Two teams of nine members each engage in a tug of war. Each of the first team’s members has an average mass of 68 kg and exerts an average force of 1350 N horizontally. Each of the second team’s members has an average mass of 73 kg and exerts an average force of 1365 N horizontally.
(a) What is magnitude of the acceleration of the two teams?
(b) What is the tension in the section of rope between the teams?

Answer :

jolis1796

Answer:

a)  a = - 0.106 m/s^2  (←)

b) T = 12215.1064 N

Explanation:

If

F₁ = 9*1350 N = 12150 N   (→)

F₂ = 9*1365 N = 12285 N  (←)

∑Fx = M*a = (M₁  +M₂)*a           (→)

F₁ - F₂ = (M₁  +M₂)*a        

→       a = (F₁ - F₂) / (M₁  +M₂ ) = (12150-12285)N/(9*68+9*73)Kg

→       a = - 0.106 m/s^2            (←)

(b) What is the tension in the section of rope between the teams?

If we apply  ∑Fx = M*a   for the team 1

F₁ - T = - M₁*a  ⇒   T = F₁ + M₁*a  

⇒   T = 12150 N + (9 * 68 Kg)*(0.106 m/s^2)

⇒ T = 12215.1064 N

If we choose the team 2 we get

- F₂ + T = - M₂*a  ⇒   T = F₂ - M₂*a  

⇒   T = 12285 N - (9 * 73 Kg)*(0.106 m/s^2)

⇒ T = 12215.1064 N

(a) The magnitude of the acceleration of the two teams is 0.11 m/s².

(b) The tension in the section of rope between the teams is 2,715 N.

The given parameters;

  • average mass of the first team, m = 68 kg
  • average force of the first team, F = 1350 N
  • average mass of the second team, m = 73 kg
  • average force of the second team, F = 1365 N

The teams will accelerate in the direction of the greater force.

The net force on the teams is calculated as follows;

[tex]\Sigma F _{net}= 1365 - 1350 = 15 \ N[/tex]

The acceleration of the teams is calculated as follows;

[tex]a = \frac{\Sigma F_{net}}{m_1 + m_2} = \frac{15 }{68 + 73} = 0.11 \ m/s^2[/tex]

The tension in the section of rope between the teams is calculated as;

[tex]T= F_1 + F_2\\\\T= 1350 \ + \ 1365\\\\T = 2,715 \ N[/tex]

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