Density is defined as (mass) per unit (volume). So in order to calculate
the density of a glob of some substance, you pretty much have to measure
its mass and its volume.
Explanation:
Load (l) = 680N
Effort (E) = 500N
Length slope (l) = 12m
Height slope (h) = 8 m
Output = load * height
680 *8 = 5.44 *103 J
The Input = effort * length = 500 *12 = 6000J
the Mechanical advantage (M.A) = load effort= 600500=1.36
the Velocity ratio (V.R) =lh=128 = 1.5
the Efficiency =M.A100%V.R= 90.6%
A) 
The total energy of the system is equal to the maximum elastic potential energy, that is achieved when the displacement is equal to the amplitude (x=A):
(1)
where k is the spring constant.
The total energy, which is conserved, at any other point of the motion is the sum of elastic potential energy and kinetic energy:
(2)
where x is the displacement, m the mass, and v the speed.
We want to know the displacement x at which the elastic potential energy is 1/3 of the kinetic energy:

Using (2) we can rewrite this as

And using (1), we find

Substituting
into the last equation, we find the value of x:

B) 
In this case, the kinetic energy is 1/10 of the total energy:

Since we have

we can write

And so we find:
