Based on the diagram of a ball rolling down hill, what statement is true?
1 answer:
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Answer:
4.15 m/s
Explanation:
As the total energy must be conserved (neglecting air resistance) the change in gravitational potential energy, must be equal to the change in kinetic energy:
ΔE = ΔK + ΔU =0
If we take as a zero reference level for the gravitational potential energy, the height of the swing seat above the ground, (which is equal to 0.21 m), we can find the initial gravitational energy, considering the height of the point where the seat is released, regarding this point:
h₀ = 1.09 m -0.21 m = 0.88 m
⇒ U₀ = m*g*h₀ = 400 N*0.88 m = 352 J
As Uf = 0, ΔU = Uf -U₀ = -352 J
As the swing starts from rest, K₀=0, so we can say:
ΔK = Kf = (1)
As ΔK = -ΔU ⇒ ΔK = 352 J (2)
From (1) and (2) we can solve for vf, as follows:
So, when the swing passes through its lowest position, Betty moves at 4.15 m/s.
The forces are:
, down
, down
, up
Explanation:
We start by finding the force of gravity on the elephant, , which is given by
(downward)
where
m = 10,000 kg is the mass of the elephant
is the acceleration of gravity
Substituting,
Now we know that the net acceleration of the elephant is
downward
We can now use Newton's second law:
where is the net force on the elephant. Substituting, we find
and it also acts downward, since it has the same direction as the acceleration.
Finally, we can write the net force on the elephant as
where the force of gravity acts downward, while the air resistance ( acts upward. The net force also acts downward, so it has the same sign of gravity.
Substituting:
And solving, we find the air resistance:
(upward)
Learn more about forces and Newton laws of motion:
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