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Two teams of nine members each engage in a tug of war. Each of the first team's members has an average mass of 73 kg and exerts an average force of 1350 N horizontally. Each of the second team's members has an average mass of 78 kg and exerts an average force of 1358 N horizontally. (a) What is magnitude of the acceleration of the two teams, and which team wins? (b) What is the tension in the section of rope between the teams?

Respuesta :

Answer:

a = 0.052 m s^{-2}

T = 12185.49 N

Explanation:

from the figure:

determine the Force [tex]F_R = NF_2i = 9*1358 i = 12222 N[/tex]

Determine the force [tex]F_L = NF_1i = 9*1350 i = - 12150ii N[/tex]

by Newton's second law, net force F_net

[tex]F_net = \sum{F_1+ F_2 +...... = ma ........(1)[/tex]

[tex]F_R +F_L = ma[/tex]

12222- 12150  = ma

[tex]a = \frac{ 72}{9(78+73)}[/tex]

a = 0.052 m s^{-2}

B) TENSION T in section of rope

by newton's second law

[tex]F_Ri -Ti = 9m_2ai[/tex]

[tex]T = F_Ri - 9m_2ai[/tex]

T = 12222i - 9*78*0.052

T = 12185.49 N

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