Persamaan tegangan tali

3 Pitakonan babagan persamaan tegangan tali

1. Gambar ing ngisor iki nuduhake telung blok, yaiku A, B lan C sing dumunung ing bidang horisontal sing alus. Yen massa A = 1 kg, massa B = 2 kg lan massa C = 2 kg lan F = 10 N, banjur temtokake rasio tegangan ing tali antarane A lan B karo tegangan ing tali antarane B lan C.

Dikenal:

Massa A (m_A) = 1 kg

Massa B (m_B) = 2 kg

Massa C (m_C) = 2 kg

Gaya tarik (F) = 10 N

Dikarepake: T_AB :T_BC

Solution:

Calculate the acceleration of the system using Newton’s Second Law formula:

ΣF = ma

F = (m_A +m_B +m_C) lan

10 = (1 + 2 + 2) a

10 = 5

a = 10 / 5

a = 2 m/s²

Use the rope tension formula to calculate T_AB

ΣF = ma

T_AB = m_A a = 1 (2) = 2 Newton

Use the rope tension formula to calculate T_BC

ΣF = ma

T_BC = (m_A +m_B) a = (1 + 2) (2) = (3)(2) = 6 Newton

2. Object A with a mass of 6 kg and object B with a mass of 3 kg are connected by a rope as shown. If the coefficient of friction is 0.3 and g = 10 m/s², determine the acceleration of the object and the tension in the ropes of each block.

Dikenal:

The mass of object A (m_A) = 6 kg

The mass of object B (m_B) = 3 kg

Coefficient of friction of block A (µ_k) = 0.3

Akselerasi amarga gravitasi (g) = 10 m/s²

The weight of block A (w_A) = m_A g = (6)(10) = 60 N

Normal force on block A (N_A) = w_A = 60 N

The weight of block B (w_B) = m_B g = (3)(10) = 30 N

Dikarepake: Percepatan sistem (a) lan tegangan ing tali (T)

Solution:

Calculate the kinetic frictional force i.e. the frictional force when block A moves:

F_k = µ_k N_A = (0,3)(60) = 18 Newton

Calculate the acceleration of the system (a):

ΣF = ma

wB – F_k = (m_A +m_B) lan

30 – 18 = (6 + 3) a

12 = 9

a = 12 / 9 = 1,3 m/s²

Calculate the tension in the string on block A (T_A):

ΣF = ma

T_A - F_k = (m_A) lan

T_A – 18 = (6)(1,3)

T_A - 18 = 7,8

T_A = 7,8 + 18 = 25,8 Newton

Calculate the tension in the rope on beam B (T_B):

ΣF = ma

w_B - T_B = m_B (a)

30 – T_B = 3 (1,3)

30 – T_B = 3,9

T_B = 30 – 3,9

T_B = 26,1 Newton

3. Two objects A and B with masses of 5 kg and 3 kg are connected by a frictionless pulley. The force P is applied to the pulley in an upward direction. If both blocks are initially at rest on the floor, what is the acceleration of block A, if the magnitude of P is 60 N?

Determine also the tension in the rope on blocks A and B.

Dikenal:

Akselerasi amarga gravitasi (g) = 10 m/s²

Massa A (m_A) = 5 kg

The weight of block A (w_A) = m_A g = (5)(10) = 50 Newton

Massa B (m_B) = 3 kg

The weight of block B (w_B) = m_B g = (3)(10) = 30 Newton

Force P = 60 N

Dikarepake: Acceleration of the system of beams A and B (a) and the tension in the rope on beam A (T_A) and beam B (T_B)

Solution:

Calculate the acceleration of the system using Newton’s Second Law formula.

ΣF = ma

w_A – w_B = (m_A +m_B) lan

50 – 30 = (5 + 3) a

20 = 8

a = 20 / 8

a = 2,5 m/s²

Use the tension force formula to calculate the tension in the rope

Tegangan tali ing balok A:

ΣF = ma

w_A - T_A = m_A a

50 – T_A = 5 (2,5)

50 – T_A = 12,5

T_A = 50 – 12,5 = 37,5 Newton

Tegangan tali ing blok B:

ΣF = ma

T_B – w_B = m_B a

T_B – 30 = 3 (2,5)

T_B - 30 = 7,5

T_B = 7,5 + 30 = 37,5 Newton