A student is investigating mass and acceleration. The student applies the same force to two boxes, as shown in the table.
Box Force Applied to Box (newtons) Acceleration (meters/second2)
1 20 5
2 20 2
The student claims that box 1 must have a smaller mass than box 2. Which argument best supports the student's claim?
a
Heavier objects require less force than lighter objects to accelerate at the same rate.
b
Lighter objects require greater force than heavier objects to start moving but will accelerate at the same rate.
c
Lighter objects require less force than heavier objects to start moving but will accelerate at the same rate.
d
Heavier objects require greater force than lighter objects to accelerate at the same rate.
d
Heavier objects require greater force than lighter objects to accelerate at the same rate.
Thank you so much for the fast answer! I greatly appreciate it.
i think it answers you automatically but i'm glad it helped
oh okay
To determine which argument best supports the student's claim, we need to understand the relationship between mass, force, and acceleration. Newton's second law of motion states that the acceleration of an object is directly proportional to the net force applied to it and inversely proportional to its mass. The formula for Newton's second law is:
F = ma
where F represents the net force, m represents the mass of the object, and a represents the acceleration.
In this scenario, both boxes are subjected to the same force (20 newtons). However, the acceleration of box 1 is 5 m/s^2, while the acceleration of box 2 is 2 m/s^2.
Using the formula F = ma, we can rearrange it to solve for mass (m):
m = F/a
For box 1:
m1 = 20 N / 5 m/s^2
m1 = 4 kg
For box 2:
m2 = 20 N / 2 m/s^2
m2 = 10 kg
Comparing the masses, we see that box 1 has a smaller mass (4 kg) compared to box 2 (10 kg).
Now let's analyze the given arguments:
a) "Heavier objects require less force than lighter objects to accelerate at the same rate." This argument is incorrect because according to Newton's second law, the force required to accelerate an object is directly proportional to its mass.
b) "Lighter objects require greater force than heavier objects to start moving but will accelerate at the same rate." This argument is also incorrect because it claims that lighter objects require a greater force to start moving, which contradicts the principles of Newton's second law.
c) "Lighter objects require less force than heavier objects to start moving but will accelerate at the same rate." This argument is correct. According to Newton's second law, lighter objects with smaller mass will require less force to start moving. However, once in motion, both lighter and heavier objects will accelerate at the same rate if subjected to the same force.
d) "Heavier objects require greater force than lighter objects to accelerate at the same rate." This argument is incorrect because it is the opposite of what Newton's second law states. It says that the force applied is directly proportional to the mass, not inversely proportional.
Therefore, the argument that best supports the student's claim is option c) "Lighter objects require less force than heavier objects to start moving but will accelerate at the same rate."