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3 years ago

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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?

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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A mass weighting 16 lbs stretches a spring 3 inches. The mass is in a medium that exerts a viscous resistance of 20 lbs when the

const2013 [10]

Answer:

The equation for the object's displacement is $u(t)=0.583cos11.35t$

Explanation:

Given:

m = 16 lb

δ = 3 in

The stiffness is:

$k=\frac{m}{\delta } =\frac{16}{3} =5.33lb/in$

The angular speed is:

$w=\sqrt{\frac{k}{m} } =\sqrt{\frac{5.33*386.4}{16} } =11.35rad/s$

The damping force is:

$F_{D} =cu$

Where

FD = 20 lb

u = 4 ft/s = 48 in/s

Replacing:

$c=\frac{F_{D} }{u} =\frac{20}{48} =0.42lbs/in$

The critical damping is equal:

$c_{c} =\frac{2k}{w} =\frac{2*5.33}{11.35} =0.94lbs/in$

Like cc>c the system is undamped

The equilibrium expression is:

$u(t)=u(o)coswt+u'(o)sinwt\\u(o)=7=0.583\\u'(o)=0\\u(t)=0.583coswt\\u(t)=0.583cos11.35t$

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3 years ago

A 0.0600-kilogram ball traveling at 60.0 meters

Vikki [24]

The momentum of ball is given by:

$\Delta Q=mv \\ \Delta Q=6*10^{-2}*60 \\ \Delta Q=3.6kg*m/s$

Since both have the same momentum, we have:

$\Delta Q=MV \\ 3.6=10^{-2}V \\ \boxed {V=360m/s}$

Number 3

If you notice any mistake in my english, please let me know, because i am not native.

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3 years ago

Issac newton how did he shape the new worldview?

gulaghasi [49]

Accordingly Newton's findings, astronomy and physics have industrialized hugely over the period. Scientists now recognize that every object in the world has a force that draws each other and the power of the force hinge on the mass of the object. Also, Newton's Laws of Motion offer individuals a better understanding of what is likely concerning movement. This is very helpful, particularly in mechanics and space travel. Generally, Newton had a huge and permanent impact on science.

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3 years ago

You can keep a 1kg apple from falling to the ground by placing it on a table. What reaction force is resisting the force of the

Gnom [1K]

The equilibrium condition allows finding the correct answer for the force that is resisting the weight of the apple is:

3. Normal force

Newton's second law gives the relationship between <em>force, mass</em> and acceleration of bodies, in the special case that the acceleration is is called the equilibrium condition.

∑ F = 0

Where F is the external force.

The free body diagram is a diagram of the forces on bodies without the details of the shape of the body, in the attached we can see a scheme of the forces.

Let's write the equilibrium condition for the apple

N - W = 0

N = W

.

We can see that the only forces acting on the apple are its weights and reaction from the table called Normal.

Let's analyze the different answers:

1. False. The apple is not moving therefore the resistance is zero

2. False. The apple is not moving so friction it with the table is

3. True. The free-body diagram shows that the normal and the weight are equal

4. False. There is nothing to pull the apple so there is no tension

5. False. Gravity is the weight of the apple that is applied to the table, not from the table to the apple.

In conclusion using the equilibrium condition we can find the correct result for the force that is resisting the weight of the apple is:

3. Normal force

Learn more here: brainly.com/question/2872207

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3 years ago

After the big bang, atoms in gas clouds experienced a greater gravitational pull to each other than atoms in other regions of th

allsm [11]

Answer:
These are the two statements with scientific facts that explain the described phenomenon
<span>
Gravitation between two objects increases when the distance between them decreases.</span>

When the mass of an object increases, its gravitational pull also increases.

Justification:

Those two facts are represented in the Universal Law of Gravity discovered by the scientific Sir Isaac Newton (1642 to 1727) and published in his book <span>Philosophiae naturalis principia mathematica.</span>

That law is represented by the equation:

F = G × m₁ × m₂ / d²

The product of the two masses on the numerator accounts for the fact that the gravitational force is directly proportional to the product of the masses, which is that as the masses increase the attraction also increase.

The term d² (square of the distance that separates the objects) in the denominator accounts for the fact that the gravitational force is inversely proportional to the square of the distance; that is as the separation of the objects increase the gravitational force decrease.

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