Two teams of nine members each engage in a tug of war. The first team's members have average masses of 64 kg and exert average forces of 1350 N horizontally. The second team's members have average masses of 69 kg and exert average forces of 1371 N horizontally.
(a) What is the acceleration of the two teams?
To find the acceleration of the two teams, we need to first calculate the total force exerted by each team. Since the force and mass are given for each team, we can use Newton's Second Law of Motion, which states that force equals mass multiplied by acceleration (F = ma).
For the first team:
Mass (m1) = 64 kg
Force (F1) = 1350 N
Acceleration (a1) = ?
Using F = ma for Team 1:
1350 N = 64 kg * a1
We can rearrange the equation to solve for acceleration:
a1 = 1350 N / 64 kg
Calculating a1:
a1 ≈ 21.09 m/s² (rounded to two decimal places)
For the second team:
Mass (m2) = 69 kg
Force (F2) = 1371 N
Acceleration (a2) = ?
Using F = ma for Team 2:
1371 N = 69 kg * a2
We can rearrange the equation to solve for acceleration:
a2 = 1371 N / 69 kg
Calculating a2:
a2 ≈ 19.87 m/s² (rounded to two decimal places)
Therefore, the acceleration of the first team is approximately 21.09 m/s², while the acceleration of the second team is approximately 19.87 m/s².
To find the acceleration of the two teams, we can use Newton's second law of motion, which states that the acceleration of an object is directly proportional to the net force acting on it and inversely proportional to its mass.
Let's first calculate the total force exerted by each team by multiplying the average force exerted by each team member by the number of team members:
- Team 1: Total force exerted = 1350 N/member * 9 members = 12150 N
- Team 2: Total force exerted = 1371 N/member * 9 members = 12339 N
Next, we can calculate the net force acting on each team by subtracting the force exerted by the other team:
- Net force on Team 1 = Force exerted by Team 1 - Force exerted by Team 2 = 12150 N - 12339 N = -189 N
- Net force on Team 2 = Force exerted by Team 2 - Force exerted by Team 1 = 12339 N - 12150 N = 189 N
Since the two teams are engaged in a tug of war and are pulling in opposite directions, the net force on Team 1 is in the opposite direction to that of Team 2.
Now, we can calculate the acceleration of each team using the formula:
Acceleration = Net force / Mass
- Team 1 acceleration = -189 N / (64 kg * 9 members) = -0.36 m/s^2 (The negative sign indicates that the acceleration is in the opposite direction to the force)
- Team 2 acceleration = 189 N / (69 kg * 9 members) = 0.24 m/s^2
Therefore, the acceleration of Team 1 is -0.36 m/s^2, and the acceleration of Team 2 is 0.24 m/s^2.