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2 years ago

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A boat can travel 2.30 m/s in still water. If the boat points its prow directly across a stream whose current is 1.80 m/s , what

is the magnitude of the velocity of the boat relative to the shore?

1 answer:

Alinara [238K]2 years ago

5 0

Answer:

A boat can travel 2.30 m/s in still water. (a) If the boat points its prow directly across a stream whose current is. ... (a) What is the velocity (magnitude and direction) of the boat relative to the shore? ... The boat's velocity with respect to the shore, , is the sum of its velocity with respect to the water

Explanation:

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A small box of mass m1 is sitting on a board of mass m2 and length L. The board rests on a frictionless horizontal surface. The

Nadusha1986 [10]

Answer:

The constant force with least magnitude that must be applied to the board in order to pull the board out from under the box is $\left( {{m_1} + {m_2}} \right){\mu _{\rm{s}}}$

Explanation:

The Newton’s second law states that the net force on an object is the product of mass of the object and final acceleration of the object. The expression of newton’s second law is,

$\sum {F = ma}$

Here, is the sum of all the forces on the object, mm is mass of the object, and aa is the acceleration of the object.

The expression for static friction over a horizontal surface is,

$F_{\rm{f}}} \leq {\mu _{\rm{s}}}mg$

Here, ${\mu _{\rm{s}}}$ is the coefficient of static friction, mm is mass of the object, and $g$ is the acceleration due to gravity.

Use the expression of static friction and solve for maximum static friction for box of mass ${m_1}$

Substitute for in the expression of maximum static friction ${F_{\rm{f}}} = {\mu _{\rm{s}}}mg$

${F_{\rm{f}}} = {\mu _{\rm{s}}}{m_1}g$

Use the Newton’s second law for small box and solve for minimum acceleration aa to pull the box out.

Substitute for , [/tex]{m_1}[/tex] for in the equation .

${F_{\rm{f}}} = {m_1}a$

Substitute ${\mu _{\rm{s}}}{m_1}g$ for ${F_{\rm{f}}}$ in the equation ${F_{\rm{f}}} = {m_1}a$

${\mu _{\rm{s}}}{m_1}g = {m_1}a$

Rearrange for a.

$a = {\mu _{\rm{s}}}g$

The minimum acceleration of the system of two masses at which box starts sliding can be calculated by equating the pseudo force on the mass with the maximum static friction force.

The pseudo force acts on in the direction opposite to the motion of the board and the static friction force on this mass acts in the direction opposite to the pseudo force. If these two forces are cancelled each other (balanced), then the box starts sliding.

Use the Newton’s second law for the system of box and the board.

Substitute for for in the equation .

${F_{\min }} = \left( {{m_1} + {m_2}} \right)a$

Substitute for in the above equation .

${F_{\min }} = \left( {{m_1} + {m_2}} \right){\mu _{\rm{s}}}g$

The constant force with least magnitude that must be applied to the board in order to pull the board out from under the box is $\left( {{m_1} + {m_2}} \right){\mu _{\rm{s}}}g$

There is no friction between the board and the surface. So, the force required to accelerate the system with the minimum acceleration to slide the box over the board is equal to total mass of the board and box multiplied by the acceleration of the system.

5 0

3 years ago

A project is located in an area with a demand-response program and on a site that has enough room for a wind-turbine to allow fo

Ksju [112]

Answer:

A. The project's energy costs will decrease

Explanation:

Since the project is located in an area with a demand-response program and on a site that has enough room for a wind-turbine to allow for on-site renewable energy.

Hence, the project's energy costs will decrease very well because it's implementing both of these strategies;

- Area with demand-response program.

- On-site renewable energy.

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3 years ago

how much water is needed to produce 1kwh of electricity at a power plant that is 30% efficient if the temperature increase 10 C

Dimas [21]

The amount of water needed is 287 kg

Explanation:

The amount of energy that we need to produce with the power plant is

$E=1 kWh = (1000W)(1h)=(1000W)(3600s)=3.6\cdot 10^6 J$

We also know that the power plant is only 30% efficient, so the energy produced in input must be:

$E_{in}=\frac{E}{0.30}=\frac{3.6\cdot 10^6}{0.3}=1.2\cdot 10^7 J$

The amount of water that is needed to produce this energy can be found using the equation

$E_{in}=mC\Delta T$

where:

m is the amount of water

$C=4186 J/kg^{\circ}C$ is the specific heat capacity of water

$\Delta T=10^{\circ}C$ is the increase in temperature

And solving for m, we find:

$m=\frac{E_{in}}{C\Delta T}=\frac{1.2\cdot 10^7}{(4186)(10)}=287 kg$

Learn more about specific heat capacity:

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2 years ago

Julia performs an experiment to measure the wavelength of four different waves and records her data in the table below.

Svet_ta [14]

The correct order they go in is "1-4-2-3" The correct answer is D.

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3 years ago

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How does kinetic energy affect the stopping distance of small vehicle compared to a large vehicle

Nadusha1986 [10]

The kinetic energy for a large vehicle is different from that of a smaller vehicle, assuming that the vehicles are travelling at the same speed and stopping the same distance. This is because for a larger vehicle the kinetic energy is higher, as the mass for a larger vehicle, is more than the smaller vehicle.

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3 years ago