Asteroid collides with Earth, new accel. of gravity?

AI Thread Summary
An asteroid collision with Earth increases its mass to 1.5 times the original and reduces its radius to 0.75 times the original. The gravitational force can be calculated using Newton's law of gravitation, F = G × m1 × m2 / r^2. To find the new acceleration due to gravity, the force must be divided by the mass of the object experiencing the gravity. The discussion highlights confusion over the calculations, with one participant arriving at an acceleration of 19.6 m/s², which differs from their test answer. Understanding the relationship between force, mass, and acceleration is crucial for solving such problems.
confusedbyphysics
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This was on my test and I took a guess because I was so confused. The question is that an asteroid hits Earth and now the Earth has a mass of 1.5 times its original mass and a radius of .75 times its original radius. What is its new force of gravity?

its driving me crazy because it seemed like it should be one of the easiest problems on the test but i was stumped for some reason. how should I have done this? Thanks!
 
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How can "g" be expressed by Newton's law of gravitation?

Can't see the point, though, because if an asteroid with mass possibly exceeding half the mass of the Earth, there will be no one about noticing the change in "g"..:wink:
 
LOL, good point.

Is it F = G X m1 X m2 / r^2?

thats all I could think of...where F is gravitational force and r is .75 X the radius of the Earth and one of the masses is 1.5 X the mass of earth. and G is 6.67 X 10^-11. but I don't know what the other mass would be. Do I just assign a number?? Or is this wrong altogether
 
confusedbyphysics said:
LOL, good point.

Is it F = G X m1 X m2 / r^2?

thats all I could think of...where F is gravitational force
Yes, that is the gravitational FORCE.
What must then the ACCELERATION be of an object with the mass m_{1} when exposed to that force?
 
a=F/m. ah, so the ms just cancel out when you set F = ma... I got a = 19.6 (not the answer I circled on the test CRAP!)
 

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