Two aluminium spheres P and Q, of masses 0.50 kg and 1.0 kg respectively, are released at the same time from the same height.
Why do they have the same acceleration?
both spheres are gravitationally attracted to the Earth
the force of attraction is proportional to the product of the mass of the sphere and the mass of the Earth
... so the larger sphere experiences twice the force of the smaller sphere
Newton's 2nd law states that the acceleration of an object is
... directly proportional to the net force
... and inversely proportional to the object's mass
... f = m a ... a = f / m
twice the force on the larger sphere with twice the mass
... means that the acceleration of the two spheres is the same
Well, they both agreed to coordinate their movements before the experiment. Safety in numbers, you know. It's called solidarity in the world of aluminum spheres. They're like the synchronized swimmers of the physics world. So, they stick together and accelerate at the same rate, just to show off their teamwork skills.
The acceleration of an object is determined by the net force acting on it and its mass, as given by Newton's second law of motion (F = ma). In this case, both spheres P and Q are released from the same height, which means they experience the same gravitational force due to their masses.
Since the gravitational force acting on an object is proportional to its mass, both spheres experience the same gravitational force. Since the mass of sphere P is 0.50 kg and the mass of sphere Q is 1.0 kg, both spheres experience the same gravitational force.
Therefore, because the net force acting on both spheres is equal, and their masses are different but proportional, the acceleration experienced by both spheres will be the same.
The acceleration of an object is determined by the gravitational force acting on it. In this case, both spheres P and Q are released from the same height, which means that they experience the same gravitational force, as gravity acts uniformly on all objects.
The force due to gravity (weight) acting on an object can be calculated using the formula F = m * g, where F is the force, m is the mass of the object, and g is the acceleration due to gravity. Since both spheres are located at the same height and are subject to the same gravitational field, the force acting on them will be the same.
Now, let's consider 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. Mathematically, this can be represented as F = m * a, where F is the net force, m is the mass of the object, and a is the acceleration.
Since both spheres experience the same gravitational force (weight), which is the net force acting on them, and the force is directly proportional to the acceleration, we can conclude that both spheres will have the same acceleration. The masses of the spheres do not affect the acceleration as long as the gravitational force remains the same.
Therefore, both spheres P and Q will have the same acceleration as they fall from the same height.