At the point of maximum displacement (a), the elastic potential energy of the spring is maximum:

while the kinetic energy is zero, because at the maximum displacement the mass is stationary, so its velocity is zero:

And the total energy of the system is

Viceversa, when the mass reaches the equilibrium position, the elastic potential energy is zero because the displacement x is zero:

while the mass is moving at speed v, and therefore the kinetic energy is

And the total energy is

For the law of conservation of energy, the total energy must be conserved, therefore

. So we can write

that we can solve to find an expression for v:
Here Change in Kinetic Energy
= Work Done by Friction
Therefore, substituting the
given values to the equation, we get
0.5 * m * (vFinal^2 -
vInitial^2) = µ m g * d
Therefore
0.5*( 5.90^2 - Vfinal^2 ) =
0.100*9.8*2.10
Therefore
vfinal = 5.54 m/sec
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Answer:
∆h = 0.071 m
Explanation:
I rename angle (θ) = angle(α)
First we are going to write two important equations to solve this problem :
Vy(t) and y(t)
We start by decomposing the speed in the direction ''y''


Vy in this problem will follow this equation =

where g is the gravity acceleration

This is equation (1)
For Y(t) :

We suppose yi = 0

This is equation (2)
We need the time in which Vy = 0 m/s so we use (1)

So in t = 0.675 s → Vy = 0. Now we calculate the y in which this happen using (2)

2.236 m is the maximum height from the shell (in which Vy=0 m/s)
Let's calculate now the height for t = 0.555 s

The height asked is
∆h = 2.236 m - 2.165 m = 0.071 m
The exact magnification of the objects is calculated by dividing the cinema. We calculate it by diving the erect image size by the object size. From the given above, we find the exact magnification by dividing 5.0 cm by 1.0 cm. Thus, the answer would be 5.