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Potential Energy (mgh) = Kinetic Energy (1/2m v^2)
m= mass
g= gravity
h= delta height
v = velocity
If you are asking to see which one would roll down on a ramp faster(lighter object/heavier), I'd say "they both come down at the same speed". The mass m on each side of the equation cancels each other so it's not going to be a matter of how heavy something is. It's exactly same for sky diving.
Few things that will affect the speed are the following:
- moment of inertia (if rolling) - hollow vs. solid
- shape (aerodynamics) - sharp spear vs free falling human
- friction (outer surface) - might result in translational movement instead of rolling(rotational), this also affect aerodynamics
If it's going down a ramp, that means there is a component of gravity acting upon it.
The only equation you should remember at this point is F = MA
Force = Mass x Acceleration
Resolves the forces acting upon the object, this will require you to use Cos and Tan since the ramp is inclined by a certain degree, therefore it's weight (which contributes to its downward movement) acts in 2 different directions.
Once you have the resultant force (product of F), then you can easily find the acceleration at which it goes down the ramp.
If you know the start time, distance, you can find the initial speed.
Despite all this, Momentum of an object is P = MV
Momentum = Mass x Velocity.
As you can see Mass/Velocity can be high respectively, and still give a high value for momentum. Faster objects have high momentum. Heavier objects also have high momentum.
Otherwise just go with potential energy equations. Once you have that, use your value for the energy to find the change in Kinetic energy.
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