 210 gm and 90 gm are connected by a light string and placed on a rough horizontal plane, the mass 90 gm is tied with another light string passing over a smooth pulley at the edge of the table and hangs from its free end a body of mass 120 gm. If the magnitude of the resistances to the motion of the two bodies 210 gm and 90 gm equal 50 gm.wt and 30 gm.wt respectively. The system started motion from rest then the string that connects the two bodies on the table is cut after 3 seconds from the begining of the motion, find the distance that the 210 gm mass covers after cutting the string to come to rest then prove that the ratio between the magnitude of the pressure on the pulley before and after cutting the string equals 19:12.
210
Facebook page : https://www.facebook.com/MrSherifYehiaAlMaraghy
Mr . Sherif Yehia Al Maraghy https://twitter.com/Mr_Sherif_yehia
01009988836 – 01009988826 Email : [email protected]
rd -85
-m gA
A 90
a
120
m gB
B
a
T T
T 30 980
B B
A
B 2
A B
B
Body B is moving under the action of resistance and new acceleration
* Body at B: m g T m a'' 5
* Body at A: T 30 980 m a'' 6
m g 120 980 30 980
By adding: a'' 420 cm / sec
m m 120 90
From 5 : m g T m
2 partnd
B
2
a'' T 120 980 120 420 67200 dyne
Then the pressure on the pulley after cutting the string is P 67200 2 dyne 7 Then the ratio between the pressures on the pulley before and after the cutting is:
1
2
P 106400 2 19
P 67200 2 12
---
Facebook page : https://www.facebook.com/MrSherifYehiaAlMaraghy
If body of mass m moves up the plane, body of mass m will move vertically downwards a 0 and if body of mass m moves down the plane body of mass m
will move vertically upwards a 0 .
To get the vertical distance between the two bodies
S S S S S Cos
Motion of a system of two bodies, one of them is moving on a smooth/rough inclined plane and the other is hanged vertically.
---
Facebook page : https://www.facebook.com/MrSherifYehiaAlMaraghy
A body of mass 600 gm is placed on the surface of smooth plane inclined at angle of 30 to theo
horizontal and is connected by a string passing over a small smooth pulley at the top of the plane and a body of mass 380 gm is hanging vertically, if the string coincides on the line of the greatest slope and the system starts motion from rest when the two bodies were on the same horizontal level then find:
a The magnitude of the acceleration of the system.
b The magnitude of the pressure on the pulley.
c The vertical distance between the two bodies after 2 seconds from the begining of the motion.
B
Then the pressure on the pulley: P 2T Cos 45 2 342000 Cos30 342000 3 dyne 2 Then the vertical distance between the two bodies is 160 80 240 cm
Facebook page : https://www.facebook.com/MrSherifYehiaAlMaraghy
A body of mass 630 gm is placed on a smooth plane inclined to the horizontal at an angle 30 iso
connected by a light string passes over a smooth pulley fixed at the top of the plane, while another body of mass 350 gm is hanged vertically from other end of the string, find the magnitude of the acceleration of the system and the magnitude of the tension in the string, and if the string is cut after 2 seconds from starting motion, then find the magnitude of the velocity of the body on the
plane and its direction after 1 second from cutting the string, then calculate the distance that the mass 630 gm will make before inverting its direction.
B
T 630 980 0.5 630 35 T 330750 dyne 337.5 gm.wt Before cutting the string: u 0 a 35 t 2
V u a t 35 2 70 cm/sec
After cutting the string: Then new acceleration appears and T 0 - m g Sin m a To find the velocity after 1 second:
u 70 a -490 t 1 V u a t V 70 490 1 -420 cm/sec
The word "before inverting its direction" means that the body comes to res
direction, so to get the distance of the body at this instant:
u 70 a -490 V 0
Facebook page : https://www.facebook.com/MrSherifYehiaAlMaraghy
A body of mass 3 kg is placed on the surface of a smooth inclined plane of 210 cm length and height of 140 cm, and this body is connected to another body of mass 4 kg by a string of length 210 cm coincides on the line of the greatest slope, the second body is hanged vertically at the top edge of the plane, if the system starts motion from rest till the biggest mass arrived to the
ground and comes to rest, find the distance that the small mass move on the plane before it stops
B
When body B reached the ground, body A made a distance S
After body B reached the ground, the string relaxed T 0 , so new acceleration appeared
2 98
To find the distance of A after relaxing the string till it stops:
u 2.8 a -98 V 0 15
V u 2 a S 0 2.8 2 98 S S 0.6 m
15 Then the total distance done by body A is
Facebook page : https://www.facebook.com/MrSherifYehiaAlMaraghy
Mr . Sherif Yehia Al Maraghy https://twitter.com/Mr_Sherif_yehia
01009988836 – 01009988826 Email : [email protected]
rd -91
-
Two bodies of masses 175, 105 gm are connected to the two ends of a string placed on the surface of a smooth plane inclined to the horizontal by angle whose Sin 1, the body 105 gm is tied by
7 another st
ring passing over a snooth pulley fixed at the top of the plane, and another body of mass 70 gm is hanged vertically from the other end of the second string, if the motion of the system starts
from rest
, find: a The magnitude of the accelerration of the system.
b The magnitude of the tension in each string.
c If the string connecting the two bodies on the plane is cut after 2 seconds from the begining of the motion, find the velocity of the three bodies after 1 second from the moment of cutting. After cutting the string connecting AC, two parts are separated:
Body C : T 0 - m g Sin m a'
Facebook page : https://www.facebook.com/MrSherifYehiaAlMaraghy
A body of mass m gm placed on a smooth plane inclined at angle to the horizontal and is connected by a light string passing over a smooth pulley fixed at the top of the plane whose other end hangs a b
ody of mass 140 gm, if the system starts motion from rest and covered a distance of 140 cm in two seconds, find the mass m and the value of given that the magnitude of the
pressure on the pulley is 15
0 3 gm.wt and the system starts motion downwards.
B
T 140 70 140 980 147000 dyne 150 gm.wt The pressure on the pulley
Facebook page : https://www.facebook.com/MrSherifYehiaAlMaraghy
Mr . Sherif Yehia Al Maraghy https://twitter.com/Mr_Sherif_yehia
01009988836 – 01009988826 Email : [email protected]
rd -92
-m1
190
m g CosA
a
m gB
m gA
T T T
T
1 oA body of mass m gm is placed on a smooth plane inclined at an angle of 30 to the horizontal and is connected by a light string passing over a smooth pulley fixed at the top of the plane, while the other end of the string holds a scale pan of mass 190 gm placed on it a body of mass m gm
2If the system starts motion from rest, so that the body which moves upwards the plane cuts a distance of 490 cm i
1
2n 2 seconds while the magnitude of the pressure of the body on the pan is 225 gm.wt, find the value of m and m .
B A
m g SinA m2
2 2 2
2 2 2
2 2
1
B B
u 0 S 490 t 2
1 1
S u t a t 490 2 a a 245 cm /sec
2 2
The pressure on the Pan
m g T m a T m g a
225 980 m 980 245 m 300 gm
To find the magnitude of m
* Body at B: m g T m a
300 190 980 T 300 190 245 T
o
A A 1 1
1 1
360150 dyne 367.5 gm.wt
* Body at A: T m g Sin m a 360150 980 m Sin 30 245 m 735 m 360150 m 490 gm
Example (6)
Answer
---
30o
Facebook page : https://www.facebook.com/MrSherifYehiaAlMaraghy
Two inclined smooth planes equal in height, one of them is inclined to the horizontal at an angle whose Sin is , and the other plane is inclined at an angle 30 and fixed at its top a small smooth3
7
pulley, a body of mass 140 gm is placed on the first plane and a body of mass 210 gm on the second
pulley, a body of mass 140 gm is placed on the first plane and a body of mass 210 gm on the second