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IceJOKER [234]
3 years ago
8

A 20.0-kg rock is sliding on a rough, horizontal surface at 8.00 m/s and eventually stops due to friction. The coefficient of ki

netic friction between the rock and the surface is 0.200.
Physics
2 answers:
Neporo4naja [7]3 years ago
5 0

Answer:

a = -1.961\,\frac{m}{s^{2}}, s = 16.318\,m, t = 4.079\,s

Explanation:

The equations of equilibrium for the rock are:

\Sigma F_{x} = -\mu_{k}\cdot N = m \cdot a

\Sigma F_{y} = N - m\cdot g = 0

After some algebraic handling, the following expression is found:

-\mu_{k}\cdot m \cdot g = m \cdot a

-\mu_{k}\cdot g = a

Deceleration experimented by the rock is:

a = - (0.2)\cdot (9.807\,\frac{m}{s^{2}} )

a = -1.961\,\frac{m}{s^{2}}

The distance travelled by the rock before stopping is:

s = \frac{(0\,\frac{m}{s} )^{2}-(8\,\frac{m}{s} )^{2}}{2\cdot (-1.961\,\frac{m}{s^{2}} )}

s = 16.318\,m

And the time is:

t = \frac{0\,\frac{m}{s}-8\,\frac{m}{s}}{(-1.961\,\frac{m}{s^{2}} )}

t = 4.079\,s

slega [8]3 years ago
4 0

The question is incomplete! The complete question along with answers and explanation is provided below.

Question:

A 20.0-kg rock is sliding on a rough, horizontal surface at 8.00 m/s and eventually stops due to friction. The coefficient of kinetic friction between the rock and the surface is 0.200

What average power is produced by friction as the rock stops?

GIven Information:

Mass of rock = m = 20 kg

Initial speed of rock = vi = 8 m/s

Coefficient of kinetic friction = μ = 0.200

Required Information:

Average power produced due to friction = ?

Answer:

Average power produced due to friction = 156.1 Watts

Explanation:

As we know the power is rate of doing work,

P = W/t

work-energy theorem relates work done and kinetic energy as

W = KE =  ½m(vf² - vi²

W = ½*20*(0 -8²)

W = -640 J

According to Newton's second law of motion,

F = ma

friction force is given by,

F = -μmg

relate the two equations

ma = -μmg

mass cancels out

a = -μg

a = -0.200*9.8

a = -1.96 m/s²

The negative sign indicates deceleration

From the kinematics equation

t = (vf - vi)/a

t = (0 - 8)/-1.96

t = -8/-1.96

t = 4.1 seconds

Therefore, the power produced to the friction is

P = 640/4.1

P = 156.1 Watts

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The question is incomplete. Here is the complete question:

A whale swims due east for a  distance of 6.9 km, turns around and  goes due west for 1.8 km and finally  turns around again and heads 3.7 km  due east.  (a) What is the total distance  traveled by the whale? (b) What are the  magnitude and direction of the displacement of the whale?

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Consider east direction as positive and west direction as negative.

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A brick of mass 5 kg is released from rest at a height of 3 m. How fast is it going when it hits the ground? Acceleration due to
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Taking into account the definition of kinetic, potencial and mechanical energy, when the brick hits the ground, it has a speed of 7,668 m/s.

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Kinetic energy is a form of energy. It is defined as the energy associated with bodies that are in motion and this energy depends on the mass and speed of the body.

Kinetic energy is defined as the amount of work necessary to accelerate a body of a given mass and at rest, until it reaches a given speed. Once this point is reached, the amount of accumulated kinetic energy will remain the same unless there is a change in speed or the body returns to its state of rest by applying a force.

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  • v is the speed measured in meters over seconds (m/s).

<h3>Potential energy</h3>

On the other hand, potential energy is the energy that measures the ability of a system to perform work based on its position. In other words, this is the energy that a body has at a certain height above the ground.

Gravitational potential energy is the energy associated with the gravitational force. This will depend on the relative height of an object to some reference point, the mass, and the force of gravity.

So for an object with mass m, at height h, the expression applied to the gravitational energy of the object is:

Ep= m×g×h

Where:

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<h3>Mechanical energy</h3>

Finally, mechanical energy is that which a body or a system obtains as a result of the speed of its movement or its specific position, and which is capable of producing mechanical work. Then:

Potential energy + kinetic energy = total mechanical energy

<h3>Principle of conservation of mechanical energy </h3>

The principle of conservation of mechanical energy indicates that the mechanical energy of a body remains constant when all the forces acting on it are conservative (a force is conservative when the work it does on a body depends only on the initial and final points and not the path taken to get from one to the other.)

Therefore, if the potential energy decreases, the kinetic energy will increase. In the same way, if the kinetics decreases, the potential energy will increase.

<h3>This case</h3>

A brick of mass 5 kg is released from rest at a height of 3 m. Then, at this height, the brick of mass has no speed, so the kinetic energy has a value of zero because it depends on the speed or moving bodies. But the potential energy is calculated as:

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So, the mechanical energy is calculated as:

Potential energy + kinetic energy = total mechanical energy

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The principle of conservation of mechanical energy  can be applied in this case. Then, when the brick hits the ground, the mechanical energy is 147 J. In this case, considering that the height is 0 m, the potential energy is zero because this energy depends on the relative height of the object. But the object has speed, so it will have kinetic energy. Then:

Potential energy + kinetic energy = total mechanical energy

0 J +  kinetic energy= 147 J

kinetic energy= 147 J

Considering the definition of kinetic energy:

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v=\sqrt{\frac{2x147 J}{5 kg} }

v=7.668 m/s

Finally, when the brick hits the ground, it has a speed of 7,668 m/s.

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brainly.com/question/11962904

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