Kinetic energy problem (masteringphysics)

In summary, the gravitational pull of the Earth on an object is inversely proportional to the square of the distance of the object from the center of the earth. At the Earth's surface this force is equal to the object's normal weight mg, where g=9.8m/s^2, and at large distances, the force is zero. To calculate the kinetic energy of an asteroid of mass 30000kg falling from a great distance onto the surface of the Earth, the formula -∆U = W = (m2v^2)/2 can be used, where U is the potential energy, G is the universal gravitational constant, m1 is the mass of the Earth, and r is the distance from the center of
  • #1
kottur
56
0

Homework Statement



The gravitational pull of the Earth on an object is inversely proportional to the square of the distance of the object from the center of the earth. At the Earth's surface this force is equal to the object's normal weight mg, where g=9.8m/s^2, and at large distances, the force is zero.

a) If a 30000kg asteroid falls to Earth from a very great distance away, how much kinetic energy will it impart to our planet? You can ignore the effects of the Earth's atmosphere.

b) What will be its minimum speed as it strikes the Earth's surface?

Homework Equations



F=Gm1m2/r
sqrt(2K/m)

The Attempt at a Solution



I've tried to put the variables in equation F=Gmm/r and I'm using the Earth's radius from Wikipedia = 6371km. Should I be using m1=m2=30000kg? Plus I don't know how to get kinetic energy out of the force equation.
For part b I need to know the kinetic energy.
 
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  • #2
Hello there, welcome to the board!
Firstly, a correction there, which is very essential.
In your equations, you should've used:
[itex]
\large
U = -\frac{Gm_1m_2}{r}
[/itex]
Which is the potential energy, not the force ;
Now you must consider this:
[itex]
\large
-\Delta{U} = W = \frac{m_2v^2}{2}
[/itex]
Recall that you're told that the comet/asteroid arrives from a great distance away, meaning that you can neglect its point of origin(somewhere in the infinity of space), and simply plug in the destination, literally, the surface of the earth.
M_1 in the above formulae is the mass of the earth(which you can also find on wikipedia), The universal gravitational constant(G) is also there, and don't forget to convert R to meters before employing it.
Have fun,
Daniel
 
  • #3
Thank you very much for the help!

From the equation U=-Gm1m2/r I got a minus value but when I plugged that into masteringphysics it told me to check my signs. Why wasn't the negative outcome correct but the positive one was? Is it because U=K2-K1 where K2 is zero?
 
  • #4
You should've taken note of this:
[itex]
\large
-\Delta{U} = W = \frac{m_2v^2}{2}
[/itex]
It's the negative change in the potential energy of a conservative force(such as gravity), that equals Work, and not just U.
Daniel
 
  • #5
Thank you!
 

1. What is Kinetic Energy?

Kinetic energy is the energy an object possesses due to its motion. It is an important concept in physics and is described by the equation KE=1/2 mv^2, where m is the mass of the object and v is its velocity.

2. How is Kinetic Energy related to potential energy?

Kinetic energy and potential energy are two forms of energy that can be possessed by an object. Kinetic energy is the energy of motion, while potential energy is the energy an object has due to its position or state. They are related because potential energy can be converted into kinetic energy and vice versa, depending on the situation.

3. What is the difference between kinetic energy and momentum?

Kinetic energy and momentum are both related to an object's motion, but they are two different concepts. Kinetic energy is a measure of the energy an object has due to its motion, while momentum is a measure of the object's mass and velocity. Kinetic energy is a scalar quantity, while momentum is a vector quantity.

4. How is Kinetic Energy used in real-life applications?

Kinetic energy is used in many real-life applications, such as in transportation systems like cars and trains. It is also used in the generation of electricity through hydroelectric power plants and wind turbines. In sports, kinetic energy is used in activities like running, jumping, and throwing.

5. How can Kinetic Energy be calculated in a problem?

To calculate the kinetic energy of an object, you need to know its mass and velocity. Then, you can use the equation KE=1/2 mv^2 to find the kinetic energy in joules. It is important to make sure that the units are consistent in the calculation. Additionally, kinetic energy can also be calculated by using the work-energy theorem, which states that the change in kinetic energy of an object is equal to the net work done on the object.

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