Newton's Theory of Gravity and impact speed

In summary, the conversation discusses the impact speed of a 1.0 kg object released from rest 500 km above the Earth, ignoring air resistance. It is suggested that energy conservation is relevant to the problem, with a potential energy reference of zero at infinity. The equation provided for calculating impact speed has dimensional inconsistencies. The question of what the impact speed would be if the Earth were flat is raised, but it is unclear what this means exactly.
  • #1
Kalie
46
0
A 1.0 kg object is released from rest 500 km above the earth.
A. What is its impact speed as it hits the ground? Ignore air resistance
B. What would the impact speed be if the Earth were flat?
I don't know how to start this.
I said that v=sqrt(2G*M_e*m/(R_e+300))= 1.33*10^9 but that is incorrect...I'm probably being stupid but please help
 
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  • #2
Kalie said:
A 1.0 kg object is released from rest 500 km above the earth.
A. What is its impact speed as it hits the ground? Ignore air resistance
B. What would the impact speed be if the Earth were flat?
I don't know how to start this.
I said that v=sqrt(2G*M_e*m/(R_e+300))= 1.33*10^9 but that is incorrect...I'm probably being stupid but please help
You seem to recognize that this problem has something to do with energy conservation. With the reference of zero potential at infinity the object has potential energy at altitude, but also when it hits the ground. You have several dimensional inconsistencies in your equation. What is 300? Why are there both M_e and m on the right and no m on the left.?

I have no idea what part C is about. Flat how? A cube? A huge plane of mass? I have no idea.
 
  • #3


A. To calculate the impact speed of the 1.0 kg object, we can use Newton's Theory of Gravity, which states that the force of gravity between two objects is directly proportional to their masses and inversely proportional to the square of the distance between them. In this case, the two objects are the 1.0 kg object and the Earth. We can use the formula F = G(m1*m2)/r^2, where G is the gravitational constant, m1 is the mass of the first object, m2 is the mass of the second object, and r is the distance between them. Since the object is released from rest, we can also use the equation v^2 = u^2 + 2as, where v is the final velocity, u is the initial velocity (which is 0 in this case), a is the acceleration due to gravity (9.8 m/s^2), and s is the distance traveled (500 km = 500000 m). Combining these equations, we get v = sqrt(2GM_e/r), where M_e is the mass of the Earth (5.97*10^24 kg) and r is the distance between the object and the center of the Earth (radius of the Earth + 500 km = 6.37*10^6 + 5*10^5 = 6.87*10^6 m). Plugging in these values, we get v = 7.97 km/s or 7970 m/s as the impact speed of the object as it hits the ground.

B. If the Earth were flat, the impact speed would be different because the distance between the object and the center of the Earth would be constant (the radius of the Earth). In this case, the impact speed would be v = sqrt(2GM_e/r), where r is the radius of the Earth. Plugging in the same values as before, we get v = 11.2 km/s or 11200 m/s as the impact speed. This is significantly higher than the impact speed when considering the Earth's curvature, highlighting the importance of understanding the true shape of the Earth when making calculations involving gravity.
 

Related to Newton's Theory of Gravity and impact speed

1. What is Newton's Theory of Gravity?

Newton's Theory of Gravity is a scientific law formulated by Sir Isaac Newton in the late 17th century. It states that every object in the universe is attracted to every other object with a force that is directly proportional to the product of their masses and inversely proportional to the square of the distance between them.

2. How does gravity affect the speed of an object?

Gravity affects the speed of an object by constantly pulling it towards the center of the Earth or any other massive body. This causes the object to accelerate towards the ground, increasing its speed as it falls. The speed of an object due to gravity is also affected by factors such as the mass of the object and the strength of the gravitational force acting upon it.

3. What is the impact speed of an object falling due to gravity?

The impact speed of an object falling due to gravity depends on several factors such as the height from which it falls, the mass of the object, and the strength of the gravitational force. However, in a vacuum, all objects will fall towards the ground with the same acceleration of 9.8 meters per second squared, resulting in a final impact speed of approximately 9.8 meters per second.

4. How does air resistance affect the impact speed of an object?

Air resistance, also known as drag, is a force that opposes the motion of an object through the air. It increases as the speed of the object increases. Therefore, air resistance can significantly affect the impact speed of an object falling due to gravity. Objects with larger surface areas, such as parachutes, will experience more air resistance and have a lower impact speed compared to smaller, more aerodynamic objects.

5. Can Newton's Theory of Gravity be applied to objects in space?

Yes, Newton's Theory of Gravity can be applied to objects in space. It is a universal theory that explains the motion of all objects in the universe, not just on Earth. It has been used to accurately predict and describe the orbits of planets and other celestial bodies, as well as the motion of objects in space such as satellites and spacecraft.

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