10 Dynamics Object connected by cord over pulley Atwood machine – Problems and Solutions
1. Block A with a masë of 5 kg, placed on a smooth horizontal plane. Block B with a mass of 3 kg hanging at one end of the cord connected with block A over a pulley. Përshpejtimi për shkak të gravitetit është 10 m/s2Çfarë është nxitim of both blocks?
I njohur:
Masa e bllokut A (mA) = 5 kg
Masa e bllokut B (mB) = 3 kg
Përshpejtimi për shkak të gravitetit (g) = 10 m/s2
peshë of block B (wB) = mB g = (3)(10) = 30 Newton
Kërkohet: Acceleration of both blocks (a)
zgjidhje:
The horizontal plane is smooth so there is no friction force. The force that accelerates both blocks is the weight of the block B.
ΣF = ma
wB = (mA +mB)
30 = (5 + 3) a
30 = 8 a
a = 30 / 8
a = 3.75 m/s2
2.
Based on the figure above, 
(1) acceleration of object = 0
(2) the object moves at a constant velocity
(3) object at rest
(4) the object moves if the weight of the object is smaller than the force that pulls the object.
zgjidhje:
(1) The acceleration of the object = 0.
Forca neto:
ΣF = m a –> nxitim (a) = 0
ΣF=0
F1 +F2 - F3 = 12 + 24 – 36 = 36 – 36 = 0 N
(2) The object moves at a constant velocity
No acceleration means object at rest or moves at a constant velocity.
(3) object at rest
No net force means object at rest.
(4) the object moves if the weight of the object is smaller than the force that pulls the object.
Weight acts on the vertical direction, while the pull force acts on the horizontal direction.
The object moves in a horizontal direction so only the horizontal forces that act on the object
3. If the coefficient of fërkim kinetik between the block A and the table surface is 0.1. Acceleration due to gravity is 10 m/s2, then what is the force acts on the block A so that the system moves to leftward in 2 m/s2.
I njohur:
Masa e bllokut A (mA) = 30 kg
weight of block A (wA) = (30 kg)(10 m/s2) = 300 kg m/s2 or 300 Njuton
Masa e bllokut B (mB) = 20 kg
weight of block B (wB) = (20 kg)(10 m/s2) = 200 kg m/s2 or 200 Njuton
Përshpejtimi për shkak të gravitetit (g) = 10 m/s2
Coefficient of kinetic friction (μk) = 0.1
Acceleration of system (a) = 2 m/s2 (to leftward)
Force of kinetic friction (fk) = μk N = = μk wA = (0.1)(300) = 30 Njuton
Kërkohet: The magnitude of force F
zgjidhje:
Newton’s second law :
ΣF = ma
The object A moves to leftward :
F – fk - wB = (mA +mB)
F – 30 – 200 = (30 + 20)(2)
F – 230 = (50)(2)
F – 230 = 100
F = 230 + 100
F = 330 Njuton
4. Two objects, A = 2 kg and B = 6 kg, attached at one end of cord over a pulley, as shown in figure below. If acceleration due to gravity is 10 ms-2 then what is the acceleration of the object B.
I njohur:
Mass of object A (mA) = 2 kg, mB = 6 kg, g = 10 m/s2
weight of object A (wA) = (mA)(g) = (2)(10) = 20 N
weight of object B (wB) = (mB)(g) = (6)(10) = 60 N
Kërkohet: Acceleration of object b (system’s acceleration).
zgjidhje:
wB > wA so that object B moves downward, object A moves upward
ΣF = ma
wB - wA = (mA +mB)
60 – 20 = (2 + 6) a
40 = (8) një
a = 5 m/s2
5. Two objects connected by a cord over a smooth pulley, as shown in figure below. If m1 = 1 kg, m2 = 2 kg, and acceleration due to gravity is 10 ms-2, then what is the tension force T.
I njohur:
Mass of object 1 (m1) = 1 kg
Mass of object 2 (m2) = 2 kg
Përshpejtimi për shkak të gravitetit (g) = 10 m/s2
weight of object 1 (w1) = m1 g = (1 kg)(10 m/s2) = 10 kg m/s2 or 10 Newton
weight of object 2 (w2) = m2 g = (2 kg)(10 m/s2) = 20 kg m/s2 or 20 Newton
Kërkohet: The tension force (T) ?
zgjidhje:
w2 > w1 so m2 moves downward, M1 moves upward.
La Ligji i dytë i lëvizjes i Njutonit :
ΣF = ma
w2 - w1 = (m1 +m2)
20 – 10 = (1 + 2 ) a
10 = (3) një
a = 3.3 m/s2
System’s acceleration = 3.3 m / s2.
m2 moves downward :
w2 - T2 = m2 a
20 - T2 = (2)(3.33)
20 - T2 = 6.66
T2 = 20 - 6.66
T2 = 13.3 Njuton
m1 moves upward :
T1 - w1 = m1 a
T1 – 10 = (1)(3.3)
T1 - 10 = 3.33
T1 = 10 + 3.33
T1 = 13.3 Njuton
The tension force (T) = 13.3 Newton.
6. Mass of m1 = 6 kg and mass of m2 = 4 kg. The horizontal surface is smooth. Acceleration due to gravity is 10 m/s2. What is the system’s acceleration.
I njohur:
Mass of m1 = 6 kg
mass of m2 = 4 kg
acceleration due to gravity (g) = 10 m/s2
weight of w1 = m1 g = (6 kg)(10 m/s2) = 60 kg m/s2 or 60 Newton
weight of w2 = m2 g = (4 kg)(10 m/s2) = 40 kg m/s2 or 40 Newton
Kërkohet: System’s acceleration (a)
zgjidhje:
m1 on a smooth horizontal plane without friction so that the system accelerated by the weight of the block 2.
Apply Newton’s second law :
ΣF = ma
w2 = (m1 +m2)
40 N = (6 kg + 4 kg) a
40 N = (10 kg) a
a = 40 N / 10 kg
a = 4 m/s2
7. Two blocks, each block has the mass of 2 kg, connected by a cord over a pulley, as shown in the figure below. The horizontal plane and pulley are smooth. If the block B is pulled by a horizontal force of 40 Newton, then what is the acceleration of block. Acceleration due to gravity is 10 m/s2.
I njohur:
mass of block A (mA) = mass of block B (mB) = 2 kg
Përshpejtimi për shkak të gravitetit (g) = 10 m/s2
Force of F = 40 N
weight of object A (wA) = m g = (2)(10) = 20 N
Kërkohet: System’s acceleration (a) ?
zgjidhje:
Apply Newton’s second law :
ΣF = ma
F – wA = (mA +mB)
40 – 20 = (2 + 2) a
20 = (4) një
a = 20 / 4
a = 5 m/s2
8. Mass of block A = 2 kg and mas of block B = 1 kg. Block B initially at rest, then accelerated downward until it hits ground. Acceleration due to gravity is 10 m/s2. What is the magnitude of the tension force.
I njohur:
Masa e bllokut A (mA) = 2 kg
Masa e bllokut B (mB) = 1 kg
Përshpejtimi për shkak të gravitetit (g) = 10 m/s2
Pesha e bllokut B (pB) = mB g = (1)(10) = 10 Newton
Kërkohet: The magnitude of the tension force (T)
zgjidhje:
Ignore the friction force.
System’s acceleration (a)
ΣF = ma
wB = (mA +mB)
10 = (2 + 1) a
10 = 3 a
a = 10/3
The tension force (T)
The tension force on the block A :
ΣF = ma
T = mA a = (2)(10/3) = 20/3 = 6.7 Newton
The tension force on the block B :
ΣF = ma
wB – T = mB a
10 – T = (1)(10/3)
10 – T = 3.3
T = 10 – 3.3 = 6.7 Newton
The tension force (T) = 6.7 Newton
9. Mass of block A = 2 kg and mass of block B = 1 kg. The friction force between object A with the horizontal plane = 2.5 Newton. Ignore friction on pulley and cord. What is the acceleration of both blocks.
I njohur:
Masa e bllokut A (mA) = 2 kg
Masa e bllokut B (mB) = 1 kg
Friction force between lock a and the horizontal plane (fkA) = 2.5 Njuton
Përshpejtimi për shkak të gravitetit (g) = 10 m/s2
Weight of block (wB) = mB g = (1)(10) = 10 Newton
Kërkohet: Acceleration of both blocks (a)
zgjidhje:
Apply Newton’s second law :
ΣF = ma
wB - fk = (mA +mB)
10 – 2.5 = (2 + 1) a
7.5 = 3 a
a = 7.5 / 3
a = 2.5 m/s2
10. Mass of block a = 30 kg, rest on a horizontal plane connected with block B with mass of 10 kg over a pulley. What is the system’s acceleration. Acceleration due to gravity is 10 ms-2.
I njohur:
Masa e bllokut A (mA) = 30 kg
Masa e bllokut B (mB) = 10 kg
Përshpejtimi për shkak të gravitetit (g) = 10 m/s2
weight of block B (wB) = mB g = (10)(10) = 100 Newton
Kërkohet: System’s acceleration (a)
zgjidhje:
ΣF = ma
wB = (mA +mB)
100 = (30 + 10) a
100 = 40 a
a = 100 / 40
a = 2.5 m/s2
