To determine which student will accelerate faster when exerting the same force of 150 N, we can apply 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. This can be represented by the equation:
\[ a = \frac{F}{m} \]
Where:
- \( a \) is the acceleration,
- \( F \) is the net force applied,
- \( m \) is the mass of the object.
Given the two students, one with a mass of 50 kg and the other with a mass of 60 kg, and both students exerting a force of 150 N, we can calculate their accelerations as follows:
- For the student with a mass of 50 kg:
\[ a_1 = \frac{F}{m_1} = \frac{150 , \text{N}}{50 , \text{kg}} = 3 , \text{m/s}^2 \]
- For the student with a mass of 60 kg:
\[ a_2 = \frac{F}{m_2} = \frac{150 , \text{N}}{60 , \text{kg}} = 2.5 , \text{m/s}^2 \]
Prediction
- The student with a mass of 50 kg (Student 1) will accelerate at \( 3 , \text{m/s}^2 \).
- The student with a mass of 60 kg (Student 2) will accelerate at \( 2.5 , \text{m/s}^2 \).
Explanation
Student 1 will accelerate faster because of their lower mass. According to Newton's second law, for the same amount of exerted force, a lighter object will experience a greater acceleration than a heavier object. This demonstrates the inverse relationship between mass and acceleration when the force is constant. Thus, the student with a lower mass of 50 kg, experiencing the same force of 150 N as the 60 kg student, will undergo a greater acceleration.
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