A boulder with a mass of 2,500kg on a ledge 200m above the ground falls. What is the speed of the boulder just before it hits the ground.

 

 

To find velocity you need to use the kinetic energy formula right? But when I tried to plug in everything, it wouldn't work. IT only looks as if the GPE formula would work... could someone help me please?

You might be able to do it with just the kinematic equations,

 

you know: u,a,s, and want to find v....so you have/want 4 of the 5 variables so yep the kinematic equations can be used here. Do you know what they are?

When it is motionless, it is at it's highest point. Here, the total mechanical energy is solely composed of potential energy. It's fastest point is when it is at height=0 and thus the total mechanical energy is solely composed of kinetic energy. If we disregard air friction, we can say that all of the potential energy was converted to kinetic energy in the fall. You can then set the initial potential energy equal to the final kinetic energy. Then you can solve for the velocity.

You might be able to do it with just the kinematic equations,

 

you know: u,a,s, and want to find v....so you have/want 4 of the 5 variables so yep the kinematic equations can be used here. Do you know what they are?

 

umm no sorry im only in 9th grade =\

Kinematics....It's usually taught first. It's the equations of motion.

 

v_f=v₀+at

x_f=x₀+vt+(0.5)at²

 

etc.

uhh what do all the variables stand for...?

Ok, you had some idea of what I said the first time. Go with that.

You can use kinetic and potential energy.

 

[math]PE = mgh[/math]

 

where m = mass, g = the acceleration due to gravity (9.8m/s²) and h = the height. All of that energy will be converted to kinetic energy by the time the object hits the ground.

 

[math]KE = \frac{1}{2} mv^2[/math]

 

where m = mass and v = velocity. So make the kinetic energy equal the potential energy you found in the first step and solve for velocity.

You can do it with energies, just equate the gravitational energy to kinetic and solve for v.

uhh.. how do i do that...

uhh.. how do i do that...

 

It's what I and Cap'n said to do.

It's what I and Cap'n said to do.

 

Indeed!

What is the speed of the boulder just before it hits the ground.

You can try with [math]v=\sqrt{2gh}[/math].

You can try with [math]v=\sqrt{2gh}[/math].

 

Which can be derived either using kinematics or energy...

The potential energy it gains by dropping 200m is found by using:

 

PE = mgh

 

You know the mass, g is acceleration due to gravity (you'll use 10, or 9.8 or 9.81) and h is the distance it falls.

 

Then you know that all of that potential energy went in to kinetic energy, and you know the formula: KE = ½mv².

 

So you say that all the PE goes to KE, therefore:

 

PE = KE

 

mgh = ½mv²

 

gh = ½v²

 

2gh = v²

 

v = √(2gh)

 

That should help. You understand now?

A boulder with a mass of 2,500kg on a ledge 200m above the ground falls. What is the speed of the boulder just before it hits the ground.

 

 

To find velocity you need to use the kinetic energy formula right? But when I tried to plug in everything, it wouldn't work. IT only looks as if the GPE formula would work... could someone help me please?

 

Remember that mass does not at all enter into solving this problem.

Remember that mass does not at all enter into solving this problem.

 

For this problem. It might not always be the case. What if we add in a electric potential into the mix?

this specific equation (of motion) does not need mass.

 

use equation:

2 2

Vf = Vi + 2a (x)

 

Vf = ?

Vi = 0

a = 9.8m.s

x = 200m

 

Vf should = 62.61m.s downwards

 

Does this help?

this specific equation (of motion) does not need mass.

Equations of motions don't really need mass on them, unless you want to find energy out of them.

Equations of motions don't really need mass on them, unless you want to find energy out of them.

 

What if your force isn't gravity at sea level?

What if your force isn't gravity at sea level?

Perhaps a little misunderstanding here but I was referring to the equations of velocity!

Perhaps a little misunderstanding here but I was referring to the equations of velocity!

 

What do you think causes the "a"? The only reason you don't need mass is because we know the acceleration at sea level due to gravity.

Also you must consider situations where the mass changes...

Also you must consider situations where the mass changes...

 

I guess thedarkshade isn't a rocket scientist.

A simple e.o.m including mass would be that for an electrically charged object with charge q in an electric field E: [math]\ddot x = qE/m[/math].