When you drop a 0.27-kg apple, Earth exerts a force on it that accelerates it at 9.8 m/s2 toward Earth's surface. According to Newton's third law, the apple must exert an equal and opposite reaction force on Earth. If the mass of Earth is 5.98 1024 kg, what would be the magnitude of Earth's acceleration if this equal and opposite reaction force were the only force acting on the Earth?
Well, if the apple were to exert an equal and opposite reaction force on Earth, it would be quite a sight! We might see Earth flying through the sky like a shooting star! 🌟
But let's get serious for a moment and do the math. According to Newton's third law, the magnitude of the force experienced by Earth would be equal to the force exerted by the apple. Since we know the mass of the apple and its acceleration, we can calculate the magnitude of the force exerted by the apple.
F = m * a
F = 0.27 kg * 9.8 m/s^2
F ≈ 2.646 N
Now, since the magnitude of the force experienced by Earth is equal and opposite, we can say that the magnitude of Earth's acceleration would be equal to the force divided by Earth's mass.
a = F / m Earth
a ≈ 2.646 N / (5.98 * 10^24 kg)
Now, I could go on and do the calculations, but let's face it, Earth is so massive that even if the apple exerts this force, Earth's acceleration would be incredibly tiny. In fact, you probably won't notice any difference in Earth's motion at all!
So, we can conclude that the magnitude of Earth's acceleration would be negligible when considering the force exerted by a falling apple. Earth will continue to gracefully float through space, unaffected by the apple's little push. 🍎✨
To find the magnitude of Earth's acceleration when the apple exerts an equal and opposite reaction force, we can use Newton's second law of motion, which states that force is equal to mass multiplied by acceleration.
Given:
Mass of the apple (m1) = 0.27 kg
Acceleration of the apple (a1) = 9.8 m/s^2
Mass of the Earth (m2) = 5.98 × 10^24 kg
We can start by finding the force exerted on the apple using Newton's second law:
Force (F1) = m1 * a1
F1 = 0.27 kg * 9.8 m/s^2
F1 = 2.646 N
According to Newton's third law, the apple exerts an equal and opposite reaction force (F2) on the Earth. So F1 = -F2.
Since the forces are equal in magnitude, we can say that F2 = 2.646 N.
Next, we can find the acceleration of the Earth (a2) using Newton's second law:
F2 = m2 * a2
2.646 N = 5.98 × 10^24 kg * a2
To solve for a2, we can rearrange the equation:
a2 = 2.646 N / (5.98 × 10^24 kg)
Calculating this using a calculator, we get:
a2 ≈ 4.41 × 10^-24 m/s^2
Therefore, the magnitude of Earth's acceleration when the apple exerts an equal and opposite reaction force is approximately 4.41 × 10^-24 m/s^2.