What is the final velocity (in m/s) of a hoop that rolls without slipping down a 3.50-m-high hill, starting from rest

The electric heater draws a current of 4.5 amps.

Using Ohm's Law, we can calculate the current drawn by the electric heater. Ohm's Law states that the current (I) flowing through a conductor is equal to the voltage (V) applied to the conductor divided by its resistance (R):

In this case, the voltage (V) is 120 V and the power (P) of the electric heater is 540 W. We can use the formula P = VI, where P is the power in watts, V is the voltage in volts, and I is the current in amperes. Solving for I, we get:

Therefore, the electric heater draws a current of 4.5 amperes (A) when operated at 120 volts (V).

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Explanation:

Reflection is the change in direction of a wavefront at an interface between two different media so that the wavefront returns into the medium from which it originated. Common examples include the reflection of light, sound and water waves.

In an equal circuit, all parts are associated across one another, subsequent in precisely two arrangements of electrically normal places.

The complete power in a series circuit is equivalent to the amount of power disseminated by the individual resistors.

The complete power disseminated will be equivalent to the amount of the power dispersed by every individual obstruction. Contingent upon the qualities that are known, blends of the power equation, also as Ohm's regulation, can be utilized to work out power disseminated (or some other obscure worth).

An equal circuit disseminates more power than a series circuit. For similar arrangements of resistors, the complete obstruction of the equal circuit is consistently lower than the all-out opposition in a series circuit.

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Answer:

If two vectors are equal, their components are also equal. For example, vector A and B both share the same x, y, and z components. By having the same components, the magnitude and direction does not change, which attest to how the vectors are identical.

So, if two vectors are equal, their components are also equal.

In vector mathematics, when two vectors are equal, it means their corresponding components are also equal. Thus, the magnitude and direction of the two vectors must be identical.

In the world of mathematics, specifically vector mathematics, if two vectors are equal, that means their corresponding components are also equal. A vector is typically described by its individual components which are its magnitude (size) and direction.

For example, if vector A and vector B are equal, and vector A = \((x_1, y_1)\) and vector B = \((x_2, y_2)\), then\(x_1 = x_2\) and \(y_1 = y_2\). This applies to vectors in two-dimensional and three-dimensional spaces as well. Therefore, equality in vectors involves the same direction and magnitude causing the corresponding components to be equal.

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Answer:

gravitational

Explanation:

gravitational force equation = Mass x Gravitational Constant

The gravitational force is also defined as the force between objects with masses.

Answer:

a = 5.256 m / s²  with the vertical direction upwards and   T = 1090.8 N

Explanation:

to find the acceleration we must use Newton's second law, in the lowest part of the motion

          T - W = m a

where the acceleration is centripetal

         a = v² / r

let's calculate

         a = 4.51² / 3.87

         a = 5.256 m / s²

As the acceleration is centripetal it is directed towards the center of the circle, which in the lower part coincides with the vertical direction upwards.

Let's find the tension of the rope with the first equation

        T = W + m a

        W = m g

let's calculate

         T = 710 + 710 5.256 / 9.8

         T = 1090.8 N

Vehicles need to be serviced for several reasons such as preventing costly repairs and improving fuel economy.

First, regular maintenance can help to prevent costly repairs down the road. Second, maintenance can help to improve fuel economy and emissions. Third, maintenance can help to keep your vehicle safe and reliable.

The servicing requirements for petrol/diesel and electric vehicles differ in a number of ways. Petrol/diesel vehicles require oil changes more frequently than electric vehicles. This is because petrol/diesel engines use oil to lubricate the moving parts, while electric motors do not. Petrol/diesel vehicles also require tune-ups more frequently than electric vehicles.

This is because petrol/diesel engines have more moving parts that need to be synchronized, while electric motors have fewer moving parts.

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The missing species of the nuclear reaction obtained is ³⁰₁₅P

The missing species of the equation can be obtain as follow:

Now, we can obtain the value of x, y and Z as follow:

²⁷₁₃Al + ⁴₂He -> ʸₓZ + ¹₀n

For x

13 + 2 = x + 0

15 = x

x = 15

For y

27 + 4 = y + 1

31 = y + 1

Collect like terms

y = 31 - 1

y = 30

For Z

ʸₓZ => ³⁰₁₅Z

From the period table, the element with atomic number of 15 is phosphorus, P. Thus, we have

ʸₓZ => ³⁰₁₅Z => ³⁰₁₅P

Therefore, we can write the complete equation as:

²⁷₁₃Al + ⁴₂He -> ³⁰₁₅P + ¹₀n

Thus, the missing species is ³⁰₁₅P

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Given that the cannon ball is launched at an 18 degree angle

Initial speed = 25 m/s

So the initial velocity in the horizontal direction (say v_x) will be

The horizontal component of velocity will be constant throughout the motion since there is no acceleration in the x-direction, only acceleration due to gravity in y-direction.

So at the peak of its arc the velocity will be the same to its initial value, i.e.

Answer: The efficiency is 97.5% or 0/975

Explanation: Efficiency = Useful output/Total Input

975/1000 = 0.975

In this instance, 975 J is the useful output and the 1000 J is the total input so you divide Useful/Total energy

The slope of the graph is 0.5 m/s² and when t = 1.5 s, the predicted displacement (d) of the object is 0.75 meters.

To plot the velocity vs. time graph, we'll use the given data points:

Duration, At (s): 2.0, 4.0, 6.0, 8.0, 10.0, 12.0

Velocity, v (m/s): 6.0, 7.0, 8.0, 9.0, 10.0, 11.0

Let's plot these points on a graph:

Time (s) [x-axis] | Velocity (m/s) [y-axis]

--------------------------------------------

2.0               | 6.0

4.0               | 7.0

6.0               | 8.0

8.0               | 9.0

10.0              | 10.0

12.0              | 11.0

After plotting the points, we can connect them with a straight line to represent the motion of the object. This line represents the velocity vs. time relationship.

Now, let's calculate the slope of this line. The slope of a line represents the rate of change of the dependent variable (velocity) with respect to the independent variable (time). In this case, it gives us the acceleration of the object.

Using the formula for calculating the slope of a line:

Slope (k) = (Change in velocity) / (Change in time)

For the first two points:

Change in velocity = 7.0 - 6.0 = 1.0 m/s

Change in time = 4.0 - 2.0 = 2.0 s

Slope (k) = 1.0 m/s / 2.0 s = 0.5 m/s²

Therefore, the slope of the graph is 0.5 m/s².

Now, to answer part B, the physical significance of the slope value is that it represents the object's acceleration. In this case, the constant acceleration experienced by the object is 0.5 m/s².

Moving on to part C, we are given the equation d = kt, where d represents the displacement and t represents time. Since the object is experiencing constant acceleration, the equation can be rewritten as d = 0.5t, where 0.5 is the acceleration (k).

To predict the value of "d" when t = 1.5 s, we can substitute the value of t into the equation:

d = 0.5 * 1.5 = 0.75 meters

Therefore, when t = 1.5 s, the predicted displacement (d) of the object is 0.75 meters.

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The probable question may be:

An object is subjected to a constant acceleration along a frictionless track. A student measures its velocity (v) after specific durations (At). The student uses a graph to analyze the truck's motion.

Duration, At, (s) :- 2.0,4.0,6.0,8.0,10.0,12.0.

Velocity, v, (m/s) :- 6.0,7.0,8.0,9.0,10.0,11.0

A. Plot the velocity (in meters/sec) vs. time (seconds). The velocity is the y-axis and time is the x-axis. Use any graphing software you like or graph this data in pencil on graph paper. Excel has a nice graphing package. Calculate the slope of this graph. You will

B. What is the physical significance of the slope value computed in part A?

C. Having determined the slope of the line, you can now write d = kt. Use this equation to predict a value of "d" when t = 1.5 s.

Answer:

The red color in the sky at sunset (and sunrise) is due to an effect called Rayleigh scattering.

Explanation:

Answer:

120

Work :

W = Fd (work = force x distance)

Force :

F = W/d

Distance :

d = W/F

Answer:

The interaction with the highest electrostatic potential energy is:

A +1 and -2 particle separated by a distance of 5 nm.

Explanation:

The electrostatic potential energy between two charged particles depends on the magnitude of their charges and the distance between them. The formula for calculating electrostatic potential energy is:

U = k * (q1 * q2) / d

where U is the electrostatic potential energy, k is Coulomb's constant, q1 and q2 are the magnitudes of the charges, and d is the distance between them.

In the given options, the interaction between +1 and -2 particles separated by a distance of 5 nm has the highest electrostatic potential energy because the charges have a higher magnitude (compared to other options) and they are close to each other, resulting in a stronger electrostatic force of attraction. The other options either have smaller charges, larger distances, or both, leading to lower electrostatic potential energy.

The given expression 3 + 2 ∙ 4 = 3 + (2 ∙ 4) is absoulutely correct so it is True.

Arithmetic operators are four basic mathematical operations in which summation, subtraction, division, and multiplication involve.,

Summation = addition of two or more numbers or variable

For example = 2 + 8 + 9

Subtraction = Minus of any two or more numbers with each other called subtraction.

For example = 4 - 8

Division = divide any two numbers or variable called division.

For example 4/8

Multiplication = to multiply any two or more numbers or variables called multiplication.

For example 5 × 7.

Given,

3 + 2 ∙ 4 = 3 + (2 ∙ 4)

We know that in every calculation we cannot separate multiplication and need to solve them first

So,

3 + 8 = 3 + 8

11 = 11

Hence, 3 + 2 ∙ 4 = 3 + (2 ∙ 4)  is absoulutely correct.

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The power loss in the bearing is 1.36 W shaft of 100 mm diameter rotates at 120 rad/s in a bearing 150 mm long.

The viscosity of a fluid is a measure of its resistance to flow. A fluid with a high viscosity resists movement because its molecular structure causes a lot of internal friction.

The viscosity of a fluid is a measure of its resistance to flow. A fluid with a high viscosity resists movement because its molecular structure causes a lot of internal friction.

To calculate the power loss in the bearing, we can use the formula:

P = F × V

To calculate the frictional force, we can use the formula:

F = μ × A × P

Where μ is the coefficient of friction, A is the area of the bearing, and P is the pressure of the lubricant.

First, we need to calculate the pressure of the lubricant:

P = μ × Viscosity × (V/D)

Where D is the diameter of the shaft.

P = (0.02) × 20 × (120/0.1) = 480 N/\(m^2\)

Next, we can calculate the area of the bearing:

A = π × (D/2)^2 × L

Where L is the length of the bearing.

A = π × (0.1/2)^2 × 0.15 = 0.001178 \(m^2\)

Now we can calculate the frictional force:

F = μ × A × P = (0.02) × 0.001178 × 480 = 0.0113 N

Finally, we can calculate the power loss:

P = F × V = 0.0113 × 120 = 1.36 W

Therefore, the power loss in the bearing is 1.36 W.

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Answer:

Explanation:

(a)

From the given information:

The initial velocity \(v_1\) = 5 m/s

The direction of the angle θ = 30°

Therefore, the component along the x-axis = \(v_1 \ cos \ \theta\)

\(v_{1 \ x } = 5 \ cos \ 30^0\)

\(v_{1x} = 4.33 \ m/s\)

The component along the y-axis = \(v_2 { \ sin \ \theta}\)

\(v_{1 \ y } = 5 \ sin \ 30^0\)

\(v_{1 \ y } = 2.5 \ m/s\)

To find the final velocity( reflected velocity)

using the same magnitude \(v_2 = 5 \ m/s\)

The angle from the x-axis can be \(\theta_r = 90^0+60^0\)

= 150°

Thus, the component along the x-axis = \(v_2 \ cos \theta _r\)

\(v_{2x} = - 0.433 \ m/s\)

The component along the y-axis = \(v_2 \ sin \theta_r\)

\(v_{2y} = 5 \ sin \ 150^0\)

\(v_{2y} = 2.5 \ m/s\)

(b)

The velocity \(v_1\) can be written as in vector form.

\(v_1 ^{\to} = v_1 x \hat {i} + v_1 y \hat {j}\)

\(v_1 ^{\to} =4.33 \ \hat {i} + 2.5 \ \hat {j}\)  ----  (1)

The reflected velocity in vector form can be computed as:

\(v_2 ^{\to} = v_2 x \hat {i} + v_2 y \hat {j}\)

\(v_2 ^{\to} =-4.33 \ \hat {i} + 2.5 \ \hat {j}\)  --- (2)

The change in velocity = \(v_2 ^{\to} - v_1 ^{\to}\)

\(\Delta v ^{\to} = - 4.33 \hat i + 2.5 \hat j - 4.33 \hat i - 2.5 \hat j\)

\(\Delta v ^{\to} = - 8.66 \hat { i }\)

(c)

The magnitude of change in velocity = \(| \Delta V |\)

\(| \Delta V |\) = 8.66 m/s

The time taken for the box to get to the storage area, given that the box is moving at a constant velocity of 40 meters per minute is 0.2 minutes

Speed is defined as the distance travelled per time as shown below:

Speed = Distance / time

Cross multiply

Speed × time = distance

Divide both sides by speed

Time = Distance / speed

The following data were obtained from the question:

The time take can be obtained as follow:

Time = Distance / speed

Time = 8 / 40

Time = 0.2 minutes

Thus, the time taken to get the storage area is 0.2 minutes

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The strength of the electric force between particles depends on two factors: the magnitude of the charges on the particles and the distance between them. Increasing the magnitude of the charges and decreasing the distance between the particles will have a significant impact on the strength of the electric force.

Firstly, increasing the magnitude of the charges on the particles will result in a stronger electric force. According to Coulomb's law, the electric force between two charged particles is directly proportional to the product of their charges. So, if the charges on both particles are increased, the force between them will increase proportionally. This is because larger charges generate a stronger electric field, leading to a greater force of attraction or repulsion between the particles.

Secondly, decreasing the distance between the particles will also strengthen the electric force. Coulomb's law states that the electric force is inversely proportional to the square of the distance between the charges. As the distance between the particles decreases, the force between them increases exponentially. This is because the electric field becomes more concentrated, resulting in a higher force of attraction or repulsion between the charges.

In summary, increasing the magnitude of the charges on particles and decreasing the distance between them will both contribute to a stronger electric force. These factors have a multiplicative effect on the force, as the force is directly proportional to the product of the charges and inversely proportional to the square of the distance. By manipulating these variables, the strength of the electric force can be significantly altered, impacting the interactions between charged particles.

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Answer:

The average velocity of a train moving along a straight track if its displacement is 192 m was during a time period of 8.0 s is 24 \(\frac{m}{s}\).

Explanation:

Velocity ​​is a physical quantity that expresses the relationship between the space traveled by an object and the time used for it. Then, the average velocity relates the change in position to the time taken to effect that change.

\(velocity=\frac{displacement}{time}\)

Velocity considers the direction in which an object moves, so it is considered a vector magnitude.

In this case, the displacement is 192 m and the time period is 8 s. Replacing:

\(velocity=\frac{192 m}{8 s}\)

Solving:

velocity= 24 \(\frac{m}{s}\)

The average velocity of a train moving along a straight track if its displacement is 192 m was during a time period of 8.0 s is 24 \(\frac{m}{s}\).

Calculating the mass of the block requires a bit of work. The formula for the volume of a rectangular solid is V = l*w*h, where V is the volume, l is the length, w is the width, and h is the height. Using the dimensions given, we can calculate the volume of the block as 30*80*60 = 144000 cubic centimeters.

The density of lead is approximately 11.34 grams per cubic centimeter. To calculate the mass of the block, we can use the formula m = V*d, where m is the mass, V is the volume, and d is the density. Plugging in the values we get m = 144000*11.34 = 1,634,400 grams or approximately 1.63 metric tons.

So, the mass of the block of lead is approximately 1.63 metric tons.

The net force on the airplane window of area 1800 cm² is 3469.47 Pa.m² .

Given:

Pressure inside the cabin: 0.95 atm

Pressure outside the cabin: 0.76 atm

Area of the airplane window: 1800 cm²

Now to find the net force on the airplane window, we can calculate the pressure difference between the inside and outside of the cabin and to calculate the pressure difference, we subtract the outside pressure from the inside pressure.

Pressure Difference = Pressure inside - Pressure outside

Pressure Difference = 0.95 atm - 0.76 atm

Pressure Difference = 0.19 atm

The area of the airplane window is given as 1800 cm². To simplify calculations in SI unit we convert the area to square meters:

Area in m² = (Area in cm²) / 10,000

Area in m² = 1800 cm² / 10,000

Area in m² = 0.18 m²

As we know,

Net Force = Pressure Difference * Area

Net Force = 0.19 atm * 0.18 m²

Net Force = 0.0342 atm·m²

To convert the net force to pascals (Pa), we use 1 atm = 101325 Pa. Multiplying the net force by 101325 Pa, we get

Net Force = 3469.47 Pa·m²

Therefore, the net force on the airplane window is approximately 3469.47 pascals times square meters (Pa.m²).

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Approximately 0.123 kg of liquid water at 26 degrees Celsius would be needed to melt 41 grams of ice.

To calculate the minimum amount of liquid water required to melt 41 grams of ice at 0°C, we need to consider the energy required for the phase change from solid to liquid, which is known as the specific heat of fusion of ice.

The energy required to melt 1 kg of ice is 3.33×105 J/kg.

Therefore, the energy required to melt 41 grams of ice is (3.33×105 J/kg) × (41/1000) kg = 13653 J.

To calculate the amount of liquid water required, we use the specific heat capacity of water, which is 4180 J/kg/°C.

Assuming the initial temperature of water is 26°C, the amount of water needed can be calculated as (13653 J) ÷ (4180 J/kg/°C) ÷ (26°C) = 0.123 kg or approximately 123 ml of water.

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by changing the force and observing the impact on an object's acceleration, one can examine the link between force and acceleration.

In conclusion, Newton's second law gives an explanation for how objects whose forces are out of balance behave. According to the law, when there are imbalanced forces acting on an item, the object will accelerate with an acceleration that is inversely proportional to the mass and directly proportional to the net force.

The student should be able to relate the magnitudes of the various forces acting on an object to its state of motion, particularly the direction of acceleration. The pupil ought to be able to connect the net force.

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The projectile left the ground at an angle of 67.4 degrees above the horizontal, if there was no air resistance.

First, let's find the time of flight. We can use the kinematic equation:

y = yo + voy*t + 0.5*a*t^2

where y is the maximum height (0.57 km), yo is the initial height (0 m), voy is the initial vertical velocity (unknown), a is the acceleration due to gravity (-9.81 m/s^2), and t is the time to reach the maximum height (unknown).

Plugging in the values and solving for t, we get:

0.57 km = 0 + voy*t + 0.5*(-9.81 m/s^2)*t^2

t = 12.19 seconds

Since the total time of flight is twice the time to reach the maximum height, we have:

total time of flight = 2*t = 24.38 seconds

Now we can use the range equation to find the initial velocity vector of the projectile:

x = vox*t

1500 m = vox*24.38 seconds

vox = 61.51 m/s

where x is the range and vox is the initial horizontal velocity.

Finally, we can use trigonometry to find the initial angle of projection, theta:

voy/vox = tan(theta)

voy = vox*tan(theta)

61.51 m/s*tan(theta) = (150 m/s)

theta = 67.4 degrees

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Answer:

360 kg m/s

Explanation:

To find the momentum all we have to do is: mass x velocity

1) Multiply

TOP TIP:

When working out momentum or any physics equation we have to make sure the units match with the formula. Eg if the units were grams and we didn't convert it to kg our answer would have been wrong!

Hope this helps, have a lovely day! :)