Calculate the final velocity of an object accelerating towards a mass

In summary, the conversation discusses the calculation of final velocity for an object accelerating towards a mass from a distance with an initial velocity. The use of calculus and conservation of energy is mentioned, and the correct formula for calculating gravitational potential energy is given. The conversation also addresses the effects of changing acceleration due to gravity and the importance of using the correct formula in calculations.
  • #1
wildkat7411
5
0
I need to be able to calculate the final velocity of an object accelerating towards a mass from a distnce with an initial velocity. From my little knowledge of calculus, I am only a junior in high school, i have figured out that this is probably a derivitive problem. But i have no knowledge of how to solve these kinds of equations. If I am right would some one please walk me through it step-by-step. If I'm wrong, please correct me and show me how to do it step by step. This is not a homework problem but a problem i made up to challenge myself. The problem is i think I am in way over my head. So any help would be amazing. Thanks
 
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  • #2


No, I think all you need here is to apply conservation of energy,

[tex]\Delta KE = -\Delta PE[/tex],

where PE is the gravitational potential energy between the two objects.
 
  • #3


But since acceleration due to gravity increases as the distance between the two objects decreases, you can't use PE=massxgravityxheight since the acceleration is constantly changing for a given height. or does that not matter? I worked it out and i got that an object of mass one kilogram starting from rest at a distnce of 3.8x10^8 meters would be traveling at 1450 m/s at the point of impact, disregarding air resistance.
 
  • #4


wildkat7411 said:
But since acceleration due to gravity increases as the distance between the two objects decreases, you can't use PE=massxgravityxheight since the acceleration is constantly changing for a given height. or does that not matter? I worked it out and i got that an object of mass one kilogram starting from rest at a distnce of 3.8x10^8 meters would be traveling at 1450 m/s at the point of impact, disregarding air resistance.
Right, you can't use [tex]PE = mgh[/tex]. Use Newton's Law of Gravitation.
 
  • #5


wildkat7411 said:
But since acceleration due to gravity increases as the distance between the two objects decreases, you can't use PE=massxgravityxheight since the acceleration is constantly changing for a given height. or does that not matter? I worked it out and i got that an object of mass one kilogram starting from rest at a distnce of 3.8x10^8 meters would be traveling at 1450 m/s at the point of impact, disregarding air resistance.

No you can't. you have to use

[tex]PE = -\frac{GMm}{r}[/tex]

Where r is the distance between the centers of m and M.

Just remember that [itex]\Delta PE[/itex] is the difference in PE between the start of the fall and the end of the fall.
 

Related to Calculate the final velocity of an object accelerating towards a mass

1. How do you calculate the final velocity of an object accelerating towards a mass?

To calculate the final velocity of an object accelerating towards a mass, you will need to use the equation: v = u + at, where v is the final velocity, u is the initial velocity, a is the acceleration, and t is the time. You will also need to know the mass of the object and the force acting on it.

2. What is the difference between acceleration and velocity?

Acceleration is the rate of change of velocity over time, while velocity is the rate of change of displacement over time. In other words, acceleration measures how quickly an object's velocity is changing, while velocity measures how quickly an object is moving and in which direction.

3. Can the final velocity of an object be negative?

Yes, the final velocity of an object can be negative if it is moving in the opposite direction of its initial velocity. For example, if an object is thrown upwards, its initial velocity is positive, but as it falls back towards the ground, its final velocity will be negative.

4. How does mass affect the final velocity of an accelerating object?

The mass of an object does not directly affect its final velocity when accelerating towards a mass. However, the force acting on the object does affect its acceleration, which in turn affects its final velocity. The greater the mass of an object, the more force is needed to accelerate it to a certain final velocity.

5. Can you calculate the final velocity of an object without knowing its mass?

No, you cannot calculate the final velocity of an object without knowing its mass. Mass is a crucial factor in determining an object's acceleration and final velocity. Without knowing the mass, you cannot accurately calculate how much force is needed to accelerate the object, and therefore, you cannot determine its final velocity.

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