To determine the acceleration of the system in this tug-of-war scenario, we need to analyze the forces acting on both sides and the total mass involved. Let's break it down step by step.
Calculating the Total Force
First, we need to find the total force exerted by both the students and the parents.
Force Exerted by Students
The students are pulling with an average force of 150 N each. Since there are 13 students, we can calculate the total force they exert:
- Total force by students = Number of students × Force per student
- Total force by students = 13 × 150 N = 1950 N
Force Exerted by Parents
Next, we calculate the total force exerted by the parents. Each parent pulls with an average force of 475 N, and there are 5 parents:
- Total force by parents = Number of parents × Force per parent
- Total force by parents = 5 × 475 N = 2375 N
Net Force Calculation
Now that we have the total forces, we can find the net force acting on the system. Since the students are pulling westward and the parents are pulling eastward, we will consider the direction of the forces:
- Net force = Force by students - Force by parents
- Net force = 1950 N (west) - 2375 N (east) = -425 N
The negative sign indicates that the net force is directed eastward, meaning the parents are winning the tug-of-war.
Calculating the Total Mass
Next, we need to find the total mass of the system to calculate the acceleration. We can find the mass of both the students and the parents:
Mass of Students
- Mass of students = Number of students × Average mass per student
- Mass of students = 13 × 50 kg = 650 kg
Mass of Parents
- Mass of parents = Number of parents × Average mass per parent
- Mass of parents = 5 × 80 kg = 400 kg
Total Mass of the System
Now we can find the total mass:
- Total mass = Mass of students + Mass of parents
- Total mass = 650 kg + 400 kg = 1050 kg
Finding the Acceleration
Finally, we can use Newton's second law of motion, which states that force equals mass times acceleration (F = ma), to find the acceleration:
- Acceleration (a) = Net force / Total mass
- Acceleration (a) = -425 N / 1050 kg
- Acceleration (a) ≈ -0.405 m/s²
The negative value indicates that the acceleration is in the direction of the net force, which is eastward. Therefore, the system accelerates eastward at approximately 0.405 m/s².
Summary
In this tug-of-war, the parents exert a greater total force than the students, resulting in a net force that accelerates the entire system eastward at about 0.405 m/s². This example illustrates the principles of force, mass, and acceleration in a practical context.
