Which object will accelerate more if the student exerts an equal amount of force on each object? (1 point) Responses 10 kg box 10 kg box two 10 kg boxes two 10 kg boxes Skip to navigation page 13 of 13
The 10 kg box will accelerate more if the student exerts an equal amount of force on each object.
If the student exerts an equal amount of force on each object, both objects will accelerate at the same rate. The mass of the objects does not affect their acceleration when the same force is applied.
To determine which object will accelerate more when the student exerts an equal amount of force on each object, we need to use Newton's second law of motion.
Newton's second law states that the acceleration of an object is directly proportional to the net force applied to it and inversely proportional to its mass. In equation form, it is represented as:
F = ma
where F represents the net force applied, m represents the mass of the object, and a represents the acceleration.
In this case, we have two options: a single 10 kg box and two 10 kg boxes.
Let's consider the single 10 kg box first. If the student exerts an equal amount of force on it, the net force applied (F) will be the same as the force (let's call it F1) exerted on the box.
Now, let's consider the two 10 kg boxes. Again, if the student exerts an equal amount of force on them, the net force applied (F) will be the same as the force (let's call it F2) exerted on both boxes combined.
Since we have the same force applied (F) in both cases, we can compare the acceleration of the two scenarios by analyzing the equation:
F = ma
For the single 10 kg box: F1 = m1 * a1
For the two 10 kg boxes: F2 = (m2 + m2) * a2
Now, since the mass (m1) of the single box is equal to the total mass (2 * m2) of the two boxes, we can rewrite the equations as:
F1 = m1 * a1
F2 = 2 * m2 * a2
Since the mass (m1) and the total mass (2 * m2) are equal, we can simplify the equations to:
F1 = m * a1
F2 = m * a2
Since the force (F) is the same in both cases, we can equate the two equations:
m * a1 = m * a2
With mass (m) being the same in both cases, we can cancel it out:
a1 = a2
This means that both the single 10 kg box and the two 10 kg boxes will accelerate by the same amount if the student exerts an equal amount of force on each object. Therefore, both options will accelerate equally.