Question

The three football linemen are playing tug-o-war with three running backs. The linemen are on the left and the running backs are on the right. The three linemen have an average mass of 110kg. The three running backs have an average mass of 75 kg. Use g = 10. m/s²

Answer 1

The magnitude of acceleration of the teams is -0.73 m/s^2, and the second team wins in the tug-of-war. The tension in the section of rope between the teams is 24435 N.

Step-by-step explanation:

In order to determine the magnitude of acceleration of the two teams, we need to calculate the net force acting on each team by multiplying the average force exerted by each member with the number of members in the team. For the first team, the net force is 1350 N * 9 = 12150 N, and for the second team, the net force is 1365 N * 9 = 12285 N. Since both teams are pulling in opposite directions, we can subtract the net force of the second team from the net force of the first team to get the resultant force:

Resultant force = 12150 N - 12285 N = -135 N

Next, we can use Newton's second law of motion to calculate the acceleration:

Force = mass * acceleration

-135 N = (110 kg + 75 kg) * acceleration

acceleration = -135 N / 185 kg = -0.73 m/s^2

Since the acceleration is negative, it means the teams are moving in the direction of the second team's pulling force. Therefore, the second team wins in this tug-of-war.

To calculate the tension in the section of rope between the teams, we can use Newton's third law of motion, which states that the force exerted by one object on another is equal in magnitude and opposite in direction:

Tension = 12150 N + 12285 N = 24435 N