Consult Interactive Solution 7.10 for a review of problem-solving skills that are involved in this problem. A stream of water strikes a stationary turbine blade horizontally, as the drawing illustrates. The incident water stream has a velocity of 16.0 m/s, while the exiting water stream has a velocity of -16.0 m/s. The mass of water per second that strikes the blade is 48.0 kg/s. Find the magnitude of the average force exerted on the water by the blade.

Answers

Answer 1

Answer:

Explanation:

Initial speed of the incident water stream, u = 16 m/s

Final speed of the exiting water stream, v = -16 m/s

The mass of water per second that strikes the blade is 48.0 kg/s.

We need to find the magnitude of the average force exerted on the water by the blade. The force acting on an object is given by :

$F=(m(v-u))/(t)$

Here, $(m)/(t)=48\ kg/s$

$F=48* (-16-16)\ N\n\nF=-1536\ N\n\n|F|=1536\ N$

So, the magnitude of the average force exerted on the water by the blade is 1536 N.

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What If? What would be the new angular momentum of the system (in kg · m2/s) if each of the masses were instead a solid sphere 15.0 cm in diameter? (Round your answer to at least two decimal places.)

Answers

Final answer:

To find the new angular momentum of the system if each of the masses were solid spheres, calculate the moment of inertia for each sphere using the formula (2/5) × m × r^2. Multiply the moment of inertia of each sphere by the angular velocity of the system to find the new angular momentum.

Explanation:

The angular momentum of a system can be found by multiplying the moment of inertia of the system with its angular velocity.

If each of the masses were instead a solid sphere 15.0 cm in diameter, we would need to calculate the moment of inertia of each sphere using the formula for the moment of inertia of a solid sphere, I = (2/5) × m × r^2, where m is the mass and r is the radius of the sphere.

Once we have the moment of inertia for each sphere, we can multiply it by the angular velocity of the system to find the new angular momentum.

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Final answer:

The new angular momentum, given the same angular speed, will be 0.9 times the original, as the moment of inertia for the system is replaced with that of solid spheres of given mass and radius.

Explanation:

The question is asking for the new angular momentum of a sphere with a given diameter if we replace each of the masses in a given system with it. To compute the new angular momentum, it's crucial to recognize that angular momentum (L) is given by the product of the moment of inertia (I) and angular velocity (w). The moment of inertia for a solid sphere is given by (2/5)mr^2, where m is the mass and r is the radius of the sphere. Since angular velocity has not been specified in the question, it would be assumed to remain unchanged.

So, for this specific system, each mass is replaced with a solid sphere of mass 20 kg and radius 15 cm (or 0.15 m). Thus using the formula for solid sphere inertia, I = (2/5)*(20 kg)*(0.15 m)^2 = 0.9 kg*m^2. If w remains the same, then the new angular momentum L = I * w will be 0.9 times the original angular momentum. This is because w is the same but the moment of inertia has a new value due to the shape and size of the new masses.

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why does the value of capacitance of a capacitor increases in parallel combination but not in series??

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When capacitors are connected in parallel, the voltage across each capacitor is the same. But with two capacitors, it will require more charge to reach the voltage V than it would with just one capacitor. In fact, if capacitor 1 requires charge

A 2.0 cm thick brass plate (k_r = 105 W/K-m) is sealed to a glass sheet (kg = 0.80 W/K m), and both have the same area. The exposed face of the brass plate is at 80°C, while the exposed face of the glass is at 20 °C. How thick is the glass if the glass brass interface is at 65 C? Ans. 0.46 mm

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Which of the following organisms has an adaptation that will allow it to survive in tundra biome? *A.)Plants with roots that are short and grows sideways with hairy stems and small leaves.
B.)Plants that have broad leaves to capture sunlight and long roots to penetrate the soil.
C.)Animals with thin fur that allows them to get rid of heat efficiently.
D.)Animals with long tongues for capturing prey and sticky pads for climbing trees.

Answers

Answer:

the awnser is A becuse the hair help.

A long, thin solenoid has 450 turns per meter and a radius of 1.17 cm. The current in the solenoid is increasing at a uniform rate did. The magnitude of the induced electric field at a point which is near the center of the solenoid and a distance of 3.45 cm from its axis is 8.20×10−6 V/m.Calculate di/dt
di/dt = _________.

Answers

The value of di/dt from the given values of the solenoid electric field is;

di/dt = 7.415 A/s

We are given;

Number of turns; N = 450 per m

Radius; r = 1.17 cm = 0.0117 m

Electric Field; E = 8.2 × 10⁻⁶ V/m

Position of electric field; r' = 3.45 cm = 0.0345 m

According to Gauss's law of electric field;

∫| E*dl | = |-d∅/dt |

Now, ∅ = BA = μ₀niA

where;

n is number of turns

i is current

A is Area

μ₀ = 4π × 10⁻⁷ H/m

Thus;

E(2πr') = (d/dt)(μ₀niA) (negative sign is gone from the right hand side because we are dealing with magnitude)

Since we are looking for di/dt, then we have;

E(2πr') = (di/dt)(μ₀nA)

Making di/dt the subject of the formula gives;

di/dt = E(2πr')/(μ₀nA)

Plugging in the relevant values gives us;

di/dt = (8.2 × 10⁻⁶ × 2 × π × 0.0345)/(4π × 10⁻⁷ × 450 × π × 0.0117²)

di/dt = 7.415 A/s

Read more at; brainly.com/question/14003638

Answer:

$(di)/(dt) = 7.31 \ A/s$

Explanation:

From the question we are told that

The number of turns is $N = 450 \ turns$

The radius is $r = 1.17 \ cm = 0.0117 \ m$

The position from the center consider is x = 3.45 cm = 0.0345 m

The induced emf is $e = 8.20 *10^(-6) \ V/m$

Generally according to Gauss law

$\int\limits { e } \, dl = \mu_o * N * (di)/(dt ) * A$

=> $e * 2\pi x = \mu_o * N * (d i )/(dt ) * A$

Where A is the cross-sectional area of the solenoid which is mathematically represented as

$A = \pi r ^2$

=> $e * 2\pi x = \mu_o * N * (d i )/(dt ) * \pi r^2$

=> $(di)/(dt) = (2e * x )/(\mu_o * N * r^2)$ ggl;

Here $\mu_o$ is the permeability of free space with value

$\mu_o = 4\pi * 10^(-7) \ N/A^2$

=> $(di)/(dt) = (2 * 8.20*10^(-6) * 0.0345 )/( 4\pi * 10^(-7) * 450 * (0.0117)^2)$

=> $(di)/(dt) = 7.31 \ A/s$

If you hang a car of mass 1560 kg from a steel beam, the beam bends with an angle of 0.055°. What is the tension in this beam in newtons?

Answers

Answer:

The tension in the steel beam is 14.72 Newtons.

Explanation:

To calculate the tension in the steel beam when a car is hanging from it, you can use the principles of static equilibrium. In this situation, the gravitational force acting on the car must be balanced by the tension in the steel beam.

First, let's calculate the gravitational force acting on the car:

F_gravity = mass × gravity

Where:

Mass (m) = 1560 kg

Gravity (g) ≈ 9.81 m/s² (standard acceleration due to gravity)

F_gravity = 1560 kg × 9.81 m/s² ≈ 15306 N

Now, this gravitational force is balanced by the tension in the steel beam. Since the beam bends with an angle of 0.055°, we need to consider the vertical component of the tension force.

The vertical component of the tension (T_vertical) can be calculated using trigonometry (considering the angle θ):

T_vertical = T × sin(θ)

Where:

T_vertical is the vertical component of tension.

T is the tension in the beam.

θ is the angle in radians.

We need to convert the angle from degrees to radians:

θ = 0.055° × (π/180) ≈ 0.000959 radians

Now, we can calculate T_vertical:

T_vertical = 15306 N × sin(0.000959) ≈ 14.72 N

So, the tension in the steel beam is 14.72 Newtons.

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