a 10-kg rock and a 20-kg rock are dropped at the same time and experience no significant air resistance. if the 10-kg rock falls with acceleration a, what is the acceleration of the 20-kg rock?
as Galileo showed, it is the same for all objects (ignoring air resistance).
Since F = ma, and a 20kg object weighs twice as much as a 10kg object,
2F = (2m)a
but a remains the same.
Well, gravity doesn't discriminate based on weight, so both rocks will fall with the same acceleration. It's like when you miss a step on the stairs - it doesn't matter if you're carrying 10 cupcakes or 20 cupcakes, you're still going to fall at the same speed! Just make sure the cupcakes are safe.
According to the law of universal gravitation, the gravitational force acting on an object is directly proportional to its mass. In this case, we can assume that the 10-kg rock and the 20-kg rock experience the same gravitational force since they are dropped at the same time.
Thus, if the 10-kg rock falls with acceleration "a," we can conclude that the 20-kg rock will also fall with the same acceleration of "a." The acceleration due to gravity is approximately 9.8 m/s² in most scenarios on Earth, assuming no air resistance.
Therefore, the acceleration of the 20-kg rock will also be "a."
To determine the acceleration of the 20-kg rock, we can use Newton's second law of motion, which states that the force acting on an object is equal to the mass of the object multiplied by its acceleration.
Let's assume that the force acting on both rocks is due to the gravitational pull, which can be calculated using the equation F = m * g, where F is the force, m is the mass, and g is the acceleration due to gravity.
For the 10-kg rock:
F1 = m1 * g
For the 20-kg rock:
F2 = m2 * g
Since both rocks are dropped at the same time and experience no significant air resistance, the force of gravity acting on both rocks will be the same.
F1 = F2
Therefore, m1 * g = m2 * g
We can cancel out the acceleration due to gravity (g) on both sides:
m1 = m2
According to the question, the mass of the 10-kg rock (m1) is 10 kg. Using this information, we can say that the mass of the 20-kg rock (m2) is 20 kg.
So, the acceleration of the 20-kg rock will be the same as the acceleration of the 10-kg rock (a).