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n200080 [17]
3 years ago
14

If you push any floating object down from equilibrium and release it, it bobs up and down. That looks like an oscillation, so le

t's analyze the restoring force driving the floating object back to equilibrium. Suppose the cube is distance y below its equilibrium position. Find an expression for the y-component of the net force exerted on it. Simplify this expression as much as possible. Does it look like a linear restoring force?
Physics
1 answer:
GarryVolchara [31]3 years ago
8 0

Answer:

  F_{y} = ( ρ_fluid g A) y

Explanation:

This exercise can be solved in two parts, the first finding the equilibrium force and the second finding the oscillating force

for the first part, let's write Newton's equilibrium equation

        B₀ - W = 0

        B₀ = W

        ρ_fluid g V_fluid = W

the volume of the fluid is the area of ​​the cube times the height it is submerged

      V_fluid = A y  

For the second part, the body introduces a quantity and below this equilibrium point, the equation is

        B - W = m a

        ρ_fluid g A (y₀ + y) - W = m a

        ρ_fluid g A y + (ρ_fluid g A y₀ -W) = m a

       ρ_fluid g A y + (B₀-W) = ma

the part in parentheses is zero since it is the force when it is in equilibrium

      ρ_fluid g A y = m a

      this equation the net force is

      F_{y} = ( ρ_fluid g A) y

we can see that this force varies linearly the distance and measured from the equilibrium position

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1) The final velocity of the two trains is 6 m/s to the right

2) It is an inelastic collision

Explanation:

1)

We can solve this problem by using the law of conservation of momentum: in fact, in absence of external forces, the total momentum of the two trains must be conserved before and after the collision.

Therefore we can write:

p_i = p_f\\m_1 u_1 + m_2 u_2 = (m_1+m_2)v  

where:  

m_1 = 6,000 kg is the mass of the first train

u_1 = 10 m/s is the initial velocity of the first train

m_2 = 4,000 kg is the mass of the second train

u_2 = 0 is the initial velocity of the second train  (initially at rest)

v is the final combined velocity of the two trains

Solving the equation for v, we find the final velocity of the two trains:

v=\frac{m_1 u_1 + m_2 u_2}{m_1+m_2}=\frac{(6000)(10)+0}{6000+4000}=6 m/s

2)

There are two types of collisions:

  • Elastic collision: in an elastic collision, both the total momentum and the total kinetic energy of the system are conserved
  • Inelastic collision: in an inelastic collision, only the total momentum is conserved, while the total kinetic energy is not (part of it is converted into thermal energy due to internal frictions)

To verify what type of collision is this, we can compare the total kinetic energy before and after the collision:

Before:

K=\frac{1}{2}m_1 u_1^2 = \frac{1}{2}(6000)(10)^2=300,000 J

After:

K=\frac{1}{2}(m_1 +m_2)v^2 = \frac{1}{2}(6000+4000)(6)^2=180,000 J

As we can see, the kinetic energy is not conserved, so this is an inelastic collision.

Learn more about momentum here:

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A block of mass 200g is oscillating on the end of a horizontal spring of spring constant 100 N/m and natural length 12 cm. When
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In order to determine the acceleration of the block, use the following formula:

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Moreover, remind that for an object attached to a spring the magnitude of the force acting over a mass is given by:

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