Respuesta :
Answer:
h = 1.15 m
Explanation:
given,
mass of the Dog = 11 Kg
dog center of mass = 0.2 m
length of dog = 0.5 m
lowest he can get his center of mass is 0.10 m above the ground,
he can no longer push against the ground is 0.60 m
maximum force dog exert = 2.1 times gravitational force
how high dog jump = ?
Work done of the gravitational force = gain in potential energy
2.1 x m g Δh = m g (h - 0.1)
2.1 x (0.6 - 0.1 ) = (h - 0.1)
h = 1.15 m
hence, the dog will jump upto the height of h = 1.15 m
The work-energy theorem and the conservation of mechanical energy allows to find the result for the maximum height that the dog can jump is:
h = 1.15 m
The work -energy theorem states that the work done by a force is equal to the variation of the kinetic energy. If there is no friction in the system, the mechanical energy, which is the sum of the kinetic energy, and the potential energy remains constant, we can relate the work to the variation of the potential energy of the body.
W = ΔK
ΔK = ΔU
W = ΔU
Where W is the work, ΔK and ΔU are the emptied of the kinetic and potential energy, respectively,
Work is defined as the scale product of force and displacement
W = F . Δx
W = F Δx cox θ
Where F is the force, Δx the displacement and θ the angle between the force and the displacement.
Indicate that the force exerted by the dog is F = 2.1 W and it can apply this force while touching the floor, where its lowest height y₀ = 0.1 m and its highest height y = 0.6 m, in the attached we can see a scheme of the jumping of the dog,
We substitute
W = 2.1 mg (y-y₀)
The variation of the potential energy is
ΔU = mg h - mg y₀
where h is the maximum height that the dog reaches.
Since the system has no friction, let's match the expression
2.1 mg (y-y₀) = m g (h-y₀o)
2,1 (y-y₀) = h-y₀
Let's calculate h
h = 2,1 (y-y₀) + y₀
h = 2.1 (0.6 -0.1) + 0.1
h = 1.15 m
In conclusion, using the work-energy theorem and the conservation of mechanical energy, we can find the result for the maximum height that the dog can jump is:
h = 1.15 m
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