10. A boy of mass 55kg runs at 12m/s and hops on a 15kg skateboard that was at rest. What is thevelocity of the boy on the skateboard afterwards?

Answer:

✨ love ✨

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Answer:

butter

Explanation:

The net force on particle q₂, located between particles q₁ and q₃, is approximately 189000 N. The force exerted by particle q₁ on q₂ is positive and equals 252000 N, while the force exerted by particle q₃ on q₂ is negative and equals -63000 N.

To find the net force on particle q₂, we need to calculate the individual forces exerted on q₂ by particles q₁ and q₃ and then determine their sum.

The force between two charged particles can be calculated using Coulomb's law:

F = k * |q₁ * q₂| / r²

Where F is the force between the particles, k is the electrostatic constant (k ≈ 9.0 x \(10^9\) Nm²/C²), q₁ and q₂ are the charges of the particles, and r is the distance between them.

First, let's calculate the force exerted on q₂ by q₁:

F₁₂ = k * |q₁ * q₂| / r₁₂²

F₁₂ = (9.0 x \(10^9\) Nm²/C²) * |(8.0 μC) * (3.5 μC)| / (0.10 m)²

F₁₂ ≈ 252000 N

The force is positive because q₁ and q₂ have opposite charges.

Next, let's calculate the force exerted on q₂ by q₃:

F₂₃ = k * |q₂ * q₃| / r₂₃²

F₂₃ = (9.0 x \(10^9\)Nm²/C²) * |(3.5 μC) * (-2.5 μC)| / (0.15 m)²

F₂₃ ≈ -63000 N

The force is negative because q₂ and q₃ have the same charge.

Finally, we can find the net force on q₂ by summing the individual forces:

Net force = F₁₂ + F₂₃

Net force = 252000 N + (-63000 N)

Net force ≈ 189000 N

The net force on particle q₂ is approximately 189000 N.

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The approximate heat transfer through 1.65 cm of air with a temperature difference of 23.0 °C is approximately 24.4 J/s.

To approximate the heat transfer through the air layer in the double-paned window, we can assume that the glass layers have a negligible impact on the heat flow. The heat transfer can be calculated using Fourier's Law of Heat Conduction, which states that the heat flow (Q) is proportional to the temperature difference (ΔT) and inversely proportional to the thickness (L) and thermal conductivity (k) of the material.

First, we need to calculate the effective thermal conductivity of the air layer due to its thickness and the thermal conductivity ratio between air and glass. Let's denote the thermal conductivity of air as k_air and the thermal conductivity of glass as k_glass. Since glass has a thermal conductivity roughly 36 times greater than air, we have k_glass = 36 * k_air.

Next, we calculate the effective thermal conductivity of the air layer as:

k_eff = (k_air * L_air) / (L_air + k_glass)

Substituting the given values, we have:

k_eff = (k_air * 0.0165 m) / (0.0165 m + 0.005 m) = 0.01309 * k_air

Now, we can calculate the heat flow per second through the air layer using the formula:

Q = (k_eff * A * ΔT) / L_air

Substituting the given values, we get:

Q = (0.01309 * k_air * 0.760 m^2 * 23.0 K) / 0.0165 m = 24.4 J/s

Therefore, the approximate heat transfer through 1.65 cm of air with a temperature difference of 23.0 °C is approximately 24.4 J/s.

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Answer:

a)  F₃ = 109.5 N ,     θ₃ = 38.35,  b)   m = 0.429 kg

Explanation:

For this force addition exercise, let's decompose the forces into a coordinate system

strength 1

          cos 70 = F₁ₓ / F₁

          sin 70 = \(F_{1y}\) / F₁

          F₁ₓ = F₁ cos 70

         F_{1y} = F₁ sin 70

          F₁ₓ = 45 cos 70 = 15.39 N

          F_{1y} = 45 sin70 = 42.29 N

Strength 2

         cos 20 = F₂ₓ / F₂

         sin 20 = F_{2y} / F₂

         F₂ₓ = F₂ cos 20

         F_{2y} = F₂ sin20

         F₂ₓ = 75 cos 20 = 70.48 N

         F_{2y} = 75 sin 20 = 25.65 N

a) in the first part we are asked to find the magnitude of force 3 so that the body is in equilibrium

X axis

         ∑ Fₓ = 0

          F₁ₓ + F₂ₓ + F₃ₓ = 0

          F₃ₓ = - F₁ₓ - F₂ₓ

          F₃ₓ = - 15.39 - 70.48

          F₃ₓ = - 85.87 N

Y Axis

         ∑ F_{y}  = 0

         F_{1y} + F_{2y} +F_{3y}  = 0

         F_{3y} = - F_{1y} -F_{2y}

         F_{3y} = - 42.29 - 25.65

         F_{3y} = - 67.94 N

the magnitude of this force can be found using the Pythagorean theorem

         F₃ = √ (F₃ₓ² + F_{3y}^2)

         F₃ = √ (85.87² + 67.94²)

         F₃ = 109.5 N

The direction of this force can be found using trigonometry

          tan θ =  F₃ = \(F_{3y}\) / F₃ₓ

          θ₃ = Tan⁻¹ (67.94 / (85.87))

          θ₃ = 38.35º

since the two vectors are negative this angle is in the third quadrant, measured from the positive side of the x axis is

          θ₃ = 180 + 38.53

          θ₃ = 218.35º

b) I think you have an error in your statement, we have two possibilities:

1) If we eliminate the third force, what is the mass

it should say: "if we apply the third force force ...", they ask that we find the masses of the vehicle, let's use Newton's second law

X axis

       F₁ₓ + F₂ₓ = m a

       15.39 + 70.48 = m 200

        m = 85.87 / 200

        m = 0.429 kg

2) If the force F3 is in the first quadrant

        F1x + F2x + F3x = m a

        m = (15.39 + 70.48 + 85.87) / 200

        m = 0.8587 kg

Answer:

force is the amount of work or pressure given to an object

motion is the action of moving one place to another place

The proper time between two events is measured by clocks at rest in a reference frame in which the two events occur at the same coordinates. (Option B)

In physics and astronomy, a frame of reference or reference frame refer to an abstract coordinate system whose origin, orientation, and scale are specified by a set of reference points which are geometric points whose position is identified both mathematically (with numerical coordinate values) and physically (signaled by conventional markers). Hence, the proper time between two events is measured by clocks at rest in a reference frame in which the two events occur at the same coordinates.

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The real cubic expansivity of the liquid is 1.98 x 10^-4 K^-1.

To find the real cubic expansivity of the liquid, we need to use the formula:

β = (1/V) (dV/dT)

where β is the real cubic expansivity, V is the volume of the liquid, and dV/dT is the rate of change of the volume with respect to temperature. We can use the fact that the two samples have the same volume to eliminate V from the equation.

The change in mass of the liquid between 0°C and 50°C is:

Δm = 44.25 g - 42.02 g = 2.23 g

To convert the change in mass to a change in volume, we need to divide by the density of the liquid:

ρ = m/V

V = m/ρ

We can use the density of the liquid at 0°C to calculate the volume:

V = 2.23 g / (density of liquid at 0°C)

Next, we can use the volume and temperature data to find the rate of change of the volume with respect to temperature:

dV/dT = (V2 - V1) / (T2 - T1)

dV/dT = (V(50°C) - V(0°C)) / (50°C - 0°C)

Finally, we can substitute these values into the formula for β:

β = (1/V) (dV/dT)

β = (1/[(2.23 g) / (density of liquid at 0°C)]) [(V(50°C) - V(0°C)) / (50°C - 0°C)]

Simplifying this expression gives:

β = (density of liquid at 0°C) [(V(50°C) - V(0°C)) / (50°C - 0°C)] / 2.23 g

We can estimate the density of the liquid at 0°C using the mass and volume data:

density of liquid at 0°C = 44.25 g / V(0°C)

Substituting this into the expression for β gives:

β = [(44.25 g / V(0°C))] [(V(50°C) - V(0°C)) / (50°C - 0°C)] / 2.23 g

Simplifying this expression gives:

β = (V(50°C) - V(0°C)) / (50°C - 0°C) / V(0°C) x 44.25/2.23

β = (V(50°C) - V(0°C)) / (50°C x V(0°C)) x 19.8

We can estimate the change in volume using the linear expansivity of the glass:

ΔV = V(50°C) - V(0°C) = V(0°C) α ΔT

ΔV = V(0°C) (1.0 x 10^-5 K^-1) (50°C)

Substituting this into the expression for β gives:

β = [V(0°C) (1.0 x 10^-5 K^-1) (50°C)] / (50°C x V(0°C)) x 19.8

β = 1.0 x 10^-5 K^-1 x 19.8

β = 1.98 x 10^-4 K^-1

Therefore, the real cubic expansivity of the liquid is 1.98 x 10^-4 K^-1 using linear expansivity.

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The skater's final angular velocity is approximately 9.86 rad/s.

The skater's final angular velocity can be calculated using the principle of conservation of angular momentum. The equation for angular momentum is given by:

L = Iω

where L is the angular momentum, I is the moment of inertia, and ω is the angular velocity.

Initially, the skater has an angular momentum of:

L_initial = I_initial * ω_initial

Substituting the given values:

L_initial = 2.12 kg m² * 3.25 rad/s

The skater's final angular momentum remains the same, as angular momentum is conserved:

L_final = L_initial

The final moment of inertia is given as 0.699 kg m². Therefore, the final angular velocity can be calculated as:

L_final = I_final * ω_final

0.699 kg m² * ω_final = 2.12 kg m² * 3.25 rad/s

Solving for ω_final:

ω_final = (2.12 kg m² * 3.25 rad/s) / 0.699 kg m²

Hence, the skater's final angular velocity is approximately 9.86 rad/s.

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Given data:

* The value of voltage is,

* The work done in transferring the charge is,

* The time taken by the lightning to reach the ground is,

Solution:

(a). The voltage between the cloud and ground in terms of the charge transferred is,

where q is the charge transferred,

Substituting the known values,

Thus, the amount of charge transferred between the cloud and ground is 24.6 C.

(b). The number of electrons transferred in terms of the net charge and fundamental charge is,

where e is the fundamental charge,

Substituting the known values,

Thus, the number of electrons transferred is,

(c). The current stricks the ground while lightning is,

Substituting the known values,

Thus, the current striking the ground is,

In the study of personality, the Five-factor model includes different traits that underlie one’s basic tendencies.

The Five-factor model is a scientific theory that states traits of the personality of an individual are due to its biology and therefore they respond to adaptations, which are central in the biology field.

In conclusion, in the study of personality, the Five-factor model includes different traits that underlie one’s basic tendencies.

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Answer:

A.  xmax = 131.49 m

B.  t = 8.74 s

C.  ymax = 220.33 m

Explanation:

A. In order to find the horizontal distance which cannon travels you first calculate the flight time. The flight time can be calculated by using the following formula:

\(y=y_o+v_osin\theta-\frac{1}{2}gt^2\)      (1)

yo: height from the projectile is fired = 200m

vo: initial velocity of the projectile = 25m/s

g: gravitational acceleration = 9.8 m/s^2

θ: angle between the direction of the initial motion of the ball and the horizontal = 53°

t: time

You need the value of t when the projectile hits the ground. Then, in th equation (1) you make y = 0m.

When you replace the values of all parameters in the equation (1), you obtain the following quadratic formula:

\(0=200+(25)sin53\°t-\frac{1}{2}(9.8)t^2\\\\0=200+19.96t-4.9t^2\) (2)

You use the quadratic formula to obtain the value of t:

\(t_{1,2}=\frac{-19.96\pm\sqrt{(19.96)^2-4(-4.9)(200)}}{2(-4.9)}\\\\t_{1,2}=\frac{-19.96\pm65.71}{-9.8}\\\\t_1=8.74s\\\\t_2=-4.66s\)

You use the positive value because it has physical meaning.

Now, you can calculate the horizontal range of the projectile by using the following formula:

\(x_{max}=v_ocos\theta t\)      

\(x_{max}=(25m/s)(cos53\°)(8.74s)=131.49m\)

The cannon ball travels a horizontal distance of 131.49 m

B. The cannon ball reaches the canon for t = 8.74s

C. The maximum height is obtained by using the following formula:

\(y_{max}=y_o+\frac{v_o^2sin^2\theta}{2g}\)     (3)

By replacing in the equation (3) the values of all parameters you obtain:

\(y_{max}=200m+\frac{(25m/s)^2(sin53\°)^2}{2(9.8m/s^2)}\\\\y_{mac}=200m+20.33m=220.33m\)

The maximum height reached by the cannon ball is 220.33m

Newton’s first law explains why roller coasters option C. need constant pulling to stay moving.

Newton's first law states that an object at rest will remain at rest and an object in motion will remain in motion with the same speed and in the same direction unless it is acted upon by an external force.

Therefore, for a roller coasters to keep moving there should be a constant pulling to stay moving. It could be concluded that the correct answer is as given above.

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The mass of the rule is 3.36 kg and the weight of the rule is 33.6 N.

The butt of the blade is designed to balance the majority of fine chef's knives. This is due to the fact that a pinch grip is used in both Western and Eastern cutting styles for improved control. Therefore it makes sense that you'd want your knife to be balanced where you'll be holding it.

To balance the meter rule, Assume the mass of the rule "M".

It is possible to determine the rule's magnitude and weight, which act downward:

weight of rule = M * g

where g = acceleration due to gravity.

weight of rule * (50 cm) = (20 g) * (100 cm - 58 cm)

M * g * (50 cm) = (20 g) * (42 cm)

M = (20 g * 42 cm) / (50 cm * g)

M = 33.6 g / g

M = 33.6 g / 10 m/s^{2}

M = 3.36 kg

(ii) The weight of the rule:

weight of rule = M * g

weight of rule = 3.36 kg * 10 m/s^{2}

weight of rule = 33.6 N

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(A) When an air particle bombards a smoke particles, the smoke particle moves to the same direction as the air particle that hit it. When another air particle hits the smoke particle, it changes its direction to that of the second air particle, and so on. This is called Brownian motion.

(B) If the temperature of the surroundings is increased the air particles would gain kinetic energy resulting in more frequent collisions with the smoke particles. Therefore, the smoke particles would be seen moving haphazardly.

(C) The microscope helps magnify the smoke particles for a much more better observation. The lens help in focusing. As the air particles are really small and cannot be observed; therefore, smoke particles are used as they are easy to see and observe; thus, ensuring a better experiment.

Answer:

Explanation:

From the given information; the diagram below shows a clearer understanding.

The blood pressure in the brain \(P_{brain} = P_{heart} - \delta ( a - g ) h\)

= 13300 - 1060 (12-9.81) 0.35

=  13300 -  1060 (2.19) 0.35

= 13300 - 812.49

= 12487.51  Pa

The blood pressure in the feet \(P_{feet} = P_{heart} + \delta (a + g) h\)

= 13300 + 1060 (12 + 9.81) 1.45

= 13300 + 1060( 21.81 ) 1.45

= 13300 + 33521.97

= 46821.97 Pa

Answer:

Explanation:

\(P_brain = P_heart - y(a - g)h\\\\P_brain = 13300 - 1060 (12-9.81)0.35\\\\P_brain = 12487.51 pa\\\\\)

\(P_feet = P_heart + y(a+g)*h_r\\\\P_feet = 13300 + 1060(12+9.81)*(1.8-0.35)\\\\P_feet = 46821.97pa\)

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When acceleration is equal to zero average velocity and the instantaneous velocity vectors are identical.

Types of velocity

Velocity is defined as the rate of displacement of an object with respect to time. It is measured in meter/ seconds and is a vector quantity.

Acceleration is defined as the rate at which velocity changes with time.

There are two types of velocity which includes:

Average velocity: This is the average rate of change of position of particles with respect to time over an interval.

Instantaneous velocity: This is defined as the specific rate of change of position with respect to time at a particular point.

The situation that will make the average velocity and the instantaneous velocity vectors to be equal or identical is when acceleration is equal to zero.

For Steven and Candace to help their children against emotional issues and risk behaviors, the best thing both of them can do set high expectations for their children for their education.

Emotional problems are those problems which affect us mentally as a result of our weakness to stand being stretched to certain life issues. We can say that a student whose admission was withdrawn from an institution due to low academic performance might deal with certain emotional issues. This will technically make them more focus, determined and take their mind off such problems.

So therefore, helping ones children to aim high in their academic pursuits can help protect them from risk behaviors and sone emotional problems.

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The mass spectrometer separates ions of different masses by utilizing the relationship between the strength of the magnetic field, the accelerating voltage, the charge-to-mass ratio of the ions, and the resulting radius of the circular path

From the formula in the question;

B is a symbol for the magnetic field's intensity as it is applied to the mass spectrometer.

The accelerating voltage used to move the ions is called Vaccelm.

The charge of the ion, specifically its charge-to-mass ratio (q/m), is represented by the letter q.

The mass spectrometer may selectively alter the radius of the circular route for various ions by varying the magnetic field's intensity (B). This makes it possible to spatially segregate ions with various masses based on their various radii. The ions' locations and masses can then be measured using detectors placed along the journey.

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Answer:

The force per unit length is \(2.66 \times 10^{-5} \ N/m\)

Explanation:

The current carrying by each wires = 2.85 A

The current in both wires flows in same direction.

The gap between the wires = 6.10 cm

Now we will use the below expression for the force per unit length. Moreover, before using the below formula we have to change the unit centimetre into meter. So, we just divide the centimetre with 100.

\(F/l = \frac{\mu _0i_1 i_2}{2\pi d} \\i_1 = 2.85 \\i_ 2 = 2.85 \\\mu _0 = 4\pi \times 10^{-7} \\d = 0.061 \\F/l = \frac{4\pi \times 10^{-7} \times 2.85 \times 2.85}{2 \pi \times 0.061} \\= 2.66 \times 10^{-5} \ N/m\)

Answer:

Shown by explanation;

Explanation:

The heat of the sample = mass ×specific heat capacity of the sample × temperature change(∆T)

Assumption;I assume the mass of the samples are : 109g and 192g

∆T= 30.1-21=8.9°c.

The heat of the samples are for 109g are:

0.109 × 4186 × 8.9 =4060.84J

For 0.192g are;

∆T= 67-30.1-=36.9°c

0.192 × 4186×36.9=29656.97J

After time t, the position function of the ball is determined as \(y(t) = h_0\ +\ v_0t \ - \ \frac{1}{2} gt^2\)

The given parameters;

The position function of the ball after time t, is calculated as follows;

\(y(t) = h_0\ +\ v_0t \ - \ \frac{1}{2} gt^2\)

The negative sign of acceleration of due to gravity is because the ball is moving upward against gravity.

Thus, after time t, the position function of the ball is determined as \(y(t) = h_0\ +\ v_0t \ - \ \frac{1}{2} gt^2\)

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Answer:

The final speed of the second package is twice as much as the final speed of the first package.

Explanation:

Free Fall Motion

If an object is dropped in the air, it starts a vertical movement with an acceleration equal to g=9.8 m/s^2. The speed of the object after a time t is:

\(v=gt\)

And the distance traveled downwards is:

\(\displaystyle y=\frac{gt^2}{2}\)

If we know the height at which the object was dropped, we can calculate the time it takes to reach the ground by solving the last equation for t:

\(\displaystyle t=\sqrt{\frac{2y}{g}}\)

Replacing into the first equation:

\(\displaystyle v=g\sqrt{\frac{2y}{g}}\)

Rationalizing:

\(\displaystyle v=\sqrt{2gy}\)

Let's call v1 the final speed of the package dropped from a height H. Thus:

\(\displaystyle v_1=\sqrt{2gH}\)

Let v2 be the final speed of the package dropped from a height 4H. Thus:

\(\displaystyle v_2=\sqrt{2g(4H)}\)

Taking out the square root of 4:

\(\displaystyle v_2=2\sqrt{2gH}\)

Dividing v2/v1 we can compare the final speeds:

\(\displaystyle v_2/v_1=\frac{2\sqrt{2gH}}{\sqrt{2gH}}\)

Simplifying:

\(\displaystyle v_2/v_1=2\)

The final speed of the second package is twice as much as the final speed of the first package.

Answer:

iIn a nuclear plant, the heat source is from the nuclear reaction whereas in a thermal power plant it is from the combustion of coal. The difference is in the inlet steam parameters to the turbine in a nuclear plant. Thermal power plants use steam at superheated conditions. ... The nuclear plant uses a 'wet steam turbine'.

Explanation:

The heat source in a nuclear power plant is the nuclear reaction, whereas the heat source in a thermal power plant is coal combustion. The difference is in the turbine's input steam characteristics.

Power plant is an industrial structure that generates electricity. The majority of power plants are linked to the electrical grid.

Nuclear power bare a form of thermal power plant. You have a reactor where fission takes place and heat is generated, a heat exchanger that transports this heat to where it is needed.

Thermal power plant equipment converts this heat into electric energy, usually via a steam turbine.

The reactor, heat exchanger, and thermal conversion technology all have different designs and technologies, but the overall architecture is quite similar to other types of thermal power plants.

The heat source in a nuclear power plant is the nuclear reaction, whereas the heat source in a thermal power plant is coal combustion. The difference is in the turbine's input steam characteristics.

Hence, the two types of power plants differ in  difference is in the turbine's input steam characteristics.

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Answer:

Y = 0.0254 m = 25.4 mm

Explanation:

The formula for the fringe spacing in Young's Double-slit experiment is given by the following formula:

\(Y = \frac{\lambda L}{d}\)

where,

Y = fringe spacing = 0.0176 m

λ = wavelength = 425 nm = 4.25 x 10⁻⁷ m

L = Distance between screen and slits

d = slit separation

Therefore,

\(\frac{0.0176\ m}{4.25\ x\ 10^{-7}\ m} = \frac{L}{d}\\\\\frac{L}{d} = 41411.76\)

Now, for:

λ = 614 nm = 6.14 x 10⁻⁷ m

\(Y = (6.14\ x\ 10^{-7}\ m)(41411.76)\\\)

Y = 0.0254 m = 25.4 mm

The resulting net electrical charge of the materials in this system is C: The net electrical charge remains neutral as electrons are transferred from one material to the other.

When two neutral materials are rubbed together, friction can cause the transfer of electrons from one material to another. Electrons, which carry a negative charge, can move from one material to the other during this process. However, it is important to note that the total number of electrons in the system remains the same.

Since electrons are transferred from one material to the other, the material that gains electrons becomes negatively charged, and the material that loses electrons becomes positively charged. These charges balance each other out, resulting in a neutral net electrical charge for the overall system.

Therefore, the net electrical charge of the materials in this system remains neutral, even though there is a transfer of electrons between them. Therefore, Option C is correct.

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Answer:

a= 4.4×10 m/s^2

Explanation:

pressure P  = E/c

Where, E = 100 W/m^2 intensity of light

c= speed of light  = 3×10^8 m/s

P = 1000/ 3×10^8

P = 3.33×10^(-6) Pa

Force F = P×A

F = 3.33×10^{-6}×6.65×10(-29)

= 2.22×10^{-6}

acceleration a  = F/m = 2.22×10^{-6}/ 5.10×10^{-27}

a= 4.4×10 m/s^2

Based on the study conducted by Rebecca, the statement that would not be an appropriate hypothesis for Rebecca's experiment is:

A hypothesis is an explanation that is given in the form of a statement to explain an observation based on limited evidence and which serves as a starting point for further investigation.

A hypothesis may or may not be true and must be investigated to prove or disprove it.

Experiments are conducted to prove or disprove a given hypothesis.

A hypothesis is divided into a null and an alternate hypothesis.

A null hypothesis is a hypothesis that state that the treatment given to the subjects of the experiment does not produce any significant effect.

An alternate hypothesis states that the treatment given to the subjects of the experiment produces significant effects on the subjects.

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Answer: D

Explanation:

If the speed of a bullet train is measured to be 312.0 mph ± 3.9 mph. then the uncertainty in this measurement would be 1.25 %

It is the relative value that represents the hundredth part of any number for example 2% of any number represents, 2 multiplied by the 1/100th of that number.

Let us understand with help of one more example as follows

7.5 % of 100 is equal to 7.5 which means, 7.5 times the 1/100th of the 100

For the given problem we have to calculate the uncertainty in this measurement, If the speed of a bullet train is measured to be 312.0 mph ± 3.9 mph.

uncertainty in this measurement = 3.9 ×100/ 312.0

                                       = 1.25 %

Thus, If the speed of a bullet train is measured to be 312.0 mph ± 3.9 mph. then the uncertainty in this measurement would be 1.25 %

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