Calculate Earth's force of gravity on each of two steel balls of masses 6.0kg and 12.0kg

I the forces of gravity on the 12-kg ball is greater than that on the other ball, why do the two balls accelerate at the same rate when dropped?

The weight force (in newtons) is the mass (in kg) multiplied by the acceleration of gravity (g), which is 9.8 m/s^2.

The 6.0 kg mass weighs 58.8 N and the 12.0 kg mass weights 117.6 N.

Different masses accelerate at the same rate because
accleration = Weight/Mass = g

Any my text book for the 12.0kg steel ball it says the answer is 1.2*10^2N, not 117.6N how did they get that answer?

To calculate the gravitational force on an object, you can use the formula:

F = m * g

Where:
F represents the gravitational force
m represents the mass of the object
g represents the acceleration due to gravity (approximately 9.8 m/s^2 on Earth)

Let's calculate the forces of gravity on the two steel balls:

For the 6.0 kg ball:
F₁ = 6.0 kg * 9.8 m/s^2

For the 12.0 kg ball:
F₂ = 12.0 kg * 9.8 m/s^2

Once you calculate the values, you will find that F₂ is twice as large as F₁. This means that the force of gravity acting on the 12.0 kg ball is twice as strong as the force of gravity acting on the 6.0 kg ball.

Now, to address your second question: Although the forces of gravity on the two balls are different, they both accelerate at the same rate when dropped. This is because their acceleration depends only on the mass of the object and the gravitational field strength, not on the force of gravity acting on the object.

The acceleration of an object due to gravity is constant, regardless of its mass. On Earth, this acceleration is approximately 9.8 m/s^2. So, when both balls are dropped, they experience the same acceleration regardless of their masses, causing them to fall at the same rate. This phenomenon is known as the equivalence principle and was famously verified by Galileo's experiments.

In summary, while the forces of gravity on the two steel balls are different, they accelerate at the same rate due to the constant acceleration of objects in the Earth's gravitational field.