A heavy object and a light object are dropped from rest at the same time in a vacuum. Which one will reach the ground first and why?
They will hit the ground at the same time.
the accelerate at the same rate of 9.8m/s^2
In a vacuum, where there is no air resistance, both a heavy object and a light object will fall with the same acceleration due to gravity. This is known as the equivalence principle, which states that the motion of objects under the influence of gravity is independent of their mass. As a result, both objects will reach the ground at the same time.
To understand why, we need to consider Isaac Newton's second law of motion, which states that the force acting on an object is equal to its mass multiplied by its acceleration. In the case of free fall, the only force acting on the objects is the gravitational force, which is the same for both. As a result, the acceleration experienced by both objects is also the same. This means that their velocities increase at the same rate, resulting in them reaching the ground simultaneously.
To calculate the time it takes for an object to reach the ground, we can use the equation for motion under constant acceleration:
s = ut + (1/2)at^2
Where:
- s is the distance traveled (which in this case is the height from which the objects are dropped),
- u is the initial velocity (which is zero since the objects are at rest),
- a is the acceleration due to gravity (which is approximately -9.8 m/s^2, where the negative sign indicates that it acts downward),
- t is the time taken.
Since we are comparing two objects, we can set their distances equal to each other and solve for time:
s1 = s2
(1/2)a1t^2 = (1/2)a2t^2
(t^2) = (t^2)
Hence, we see that the time taken for both objects to hit the ground is the same.
In conclusion, both the heavy and light objects will reach the ground at the same time when dropped from rest in a vacuum because their motion is solely determined by the acceleration due to gravity.