When you drop a 0.37 kg apple, Earth exerts
a force on it that accelerates it at 9.8 m/s
2
toward the earth’s surface. According to Newton’s third law, the apple must exert an equal
but opposite force on Earth.
If the mass of the earth 5.98 × 1024 kg, what
is the magnitude of the earth’s acceleration
toward the apple?
Answer in units of m/s2
The force is the same.
F = ma
so a = 0.37*9.8 / 5.98x10^24 m/s^2
Well, gravity seems to be quite the apple aficionado! According to Newton's third law, if the apple exerts a force on the Earth, the Earth must exert an equal and opposite force on the apple. So, if the apple is accelerating towards the Earth's surface at 9.8 m/s^2, then the Earth must also be accelerating towards the apple with the same magnitude of acceleration.
Since the mass of the Earth is 5.98 × 10^24 kg, it doesn't exactly sprout wings and fly towards the apple (that would be quite a sight!). Instead, we can calculate the acceleration using the formula F = ma, where F is the force and m is the mass. In this case, the force between the Earth and the apple is the gravitational force, which can be calculated using Newton's law of universal gravitation.
But, uh-oh, it seems like this time I've gone on a serious tangent! To make a long story short, the magnitude of the Earth's acceleration towards the apple is also 9.8 m/s^2. So, be warned folks, next time you eat an apple, make sure to hold on tight or you might witness some serious gravitational shenanigans!
To find the magnitude of the Earth's acceleration towards the apple, we can use Newton's second law of motion.
According to Newton's third law, the force exerted by the apple on the Earth is equal in magnitude but opposite in direction to the force exerted by the Earth on the apple.
The force exerted by the apple on the Earth can be determined using the equation F = ma, where F is the force, m is the mass, and a is the acceleration.
Given that the mass of the apple is 0.37 kg, and the acceleration is 9.8 m/s^2, we can calculate the force exerted by the apple on the Earth: F = (0.37 kg)(9.8 m/s^2) = 3.626 N.
Since the force exerted by the apple on the Earth is equal in magnitude but opposite in direction to the force exerted by the Earth on the apple, the force exerted by the Earth on the apple is also 3.626 N.
To find the Earth's acceleration towards the apple, we can rearrange Newton's second law of motion equation to solve for acceleration: a = F/m.
The mass of the Earth is given as 5.98 × 10^24 kg.
Substituting the values into the equation, we have: a = (3.626 N) / (5.98 × 10^24 kg).
Evaluating the expression using a calculator, we find that the magnitude of the Earth's acceleration toward the apple is approximately 6.07 × 10^(-24) m/s^2.
To find the magnitude of the Earth's acceleration toward the apple, we can use Newton's second law, which states that force is equal to mass multiplied by acceleration (F = ma).
Since the apple exerts a force on the Earth and the mass of the Earth is much larger than the mass of the apple, we can consider the apple's force on the Earth negligible. Therefore, the force exerted on the Earth by the apple can be approximated as zero.
From Newton's third law, we know that the force exerted on the apple by the Earth is equal in magnitude but opposite in direction to the force exerted on the Earth by the apple. Therefore, the force exerted on the apple by the Earth is equal to the weight of the apple, which is given by the formula F = mg, where m is the mass of the apple and g is the acceleration due to gravity.
Given:
Mass of the apple (m) = 0.37 kg
Acceleration due to gravity (g) = 9.8 m/s^2
So, the force exerted on the apple by the Earth is F = mg = (0.37 kg)(9.8 m/s^2) = 3.626 N
Now, since the mass of the Earth is significantly larger than the mass of the apple, the Earth's acceleration toward the apple can be calculated using Newton's second law.
F = ma
3.626 N = (mass of the Earth)(acceleration of the Earth)
Mass of the Earth (M) = 5.98 × 10^24 kg (given)
Acceleration of the Earth (a) = ?
Rearranging the equation, we have:
a = F / M
a = 3.626 N / (5.98 × 10^24 kg)
Calculating this value, we find that the magnitude of the Earth's acceleration toward the apple is approximately 6.06 × 10^-24 m/s^2.