How Does Time Impact the Force Calculation in F=ma for a Falling Object?

[jnorman]

i am an idiot.
i am going to drop a rock from the top of a building.
i want to know the force with which the rock will impact the ground.
i know the rock's mass is 1kg.
i know that the rock will accelerate at 9.8m/sec/sec.
if i use the equation F=ma, i get a fixed result/answer - 9.8N or 9.8kg-m/sec/sec (correct?).

without inputing some time variable into this, so i can know how long the rock undergoes acceleration, i cannot determine how fast the rock is going when it hits the ground. if i don't know how fast the rock is going, i cannot know how much force the rock will exert on the ground when it hits.

what am i missing here?

thanks.

 

[russ_watters]

Not a stupid question. What you are missing is you don't know how long it takes the rock to stop so you don't know the acceleration.

 

[sophiecentaur]

The Force when it hits the ground is hard to specify and I don't think you actually want to know that. It will depend on other factors like the surface of the ground and the nature of the falling object. I think what you are really after is the speed of the object - which will tell you the Kinetic Energy or the Momentum.

The Energy the rock will have when it hits the ground will be given by mgh, where g is gravity (9.81m/s/s), m is its mass and h is the height. You could find the speed from this value of Kinetic Energy. You don't need the 'equations of motion' or how long it takes. In fact, if you ignore friction, the rock could go down a helterskelter and its speed when it arrives would be the same as if it fell directly (not a realistic answer, really but true in principle).

If the rock landed on thick mud, it would spend a long time decelerating and the force could be very low. On the other hand, if it landed on a block of granite, there would be a much higher force.

 

[KingNothing]

If it helps you understand, this is why car companies put airbags in vehicles. If you hit your head on the dashboard, it will slow down almost instantly and experience a ton of force. If you instead hit an airbag, your head slows down a lot slower, and you experience less force.

Also the reason they don't use concrete as a landing pad for pole vaulters.

 

[sophiecentaur]

@jnorman
Have you heard of the quantity Impulse? It describes the amount of momentum change of an object (for instance, bringing it to a halt) and is equal to a Force times the Time it acts for. There are many combinations of Force and Time which will give the same Impulse.

 

[Physicist1231]

i think you may be reading the formula incorrectly... F is the amount of force needed to be applied to the mass (M) to achieve the desired acceleation. This is not the formula to calculate how much energy or how hard the object will hit the ground. This will actually tell you how much force gravity (the acceleration from the earth) is is exerting on the object falling (M).

That is why you don't have Time or distance in this formula... you don't need it.

Instead try this

http://en.wikipedia.org/wiki/Momentum

P=MV