which object will accelerate more if the student exerts an equal amout of force on each object
Person A box = 10kg
Person B boxes = 10kg and 10kg
A. 10kg box
B. two 10kg boxes
A. 10kg box
The acceleration of an object is inversely proportional to its mass. If the student exerts an equal amount of force on each object, the lighter object (10kg box) will accelerate more compared to the heavier object (two 10kg boxes).
To determine which object will accelerate more, we can use Newton's second law of motion, which states that the acceleration of an object is directly proportional to the net force applied to it and inversely proportional to its mass.
Let's calculate the acceleration for each scenario:
A. 10kg box:
Since the mass of the box is 10kg, and the force applied to it is the same as Person B's force, the acceleration can be calculated using Newton's second law:
Acceleration = Net force / Mass
Acceleration = Force / Mass
Acceleration = Force / 10 kg
B. Two 10kg boxes:
In this case, there are two boxes with a total mass of 10 kg + 10 kg = 20 kg. The force applied to this system is the same as in scenario A.
Acceleration = Force / Mass
Acceleration = Force / 20 kg
Comparing the two scenarios, we can see that the acceleration of the 10kg box (scenario A) will be greater than the acceleration of the two 10kg boxes (scenario B). This is because in scenario A, the force is applied to a smaller mass, resulting in a larger acceleration.
To determine which object will accelerate more, we need to 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.
Let's calculate the acceleration for each scenario:
A. 10kg box:
The force applied by the student is the same for both objects, so the net force on this box is the force exerted by the student. Let's assume the force is 100 Newtons (N) for simplicity.
Using Newton's second law of motion:
Net force = mass * acceleration
100N = 10kg * acceleration
Dividing both sides of the equation by 10kg, we find:
acceleration = 10N/kg
Therefore, the acceleration for the 10kg box is 10 meters per second squared (m/s^2).
B. Two 10kg boxes:
In this scenario, the force applied by the student is still 100N, but now it is distributed across two 10kg boxes.
The net force acting on each box is 100N / 2 = 50N.
Using Newton's second law of motion:
50N = 10kg * acceleration
Dividing both sides of the equation by 10kg, we find:
acceleration = 5N/kg
Therefore, the acceleration for each 10kg box is 5 m/s^2.
Comparing the accelerations, we can see that the 10kg box (Option A) will accelerate more than the two 10kg boxes (Option B).