Mixed powders may be categorized as
1 answer:
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Answer:
(a) -472.305 J
(b) 1 m
Explanation:
(a)
Change in mechanical energy equals change in kinetic energy
Kinetic energy is given by
Initial kinetic energy is
Since he finally comes to rest, final kinetic energy is zero because the final velocity is zero
Change in kinetic energy is given by final kinetic energy- initial kinetic energy hence
0-472.305 J=-472.305 J
(b)
From fundamental kinematic equation
Where v and u are final and initial velocities respectively, a is acceleration, s is distance
Making s the subject we obtain
but a=\mu g hence
The concept of conservation of energy and harmonic motion allows to find the result for the power where the kinetic and potential energy are equal is:
x = 0.135 cm
Given parameters
- The mass m = 220 g = 0.220 kg
- The spring cosntnate3 k = 7.0 N / m
- Initial displacement A = 5.2 cm = 5.2 10-2 m
To find
- The position where the kinetic and potential energy are equal
A simple harmonic movement is a movement where the restoring force is proportional to the displacement, the result of this movement is described by the expression.
x = A cos wt + fi
w² =
Where x is the displacement from the equilibrium position, A the initial amplitude of the system, w the angular velocity t the time, fi a phase constant determined by the initial conditions, k the spring constant and m the mass.
The speed is defined by the variation of the position with respect to time.
v =
let's evaluate
v = - A w sin (wt + Ф)
Since the body releases for a time t = 0 the velocity is zero, therefore the expression remains.
0 = - A w sin Ф
For the equality to be correct, the sine function must be zero, this implies that the phase constant is zero
x = A cos wt
Let's find the point where the kinetic and potential energy are equal.
K = U
½ m v² = m g x
we substitute
½ A² w² sin² wt = g A cos wt
sin² wt = cos wt
let's calculate
w =
w = 5.64 rad / s
sin² 5.64t = 2 9.8 / 0.052 cos 5.64t
sin² 5.64t = 376.92 cos 5.64 t
1 - cos² 5.64t = 376.92 cos 5.64t
cos² 5.64t -376.92 cos564t -1 = 0
we make the change of variable
x = cos 5.64t
x²- 376.92 x - 1 = 0
x = 0.026
cos 5.64t = 0.026
Let's find the displacement for this time
x = 5.2 10-2 0.026
x = 1.35 10-3 m
In conclusion Using the concepts of conservation of energy and harmonic motion we can find the result for the could where the kientic and potential enegies are equal is:
x = 0.135 cm
Learn more here: brainly.com/question/15707891