A student is investigating mass and acceleration. The student applies the same force to two boxes, as shown in the table.( Box 1: 20 newtons, 5 m/s; Box 2: 20 newtons, 2 m/s ) The student claims that box 1 must have a smaller mass than box 2. Which argument best supports the student’s claim?

Answer 1

To support the student's claim that Box 1 must have a smaller mass than Box 2, we can use Newton's second law of motion, which states that \( F = ma \), where \( F \) is the force applied, \( m \) is the mass, and \( a \) is the acceleration.

Since both boxes are subjected to the same force of 20 newtons, we can analyze the relationship between mass and acceleration:

1. For Box 1:

   • Force (F) = 20 N
   • Acceleration (a) = 5 m/s²
   • Using \( F = ma \), we can rearrange it to find mass: \( m = \frac{F}{a} = \frac{20 \text{ N}}{5 \text{ m/s}²} = 4 \text{ kg} \).

2. For Box 2:

   • Force (F) = 20 N
   • Acceleration (a) = 2 m/s²
   • Again using \( m = \frac{F}{a} = \frac{20 \text{ N}}{2 \text{ m/s}²} = 10 \text{ kg} \).

From this analysis, we can see that Box 1 has a mass of 4 kg while Box 2 has a mass of 10 kg. Therefore, the argument that best supports the student's claim is that since both boxes are exerting the same force but Box 1 is accelerating more (5 m/s² compared to 2 m/s² for Box 2), Box 1 must indeed have a smaller mass than Box 2, because the same force results in a higher acceleration for a lower mass according to Newton's second law.