Calculating Maximum Velocity of a Dropped Object

In summary, the greatest velocity a ball of mass .5 kg will have just before hitting the ground when dropped from a height of 5 m is 9.8 m/s. Mass does not affect the acceleration due to gravity in free fall, so it is not a significant factor in this kinematical problem.
  • #1
tengtou
4
0
A ball of mass .5 kg is dropped from a height of 5 m. What is the greatest velocity it will have just before hitting the ground?

vf squared = vi squared + 2ad

vf squared = 0 squared + 2(9.8)(5)

vf = 9.8 m/s

So the greatest velocity is 9.8 m/s, right?

I am still very confuzzled and I think this is the right answer because where did the mass go? Or it doesn't even matter? Can someone verify?

Thanks!
 
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  • #2
Yes. Mass does not matter in the free fall under gravity. All the body get accelerated equally.
 
  • #3
Welcome to the forums! No, mass doesn't matter. The acceleration downwards is g, independent of mass, ask Galileo. It's a purely kinematical problem.
 
  • #4
Thanks! So is my answer correct?
 
  • #5
Approximately, yes. I would round the answer to 9.9m/sec. But that's a detail.
 
  • #6
Sweet! Thanks!
 
  • #7
I don't know why the question had mass in it. Trick question or something haha.
 
  • #8
In real world problems YOU have to figure out what's important and what isn't. It's just practice.
 

1. What is the relationship between mass and free fall?

The relationship between mass and free fall is that the mass of an object does not affect the rate at which it falls due to gravity. This is known as the principle of equivalence, which states that the acceleration of an object in a gravitational field is independent of its mass.

2. How does mass affect the force of gravity in free fall?

Mass does not affect the force of gravity in free fall. The force of gravity on an object is determined by its mass and the strength of the gravitational field it is in. However, in free fall, the force of gravity is the only force acting on the object, so it will accelerate at a constant rate regardless of its mass.

3. What is the acceleration of an object in free fall?

The acceleration of an object in free fall is 9.8 meters per second squared (m/s^2) near the surface of the Earth. This is also known as the acceleration due to gravity, and it is the same for all objects in a gravitational field, regardless of their mass.

4. How does air resistance affect the mass and free fall of an object?

Air resistance does not affect the mass of an object, but it does affect the free fall of an object. As an object falls, it moves through the air, and the air exerts a force on the object in the opposite direction of its motion. This force of air resistance increases as the speed of the object increases, ultimately reaching a point where it is equal to the force of gravity. At this point, the object will stop accelerating and reach a constant speed, known as terminal velocity.

5. Can an object with a larger mass fall faster than an object with a smaller mass?

No, an object with a larger mass cannot fall faster than an object with a smaller mass. As stated earlier, the acceleration due to gravity is the same for all objects in a gravitational field. However, a larger mass object will have a greater gravitational force acting on it, so it will require a greater force of air resistance to reach its terminal velocity. This means that the larger mass object will take longer to reach its terminal velocity and will therefore fall at the same rate as the smaller mass object.

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