The force on an object is F⃗ =−17j⃗ . For the vector v⃗ =2i⃗ +3j⃗ , find: (a) The component of F⃗ parallel to v⃗

Answer:

in scientific notation 26500 is 2.65×10⁴

Answer:

2.56*10^4

26500

(We have to move the decimal 4 places)

2.6500*10^4

So the answer is 2.6500*10^4 or 2.56*10^4

Hope this helps! :)

Answer:

science is the knowledge gained through observations and experimentations

Characteristics

consistency

observability

predictability

testability

tentativeness

components of nature are soil,atmosphere and radiation

Answer:

Explanation:

An impulse describes a change in momentum. The change in momentum of an object is its mass times the change in its velocity.

The change in moment is given by the expression below

Δp=m⋅(Δv)=m⋅(vf−vi) .

Given data

mass m= 0.140-kg

initial velocity vi= 120 m/s

final velocity vf= 1 m/s

substituting we have

Δp=m⋅(Δv)=0.14⋅(1−1.2)

Δp=m⋅(Δv)=0.14⋅(-0.2)

Δp= 0.028 kg m/s

The change in momentum was found to be Δp= 0.028 kg m/s

Answer:

AFter 3.5 s, the wagon is moving at:   [tex]4.62\,\,\frac{m}{s}[/tex]

Explanation:

Let's start by finding first the net force on the wagon, and from there the wagon's acceleration (using Newton's 2nd Law):

Net force = 250 N + 178 N = 428 N

Therefore, the acceleration from Newton's 2nd Law is:

[tex]F=m\,*\,a\\a = \frac{F}{m} \\a= \frac{428}{325}\, \frac{m}{s^2} \\a\approx 1.32 \,\,\frac{m}{s^2}[/tex]

So now we apply this acceleration to the kinematic expression for velocity in an object moving under constant acceleration:

[tex]v_f=v_i+a\,*\,t\\v_f=0+1.32\,*\,3.5\,\,\frac{m}{s} \\v_f=4.62\,\,\frac{m}{s}[/tex]

"Should wolves be reintroduced into national parks" is a question that cannot be answered through making measurements, therefore the correct answer is option C.

A unit of measurement is a specified magnitude of a quantity that is established and used as a standard for measuring other quantities of the same kind. It is determined by convention or regulation. Any additional quantity of that type can be stated as a multiple of the measurement unit.

A length, for instance, is a physical quantity. A defined, predetermined length is represented by the length unit known as the meter.

A qualitative type of question cannot be answered while making a quantitative measurement.

Thus, the question of whether wolves should be reintroduced into national parks cannot be answered by taking measurements, so option C is the appropriate response.

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Answer:

Weight of the woman in Newton

   [tex]x = 698.6 \ N[/tex]

 Mass of the woman in slug

  [tex]Mass = 4.86 \ slug[/tex]

 Mass of the woman in kg

   [tex]Mass = 16 \ kg[/tex]

  My weight in Newton

  [tex]W = 784 \ N[/tex]

Explanation:

From the question we are told that

   The weight of the woman in pounds is  [tex]W = 157 \ lb[/tex]

Converting to Newton

    1 N  =  0.22472 lb

    x N  =  157

=>   [tex]x = \frac{157 * 1}{0.22472}[/tex]

=>   [tex]x = 698.6 \ N[/tex]

Obtaining the mass in slug

   [tex]Mass = \frac{W}{g}[/tex]

Here  [tex]g = 32.2 ft/s^2[/tex]

So

     [tex]Mass = \frac{157 }{32.2}[/tex]

       [tex]Mass = 4.86 \ slug[/tex]

Obtaining the mass in kilogram

     [tex]Mass = \frac{W}{g}[/tex]

Here  [tex]g = 9.8 \ m/s[/tex]

So

   [tex]Mass = \frac{157 }{9.8}[/tex]

   [tex]Mass = 16 \ kg[/tex]

Generally weight is mathematically represented as

     [tex]W = m * g[/tex]

Given that my mass is   80 kg   then my weight is  

     [tex]W = 80 *9.8[/tex]

      [tex]W = 784 \ N[/tex]

Answer:

The correct one is that the force on B is half of the force on A

Explanation:

Because radius for the inside of the curve is half the radius for the outside and Car A travels on the inside while car B, travels at equal speed on the outside of the curve. Thus force on B will be half on A

Answer:

175 N/m

Explanation:

Given:

Force = F=  14.0 N

Distance = x = 8.00 cm = 0.08 m

To find:

spring constant

Solution:

spring constant is calculated by using Hooke's law:

k =  F/x

Putting the values in above formula:

k = 14.0 / 0.08

k = 175 N/m

Answer:

The atomic nucleus is the small, dense region consisting of protons and neutrons at the center of an atom, discovered in 1911 by Ernest Rutherford based on the 1909 Geiger–Marsden gold foil experiment.

Explanation:

Answer:

No, the pendulum's period of oscillation does not depend on initial angular displacement.

Explanation:

Given that,

For small angle, the pendulum's period of oscillation depend on initial angular displacement from equilibrium.

We know that,

The time period of pendulum is defined as

[tex]T=2\pi\sqrt{\dfrac{l}{g}}[/tex]

Where, l = length of pendulum

g = acceleration due to gravity

So, The time period of pendulum depends on the length of pendulum and acceleration due to gravity.

It does not depend on the initial angular displacement.

Hence, No, the pendulum's period of oscillation does not depend on initial angular displacement.

Answer:

the nucleus-containing central part of a neuron exclusive of its axons and dendrites that is the major structural element of the gray matter of the brain and spinal cord, the ganglia, and the retina. — called also perikaryon, soma.

Answer:

Your body cells use the oxygen you breathe to get energy from the food you eat. This process is called cellular respiration. During cellular respiration the cell uses oxygen to break down sugar. The opposite takes place in the cells where the blood releases oxygen and picks up carbon dioxide.

Answer:

Average speed = 2.22m/s

Velocity = 0.89 m/s west

Explanation:

(i) Since speed is a scalar quantity, the direction of movement by the person is irrelevant. Therefore,

Average speed = total distance traveled / time taken

Where;

Total distance = 70m + 30m = 100m

Time taken = 45 seconds

Average speed = 100 / 45 = 2.22m/s

(ii) However, velocity is a vector quantity and so the direction of movement by the person is of utmost importance. Therefore,

Velocity = displacement / time taken

Where;

displacement = -70m + 30m    [West direction is taken as negative and east is taken as positive]

displacement = -40m     [The negative sign just means that the net displacement is in the direction of the West].

Thus, displacement can be written as 40m west.

Therefore,

Velocity = 40 / 45 = 0.89m/s west

Answer:

The new period is 16 s

Explanation:

The period of a simple pendulum is given by

[tex]T=2\pi \sqrt{\frac{L}{g} }[/tex]

Where [tex]T[/tex] is the period

[tex]L[/tex] is the length of the string

[tex]g[/tex] is the acceleration due to gravity

2π is constant

For the first experiment,

[tex]T =8 s[/tex]

[tex]g = gE[/tex]

Then,

[tex]8 = 2\pi \sqrt{\frac{L}{gE} } \\[/tex]

[tex]8\sqrt{gE} = 2\pi \sqrt{L}[/tex] ....... (1)

For the second experiment

[tex]T = T_{2}[/tex]

[tex]g = \frac{1}{4} gE[/tex]

Hence,

[tex]T=2\pi \sqrt{\frac{L}{g} }[/tex] becomes

[tex]T_{2} =2\pi \sqrt{\frac{L}{\frac{1}{4}gE } }[/tex]

Then,

[tex]T_{2} \sqrt{\frac{1}{4}gE } = 2\pi\sqrt{L}[/tex] ....... (2)

Since 2π is constant and

The same pendulum is used for the second experiment, then [tex]L[/tex] is also constant.

∴ [tex]2\pi \sqrt{L}[/tex] is constant for both experiment.

Hence, we can equate equations (1) and (2) such that

[tex]8\sqrt{gE} = T_{2} \sqrt{\frac{1}{4}gE }[/tex]

Then,

[tex]\frac{8\sqrt{gE} }{\sqrt{\frac{1}{4}gE } } = T_{2} \\\frac{8\sqrt{gE} }{\frac{1}{2}\sqrt{gE} } } } = T_{2} \\ 16 = T_{2} \\T_{2} = 16 s[/tex]

Hence, the new period is 16 s

A simple pendulum swings for 8 seconds. The new period is determined by repeating the pendulum experiment on a plant with g = 1/4 gE.

Move to a position where the gravitational acceleration is greater.

- Reduce the pendulum's length.

Explanation: The frequency of a simple pendulum is given by where L is the length of the pendulum g is the gravitational acceleration

From the formula, we notice that - As the value of g increases, the frequency of the pendulum increases as well

- As the value of L increases, the frequency of the pendulum decreases

So, in order to increase the frequency of the pendulum, we can: - Move to a location where the acceleration due to gravity, g, is larger
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Answer:

E₁ / E₂ = M / m

Explanation:

Let the electric field be E₁ and E₂ for ions and electrons respectively .

Force on ions = E₁ e where e is charge on ions .

Acceleration on ions a = E₁ e / M . Let initial velocity of both be u . Final velocity v = 0

v² = u² - 2as

0 = u² - 2 x E₁ e d  / M  

u² = 2 x E₁ e d  / M

Similarly for electrons

u² = 2 x E₂ e d  / m

Hence

2 x E₁ e d  / M =  2 x E₂ e d  / m

E₁ / E₂ = M / m

Answer:

1.9×10⁻⁵ °C⁻¹

Explanation:

Coefficient of linear expansion: This can be defined as as increase in length of a material, per unit length per degree rise in temperature, The S.I unit is (K⁻¹).

From the question above,

α = ΔL/L(T₂-T₁)................... Equation 1

Where α = coefficient of linear expansion, ΔL = Change in length, L = original length, T₁ = Initial Temperature, T₂ = Final temperature.

Given: ΔL = 1.4 cm = 0.014 m, L = 24.5 m, T₁ = 4.00°C, T₂ = 34°C

Substitute these values into equation 1

α = 0.014/[24.5(34-4)]

α = 0.014/735

α = 1.9×10⁻⁵ °C⁻¹

Answer:

Therefore, the situation in which both the instantaneous velocity and acceleration become zero, is the situation when the ball reaches the highest point of its motion.

Explanation:

When a ball is thrown upward under the free fall action of gravity, it starts to loose its Kinetic Energy as it moves upward. As the ball moves in upward direction, its kinetic energy gradually converts into its potential energy. As a result the speed of the ball starts to decrease as it moves up. Therefore, at the highest point during its motion, the velocity of ball becomes zero and it stops at the highest point for a moment, and then it starts to fall back down, under the influence of gravitational force.

Therefore, the situation in which both the instantaneous velocity and acceleration become zero, is the situation when the ball reaches the highest point of its motion.

Answer:

(c) is accelerating upward

Explanation:

When a person stand in an elevator moving upwards, he feels heavier because the elevator's floor presses harder on his feet, and the scale will show a higher reading than when the elevator is at rest.

According to Newton's second law

R = mg + ma

where;

R is the reading of the scale = apparent weight of the person

mg is the normal weight of the person

ma is the upward force acting on the person

Therefore, his apparent weight will be the greatest when the elevator is accelerating upward

(c) is accelerating upward

Answer:

A. a meteor traveling unhindered through space

Explanation:

Answer:

5.2 centimicro meter or 5.2 cμm

Explanation:

Prefixes allow scientists report numbers logically depending on the order of the magnitude of the numbers. For example to represent 4 x 10⁻³m, it is more handy to say : 4 millimetre, where milli- is the prefix for 10⁻³.

Common prefixes are:

deci = 10⁻¹                     deca = 10¹                    

centi = 10⁻²                   hecto = 10²

milli  = 10⁻³                    kilo  = 10³                      

micro = 10⁻⁶                  mega = 10⁶

nano = 10⁻⁹                   giga = 10⁹

pico = 10⁻¹²                   terra = 10¹²

femto = 10⁻¹⁵                peta = 10¹⁵

Now, let's represent the given diameter: 5.2 x 10⁻⁸ m

Since the 10⁻⁸ prefix is not common (or maybe doesn't even exist), the way around this is to break it into bits such as:

10⁻⁸ = 10⁻² x 10⁻⁶           [10⁻² = centi,  10⁻⁶ = micro ]

10⁻⁸ = centimicro

Therefore, 5.2 x 10⁻⁸ m becomes 5.2 centimicro meter.

The symbol is 5.2 cμm

Where c = centi, μ = micro.

Answer:

A

Explanation:

Ansthe answer is A

Explanation:

It is constructed in such a way that possible answers can be

tested.

(1) -2.0025m/s.

(2) It moves west.

(3) 3.3375m/s.

(4) It moves east.

Assuming the collision occurred in an isolated system. This means that total momentum of the system of pucks is conserved. Since no external forces are acting on these pucks, the momentum of the pucks before collision is equal to the momentum of the pucks after collision. i.e

(p₁)₀ + (p₂)₀ = (p₁)₁ + (p₂)₁              -------------(i)

Where;

(p₁)₀ = momentum of the 0.45kg puck before collision

(p₂)₀ = momentum of the 0.990kg puck before collision

(p₁)₁ = momentum of the 0.45kg puck after collision

(p₂)₁ = momentum of the 0.990kg puck after collision

But;

(p₁)₀ = m₁ u₁  

[m₁ = mass of the 0.45kg, u₁ = speed of the 0.45kg before collision]

(p₂)₀ = m₂u₂

[m₂ = mass of the 0.990kg, u₂ = speed of the 0.990kg before collision]

(p₁)₁ = m₁v₁

[m₁ = mass of the 0.45kg, v₁ = speed of the 0.45kg after collision]

(p₂)₁ = m₂v₂

[m₂ = mass of the 0.990kg, v₂ = speed of the 0.990kg after collision]

Equation (i) then becomes;

m₁ u₁ + m₂u₂ = m₁v₁ + m₂v₂    ----------------(ii)

From the question:

m₁ = 0.450kg

u₁ = +5.34m/s   [Taking east direction as positive]

m₂ = 0.990kg

u₂ = 0m/s    [since the second puck is initially at rest]

Substitute these values into equation (ii)

(0.450 x 5.34) + (0.990 x 0) = 0.45 v₁ + 0.990 v₂

2.403 + 0 = 0.45 v₁ + 0.990 v₂

2.403 = 0.45 v₁ + 0.990 v₂           ------------------(iii)

Also, since the collision is perfectly elastic, it means that the kinetic energy is conserved. i.e the total kinetic energy before collision is equal to the total kinetic energy after collision.

=> [tex]\frac{1}{2}[/tex]m₁ u²₁ + [tex]\frac{1}{2}[/tex]m₂u²₂ = [tex]\frac{1}{2}[/tex]m₁v²₁ + [tex]\frac{1}{2}[/tex]m₂v²₂

Substitute the necessary values into the above equation:

[[tex]\frac{1}{2}[/tex] x 0.45 x 5.34²] + [0] = [[tex]\frac{1}{2}[/tex] x 0.45 x v²₁] + [[tex]\frac{1}{2}[/tex] x 0.990 x v²₂]

[6.41601] = [0.225 x v²₁] + [0.495 x v²₂]  ------------------(iv)

Now let's solve equations (iii) and (iv) simultaneously

2.403 = 0.45 v₁ + 0.990 v₂

6.41601 = 0.225 x v²₁ + 0.495 x v²₂

let

v₁ = x

v₂ = y

2.403 = 0.45 x + 0.990 y                  ------------(5)

6.41601 = 0.225 x² + 0.495 y²         -------------(6)

From equation (5), make x subject of the formula

2.403 = 0.45x + 0.990y

0.45x = 2.403 - 0.990y         [divide through by 0.45]

x = 5.34 - 2.2y    ----------------(m)

Substitute x into equation (6)

6.41601 = 0.225 (5.34 - 2.2y)² + 0.495 y²     [expand bracket]

6.41601 = 0.225 [28.5156 - 23.496y + 4.84y²] + 0.495 y²   [remove bracket]

6.41601 = 6.41601 - 5.2866y + 1.089y² + 0.495 y²

1.584y² - 5.2866y = 0

y(1.584y - 5.2866) = 0

y = 0       or       1.584y - 5.2866 = 0

y = 0       or       1.584y = 5.2866

y = 0       or       y = 3.3375

Since y = v₂ cannot be zero because the puck will definitely move after collision, the second value of y = 3.3375 is considered.

Substitute this value into equation (m)

x = 5.34 - 2.2y

x = 5.34 - 2.2(3.3375)

x = 5.34 - 7.3425

x = -2.0025

Therefore,

x = v₁ = -2.0025m/s

y = v₂ = 3.3375m/s

(1) From the analyses above, the speed of the 0.450kg puck after collision is -2.0025m/s.

(2) Since the speed is negative, it shows that the 0.45kg puck moves opposite the direction at which it was moving before collision. It moves west.

(3) The speed of the 0.990kg puck after collision is 3.3375m/s.

(4) Since the speed is positive, it shows that the 0.990kg puck moves east. Remember that east has been taking as the positive direction.

Answer:

1.14*10^-3m

Explanation:

We know that

Volume= mass/ density

But

Area x depth= mass/density

πr²*depth= mass/density

r²=m/πdp

So

r= √0.35/3.142*0.085*1000

r= 1.14*10^-3m

All known species are made up of small structures called cells, according to observations obtained using a microscope; this theory is supported by empirical data..Option A is corect.

An investigation is defined as a thorough search or inspection. The investigative process is a series of tasks or procedures that include obtaining evidence, analyzing the material, and developing and validating theories.

Respectfully recognize any information or points of view that contradict your contention. You have to demonstrate to the reader in the refutation why your position is superior to the opposing notion.

Observations made using microscopes reveal that all known organisms are composed of tiny structures called cells the explanation is based on scientific evidence.

Hence option A is corect.

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"Acceleration" means the rate at which velocity is changing.

If velocity is constant, then it isn't changing.

If velocity isn't changing, then acceleration is zero.

Explanation:

It is given that,

Wavelength of x-rays = 2 nm

Plane spacing, d = 0.281 nm

It is assumed to find the scattering angle for second order maxima.

For 2nd order, Bragg's law is given by :

[tex]2d\sin\theta=n\lambda[/tex]

For second order, n = 2

[tex]\sin\theta=\dfrac{n\lambda}{2d}\\\\\sin\theta=\dfrac{2\times 2\ nm}{2\times 0.28\ nm}\\\\\theta=\sin^{-1}(7.14)[/tex]

Here, θ is not defined. Also, the wavelength of x-rays is more than the plane spacing. It means that it cannot produce any diffraction maximum.

Answer:

the work done by the steam during this process = 119.575 kJ

Explanation:

From the information given:

At state 1

Let obtain the specific volume of the saturated vapor from the Saturated water- Pressure table A-5 at the pressure of 100 kPa

[tex]v_1 = v_{g \ 100 \ kPa)[/tex]

[tex]v_1 = 1.6941 \ m^3 /kg[/tex]

where [tex]v_1[/tex] is the specific volume of the saturated vapor at state 1.

At state 2:

From the tables A-6 of Superheated water at the pressure of 100 kPa or 0.1 MPa and at the temperature of 200°C, the specific volume [tex]v_2 = 2.1724 \ m^3 /kg[/tex]

where [tex]v_2[/tex] is the specific volume of the superheated water at state 2.

The workdone by the steam during the process can be expressed by the formula:

[tex]W = P(V_2 -V_1)[/tex]

[tex]W = mP(v_2-v_1)[/tex]

where;

m = mass of the saturated water vapor

P = pressure of the saturated water vapor

[tex]V_2 =[/tex] volume of the superheated water at state 2

[tex]V_1 =[/tex] volume of the saturated water at state 1

Replacing our values ;

W = 2.5 (100) ( 2.1724 -1.6941)

W = 250(0.4783 )

W = 119.575 kPa.m³ [tex]\times \dfrac{1 \ kJ}{1 \ kPa.m^3}[/tex]

W = 119.575 kJ

∴

the work done by the steam during this process = 119.575 kJ

Answer:

The critical angle is 34 degree.

Explanation:

Given the index refraction = 1.77

We have to find the critical angle of sapphire when the air has the index of refraction of 1.0.

Use the below formula to find the angle.

sin(θ)c = 1 / n

sin(θ) c  = 1 / 1.77

(θ) c  = Sin^-1 (0.565)

= 34.4 degree

= 34 degrees.

Thus, the critical angle is 34 degree.

Answer:

Explanation:

The minimum magnitude of acceleration = 3 m /s²

displacement at t = 1

s = ut + 1 /2 at²

= -3 x 1 + .5 x 3 x 1²

= - 3 + 1.5

= - 1.5 m

position at t = 1 s

= 10 - 1.5

= 8.5 m

The maximum  magnitude of acceleration = 6 m /s²

displacement at t = 1

s = ut + 1 /2 at²

= -3 x 1 + .5 x 6 x 1²

= - 3 + 3

=  0

position at t = 1 s

= 10 +0

= 10  m

So range of position is 8.5 m to 10 m .

We want to find the range of possible positions for the cart at t = 1s.

The range is:

14.5m ≤ p ≤ 16m

First, we know that the acceleration of the cart is a, a constant (but we don't know the exact value yet) so we write the acceleration as:

a(t) = a

To get the velocity equation we integrate over time, and we know that the velocity at t = 0s is 3m/s, so that will be the constant of integration.

v(t) = a*t + 3m/s

To get the position we integrate again, the initial position is x = 10m, so that will be the constant of integration.

p(t) = (a/2)*t^2 + (3m/s)*t + 10m

Now, to get the range of possible positions for t = 1s we need to use the minimum and maximum accelerations and evaluate the position equation in t = 1s.

The minimum acceleration is a = 3m/s^2, so we have the minimum position:

p(1s) = (3m/s^2/2)*(1s)^2 + (3m/s)*1s + 10m = 14.5m

The maximum acceleration is 6m/s^2, so the maximum position is:

P(1s) =  (6m/s^2/2)*(1s)^2 + (3m/s)*1s + 10m = 16m

So the range of the position at t = 1s is:

14.5m ≤ p ≤ 16m

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Answer:

m = 312.5

Explanation:

Given that,

The focal length of the objecive lens, [tex]f_o=1\ cm[/tex]

The focal length of eye piece, [tex]f_e=2\ cm[/tex]

length of the tube, L = 25 cm

We need to find the magnitude of the overall magnification of the microscope. It is given by the formula as follows :

[tex]m=\dfrac{L}{f_o}\times \dfrac{D}{f_e}[/tex]

D = 25 cm

So,

[tex]m=\dfrac{25}{1}\times \dfrac{25}{2}\\\\m=312.5[/tex]

So, the overall magnification of the microscope is 312.5.