A student is investigating mass and acceleration. The student applies the same force of 40 N force to two boxes that have the same size and shape. Box 1 experiences an acceleration of 10 m/s^2 and box 2 experiences an acceleration of 5m/s^2.
The student claims that box 1 must have a smaller mass than box 2. Which argument best supports the student's claim?(1 point)
The argument that best supports the student's claim is that the acceleration of an object is inversely proportional to its mass. The acceleration of an object is given by the equation F = ma, where F is the force applied to the object, m is the mass of the object, and a is the acceleration of the object.
Since the force applied to both boxes is the same (40 N), and the acceleration of box 1 is greater than the acceleration of box 2, it means that the mass of box 1 must be smaller than the mass of box 2. This is because according to the equation F = ma, if the force is constant, then a smaller mass will result in a greater acceleration. Therefore, the student's claim is supported by the fact that box 1 experiences a greater acceleration with the same applied force.
The student's claim that box 1 must have a smaller mass than box 2 can be supported by the argument that the acceleration of an object is inversely proportional to its mass when the force acting on it is constant. In this case, since both boxes experience the same force of 40 N, the box with a larger acceleration (box 1 with 10 m/s^2) must have a smaller mass compared to the box with a smaller acceleration (box 2 with 5 m/s^2). This is because a smaller mass will result in a larger acceleration when the force is kept constant. Therefore, the student's claim is supported by the fact that box 1 experiences a higher acceleration, suggesting that it has a smaller mass than box 2.
To support the student's claim that box 1 must have a smaller mass than box 2, we need to examine the relationship between mass and acceleration.
According to Newton's second law of motion, the acceleration of an object is directly proportional to the net force applied to it and inversely proportional to its mass. The equation representing this relationship is:
F = ma
Where:
F = net force applied to the object
m = mass of the object
a = acceleration of the object
In this case, the student applied the same force of 40 N to both boxes. However, box 1 experienced an acceleration of 10 m/s^2 while box 2 experienced an acceleration of 5 m/s^2.
If we rearrange the equation to solve for mass, we get:
m = F / a
Now, let's compare the values:
For box 1:
F = 40 N
a = 10 m/s^2
m1 = 40 N / 10 m/s^2
m1 = 4 kg
For box 2:
F = 40 N
a = 5 m/s^2
m2 = 40 N / 5 m/s^2
m2 = 8 kg
From the calculations, we can see that the mass of box 1 is 4 kg, while the mass of box 2 is 8 kg. Therefore, the student's claim that box 1 has a smaller mass than box 2 is supported.