Isabella drops a chunk of iron of mass m from the roof of her high school and it accelerates at g. Then she ties two chunks of iron together of mass 2m. Show that when she drops the double chunk, the acceleration of fall is also g.
Thank you :)
Acceleration = Force/Mass
= 2 m*g/(2m) = g
As Galileo showed at the Tower of Pisa, acceleration is independent of mass.
F=ma shows that the force needed to pull both down is the same so the gravitational pull is the same.
To show that when Isabella drops the double chunk of iron, the acceleration of fall is also g, we can use Newton's second law of motion.
Newton's second law states that the force acting on an object is equal to the mass of the object multiplied by its acceleration (F = ma).
When Isabella drops the chunk of iron of mass m, the force acting on it is the force of gravity, which can be calculated using the equation F = mg, where m is the mass of the object and g is the acceleration due to gravity.
So, when Isabella drops the chunk of iron with mass m, the force of gravity acting on it is F = mg. Since the only force acting on the chunk of iron is the force of gravity, we can equate it to the mass of the object multiplied by its acceleration (ma = mg).
Dividing both sides of the equation by m, we get a = g. Hence, the acceleration of the chunk of iron with mass m is equal to g.
Now, let's consider the double chunk of iron with mass 2m. When Isabella drops the double chunk, the force of gravity acting on it is F = (2m)g. Similarly, we can equate this force to the mass of the object multiplied by its acceleration (ma = (2m)g).
Dividing both sides of the equation by 2m, we get a = g. Hence, the acceleration of the double chunk of iron with mass 2m is also equal to g.
Therefore, we have shown that when Isabella drops the double chunk of iron, the acceleration of fall is also g.
To show that the acceleration of the double chunk when dropped is also g, we can apply Newton's second law of motion, which states that the force acting on an object is equal to the mass of the object times its acceleration (F = m * a).
In the first scenario, when Isabella drops a single chunk of iron of mass m, the force acting on it is its weight, given by F1 = m * g. Since the only force acting on the chunk is its weight, we can equate this to Newton's second law:
m * g = m * a1
Simplifying, we find:
a1 = g
So, the acceleration of the single chunk is indeed equal to g.
Now, let's consider the second scenario, where Isabella ties two chunks of iron together to form a double chunk with mass 2m. When she drops the double chunk, the force acting on it is still its weight, given by F2 = (2m) * g.
Let's calculate the acceleration of the double chunk using Newton's second law:
(2m) * g = (2m) * a2
Canceling out the common terms (2m) on both sides, we find:
g = a2
Therefore, in the second scenario as well, the acceleration of the double chunk when dropped is also g.