A jet of water issuing from a stationary nozzle at 10 m/ s(aj = 0. l m2) strikes a turning vane mounted on a cart as shown. the vane turns the jet through angle fj = 40°. determine the value of m required to hold the cart stationary

Answer:

2.19 m/s

Explanation:

The momentum (p) is the product of the mass (m) and velocity (v) of an object.

p = m × v

The momentum of a 0.0075 kg bullet traveling at a speed of 365 m/s is:

p(bullet) = 0.0075 kg × 365 m/s = 2.74 kg.m/s

We want the 1.25 kg-coffee cup to have the same momentum than the bullet.

p(cup) = p(bullet) = 2.74 kg.m/s

p (cup) = m(cup) × v(cup)

2.74 kg.m/s = 1.25 kg × v(cup)

v(cup) = 2.19 m/s

To make cars and airplanes lighter, engineers use materials with high strength-to-weight ratios and apply aerodynamic principles to reduce drag. The balance of strength versus mass is resolved through materials selection and careful design optimization, including computer simulations and wind tunnel tests to create vehicles that are strong, lightweight, and efficient.

When designing cars or airplanes, the challenge is to reduce the mass of the vehicle while maintaining structural integrity. One way to achieve a lighter car is to incorporate plastics instead of metal in parts of its construction. For airplanes, advanced composite materials such as carbon fiber are often used because of their strength-to-weight ratios. Aerodynamics play a critical role in this process, as reducing drag through aerodynamic shaping can not only decrease fuel consumption but also reduce the required structural mass.

The balance between strength and mass is resolved through the use of advanced materials and design strategies. Modern design approaches involve analyzing aerodynamic forces and optimizing the shape and structures to endure these forces. With the help of computer simulations and wind tunnel testing, engineers can fine-tune designs to achieve the desired balance. The selection of materials follows a criterion that ensures they are lightweight yet able to withstand the high stresses experienced during operation. Often, the design includes failsafes that account for the worst expected loads.

Ultimately, the goal is to meet specific design objectives that include performance metrics like range, payload capacity, and fuel efficiency. Designers look at comparator aircraft or vehicles and use their data as references for optimizing wing loading, thrust-to-weight ratio, and other design parameters. Thus, the optimal design is often a trade-off between various competing factors including mass, strength, and aerodynamic efficiency.

The velocity of a 2kg mass with a kinetic energy of 16 J is 4 m/s. This result is obtained by rearranging and plugging the given values into the kinetic energy formula.

To find the velocity of a 2kg mass when its kinetic energy (KE) is 16 J, we can use the kinetic energy formula:

KE = (1/2)mv²

where:

By rearranging the formula to solve for v, we get:

v = √(2KE/m)

Substituting the given values:

v = √(2 × 16 J / 2 kg)

v = √(16 J / kg) = 4 m/s

So, the velocity of the 2kg mass when its kinetic energy is 16 J is 4 m/s.

The velocity of a 2 kg mass with 16 J of kinetic energy is 4 m/s, calculated using the kinetic energy formula KE = 0.5 * m * v² and solving for v.

To find the velocity of a 2 kg mass when its kinetic energy is 16 J, we can use the kinetic energy formula:

KE = ½mv²

where:

KE is the kinetic energy,

m is the mass,

v is the velocity.

First, we can solve for v:

v = √(2KE/m)

Substitute the given values (KE = 16 J and m = 2 kg) into the formula:

v = √(2*16 J / 2 kg)

v = √(16 J/kg)

v = 4 m/s

Therefore, the velocity of the 2 kg mass is 4 m/s.

Final answer:

To determine the maximum volume flow rate of water, we need to calculate the power supplied by the pump. Plugging in the values, the maximum volume flow rate of water is approximately 0.0019 m³/s.

Explanation:

Answer:

To determine the maximum volume flow rate of water, we need to calculate the power supplied by the pump. The formula to calculate power is power = force * velocity. If we convert the horsepower of the pump to watts (

1 hp = 746 watts), we can use the formula power = (7 hp * 746 W/hp) * (0.82 efficiency) to find the power supplied by the pump. Next, we can use the formula power = work/time = force * distance/time = force * velocity to find the force exerted by the pump. Finally, we can use the formula volume flow rate = velocity * area, where the area can be calculated using the equation area = π * (diameter/2)^2, to find the maximum volume flow rate of water. Plugging in the values, the maximum volume flow rate of water is approximately 0.0019 m³/s.

Assuming pulley is frictionless. Let the tension be ‘T’. See equation below.

The expression for the acceleration of the red block after it is released from the rest is

[tex]\fbox{\begin{minispace}\\{a = \dfrac{{\left( {{m_g} - \mu {m_r}} \right)g}}{\left( {{m_g} + {m_r}} \right)}}\end{minispace}}[/tex]

Further Explanation:

The friction force acting on the red block placed on the table is acting opposite to the direction of motion of block. The motion of the system, of red block and grey block, is vertically downward direction. It implies that the tension on the string is less than the weight on the grey block.

Given:

The mass of the red block is [tex]{m_r}[/tex].

The mass of the grey block is [tex]{m_g}[/tex].

The coefficient of friction between red block and table is [tex]\mu[/tex].

Concept:

The net force on the red block is acting along the direction of motion of the system and is equal to the difference between the tension in the string and friction force.

The net force on the red block is:

[tex]{m_r}a = T - f[/tex]

Rearrange the above expression.

[tex]T = {m_r}a + f[/tex]

Substitute [tex]\mu {m_r}g[/tex] for [tex]f[/tex] in above equation.

[tex]\fbox{\begin\\T = {m_r}a + \mu {m_r}g\end{minispace}}[/tex]                                                           …… (1)

Here,  [tex]T[/tex] is the tension on the string, [tex]{m_r}[/tex] is the mass of the red block, [tex]a[/tex] is the acceleration of the system and [tex]g[/tex] is the acceleration due to gravity.

The net force on the grey block is along the direction of motion of the system and it is equal to the difference between the weight on grey block and tension on the string.

The net force on the grey block is:

[tex]{m_g}a = {m_g}g - T[/tex]                                                                        …… (2)

Here, [tex]{m_g}[/tex] is the mass of the grey block.

Substitute [tex]{m_r}a + \mu {m_r}g[/tex] for [tex]T[/tex] in equation (2).

[tex]{m_g}a = {m_g}g - \left( {{m_r}a + \mu {m_r}g} \right)[/tex]

Rearrange the above expression.

[tex]{m_g}a + {m_r}a = {m_g}g - \mu {m_r}g[/tex]

Simplify the above expression.

[tex]\fbox{\begin{minispace}\\{a = \dfrac{{\left( {{m_g} - \mu {m_r}} \right)g}}{\left( {{m_g} + {m_r}} \right)}}\end{minispace}}[/tex]

Learn more:

1. Change in momentum  https://brainly.com/question/9484203

2.  The motion of a body under friction brainly.com/question/4033012

3. A ball falling under the acceleration due to gravity brainly.com/question/10934170

Answer Details:

Grade: College

Subject: Physics

Chapter: Kinematics

Keywords:

Acceleration, friction, tension, system of two blocks, pulley mass system, motion, net force, string, block placed on the table, block hanging through a pulley, block is released from rest.

Answer:

Work done, [tex]W=1.03\times 10^6\ J[/tex]

Explanation:

It is given that,

Mass of the car, m = 950 kg

Distance up to the incline, d = 710 m

Angle of inclination of the car is 9 degrees.

When the car is push in the inclined path, the vertical component of the force will act on it such that the work done is given by :

[tex]W=mg\ sin\theta\times d[/tex]

[tex]W=950\times 9.8\times \ sin(9) \times 710[/tex]  

[tex]W=1.03\times 10^6\ J[/tex]

So, the minimum work needed to push a car is [tex]1.03\times 10^6\ J[/tex]. Hence, this is the required solution.

The minimum work needed to push a car up an incline can be found by calculating the work done against gravity. This is done by multiplying the mass of the car by the gravitational acceleration and the height, which can be deduced from the sin of the incline angle and the distance.

The question is asking for the minimum work done to push a car up an inclined plane. To solve this, you use the concept of work done against gravity. The formula for work done against gravity is Work = m * g * h, where m is the mass, g is the gravitational acceleration and h is the height. Since the distance and incline angle are provided, we can calculate the height with the trigonometric function sine, h = sin(angle) * distance. Substituting these values, we get Work = 950kg * 9.81m/s² * sin(9.0°) * 710m. The required calculation will then provide the answer to the work done in pushing the car up the incline.

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The force does 195 Joules of work on the object.

To calculate the work done by a force, we use the formula:

Work = Force x Distance x cos(theta)

Given that the force is 25 N, the angle is 30 degrees, and the distance is 3 m, we can substitute these values into the formula to calculate the work:

Work = 25 N x 3 m x cos(30 degrees) = 195 J

Therefore, the force does 195 Joules of work on the object.

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The motion of an unanchored rowboat when a water wave passes, the boat moves along with the waves. The boat doesn't move forward as waves could not take the boat along with it.

The water waves are waves that have a combination of both longitudinal and transverse waves. Longitudinal waves are the waves that cause the medium to move parallel to the direction of the waves.

Transverse waves are the waves that cause the medium to move perpendicular to the direction of the waves. When the waves travel through the water, the particles move in a clockwise direction. Most of the waves are formed by the winds.

The motion of the unanchored rowboat, when water pass is a boat, is moved up and down along with the wave. But the boat does not move forwards along with the wave. Because the wave does not carry the boat with it.

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The semimajor axis is equal to 270 Km. The eccentricity of the orbit is 0.33 Km.

An elliptic orbit or elliptical orbit can be described as a Kepler orbit with an eccentricity of less than 1. It is a circular orbit with an eccentricity equal to 0. It is a Kepler orbit with an eccentricity greater than 0 and less than 1 and a Kepler's orbit with negative energy. The radial elliptic orbit has an eccentricity equal to 1.

Given the satellite, moving in an elliptical orbit has the farthest point from the  above earth's surface, [tex]R_a[/tex] = 360 Km

The closest point from the  above earth's surface, [tex]R_p[/tex] = 180 Km

Semi-major axis can be calculated as , [tex]{\displaystyle a = \frac{R_a+R_p}{2}[/tex]

[tex]{\displaystyle a = \frac{360 + 180}{2}[/tex]

a = 270 km

The eccentricity of the elliptical orbit, we can calculate as shown below:

[tex]{\displaystyle e = \frac{a- R_p}{a}[/tex]

e = (270 - 180)/270

e = 1/3

e = 0.33 km

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Final answer:

There are at least two fundamental action-reaction pairs of forces when a girl stands on a sofa, including the force of gravity and the normal force, as well as any frictional forces if there is lateral movement.

Explanation:

Action-Reaction Pairs

In the scenario where a girl stands on a sofa, there are several action-reaction pairs of forces at play. According to Newton's third law, every action has an equal and opposite reaction. When the girl exerts a force on the sofa (due to her weight), the sofa exerts an equal and opposite force back onto the girl. This is one pair. Additionally, if the girl were to push on the sofa to stand up or adjust her position, the sofa would push back with an equal force in the opposite direction, forming another action-reaction pair.

The number of action-reaction pairs can vary based on what specific interactions are being considered. Generally, in this scenario, we consider at least two fundamental pairs: the force of gravity on the girl (action) and the normal force from the sofa on the girl (reaction), and if there's any lateral movement while standing, there would be a frictional force between the sofa and the girl's feet (action), and an equal and opposite frictional force from the girl's feet on the sofa (reaction).

Answer:

it will become charged by Q = 5C

Explanation:

When electron is removed from matter then the system will get positively charged

So we will have

[tex]Q = Ne[/tex]

here N = number of electrons that is removed

[tex]N = 31.25 \times 10^{18}[/tex]

also we know that charge on one electron is given as

[tex]e = 1.6 \times 10^{-19}[/tex]

here we have

[tex]Q = Ne[/tex]

[tex]Q = (31.25 \times 10^{18})(1.6 \times 10^{-19})[/tex]

[tex]Q = 5 C[/tex]

so it will become charged by Q = 5C

We have first velocity equals 8 m/s and the kinetic energy is 480 J

The order is the mass of the object

We have this formula K= mv2/2 isolating the mass we have m=k/v2

Now we will have m=480/8×8 > m= 480/64 m= 7.5kg now we deternimed the mass it's 7.5 kg

As per the statement, Manny walks about 3 miles and the reference point for calculating the distance is the same as the starting point.  

Hence the option B is correct.

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Contact forces occur when two objects are in contact while Non-contact forces occur without any physical contact.

Force is the action of push or pull which cause an object to move or stop.

Contact forces are the forces that come into existence when two objects come in contact to apply a force, For example: Frictional Force.

Non-contact forces takes place without any physical contact. For example: Gravitational force, Electric force, Magnetic force.

Thus, Contact forces occur when two objects are in contact while Non-contact forces occur without any physical contact.

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Answer: The entire process is mentioned in  step-wise below-

Remember that the total velocity of the motion is the vector sum of the velocity you would have in still water and the stream. Always place the vectors carefully to be able to come up with an accurate sum vector.

Final answer:

Despite their different masses, two objects with equal speeds moving on a frictionless incline reach the same height because mechanical energy is conserved and potential energy at a given height is not dependent on mass.

Explanation:

In a scenario where two objects with different masses but equal speeds slide up a frictionless incline, the laws of physics tell us that both objects should reach an equivalent height. This is because the mechanical energy (kinetic plus potential energy) in a closed system without any external forces (like friction) is conserved. Since both objects start with the same kinetic energy (due to equal speeds) and potential energy is directly related to height (not mass), they should convert their kinetic energy into the same amount of potential energy, meaning they should rise to the same height before coming to a stop and sliding back down.

It's important to note that if there were friction or some other external force acting on the objects, the outcomes could be different as the mechanical energy would no longer be conserved in the same way, but in a frictionless situation, mass does not affect the height an object reaches if it starts with the same kinetic energy.

Answer:a) a force acting on an object in motion causes it to stop moving

Explanation: gradpoint