Answer:
(a) [tex]\vec F_{\parallel} = -\frac{102}{13}\,i-\frac{103}{13}\,j[/tex] , (b) [tex]\vec F_{\perp} = \frac{102}{13}\,i -\frac{68}{13}\,j[/tex], (c) [tex]W = -51[/tex]
Explanation:
The statement is incomplete:
The force on an object is [tex]\vec F = -17\,j[/tex]. For the vector [tex]\vec v = 2\,i +3\,j[/tex]. Find: (a) The component of [tex]\vec F[/tex] parallel to [tex]\vec v[/tex], (b) The component of [tex]\vec F[/tex] perpendicular to [tex]\vec v[/tex], and (c) The work [tex]W[/tex], done by force [tex]\vec F[/tex] through displacement [tex]\vec v[/tex].
(a) The component of [tex]\vec F[/tex] parallel to [tex]\vec v[/tex] is determined by the following expression:
[tex]\vec F_{\parallel} = (\vec F \bullet \hat {v} )\cdot \hat{v}[/tex]
Where [tex]\hat{v}[/tex] is the unit vector of [tex]\vec v[/tex], which is determined by the following expression:
[tex]\hat{v} = \frac{\vec v}{\|\vec v \|}[/tex]
Where [tex]\|\vec v\|[/tex] is the norm of [tex]\vec v[/tex], whose value can be found by Pythagorean Theorem.
Then, if [tex]\vec F = -17\,j[/tex] and [tex]\vec v = 2\,i +3\,j[/tex], then:
[tex]\|\vec v\| =\sqrt{2^{2}+3^{3}}[/tex]
[tex]\|\vec v\|=\sqrt{13}[/tex]
[tex]\hat{v} = \frac{1}{\sqrt{13}} \cdot(2\,i + 3\,j)[/tex]
[tex]\hat{v} = \frac{2}{\sqrt{13}}\,i+ \frac{3}{\sqrt{13}}\,j[/tex]
[tex]\vec F \bullet \hat{v} = (0)\cdot \left(\frac{2}{\sqrt{13}} \right)+(-17)\cdot \left(\frac{3}{\sqrt{13}} \right)[/tex]
[tex]\vec F \bullet \hat{v} = -\frac{51}{\sqrt{13}}[/tex]
[tex]\vec F_{\parallel} = \left(-\frac{51}{\sqrt{13}} \right)\cdot \left(\frac{2}{\sqrt{13}}\,i+\frac{3}{\sqrt{13}}\,j \right)[/tex]
[tex]\vec F_{\parallel} = -\frac{102}{13}\,i-\frac{153}{13}\,j[/tex]
(b) Parallel and perpendicular components are orthogonal to each other and the perpendicular component can be found by using the following vectorial subtraction:
[tex]\vec F_{\perp} = \vec F - \vec F_{\parallel}[/tex]
Given that [tex]\vec F = -17\,j[/tex] and [tex]\vec F_{\parallel} = -\frac{102}{13}\,i-\frac{153}{13}\,j[/tex], the component of [tex]\vec F[/tex] perpendicular to [tex]\vec v[/tex] is:
[tex]\vec F_{\perp} = -17\,j -\left(-\frac{102}{13}\,i-\frac{153}{13}\,j \right)[/tex]
[tex]\vec F_{\perp} = \frac{102}{13}\,i + \left(\frac{153}{13}-17 \right)\,j[/tex]
[tex]\vec F_{\perp} = \frac{102}{13}\,i -\frac{68}{13}\,j[/tex]
(c) The work done by [tex]\vec F[/tex] through displacement [tex]\vec v[/tex] is:
[tex]W = \vec F \bullet \vec v[/tex]
[tex]W = (0)\cdot (2)+(-17)\cdot (3)[/tex]
[tex]W = -51[/tex]
26500 in scientific notation
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! :)
If you are driving at a constant velocity of 5 m/s what is your
acceleration?
"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.
What If? Fluoride ions (which have the same charge as an electron) are initially moving with the same speed as the electrons from part (a) through a different uniform electric field. The ions come to a stop in the same distance d. Let the mass of an ion be M and the mass of an electron be m. Find the ratio of the magnitude of electric field the ions travel through to the magnitude of the electric field found in part (a). (Use the following as necessary: d, K, m, M, and e for the charge of the electron.)
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
two horses are pulling a 325 kg wagon, initially at rest. The horses exert 250 N and 178 N forward forces, respectively. Ignoring friction, how fast is the wagon moving 3.50 s later?
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]
A person stands on a scale in an elevator. His apparent weight will be the greatest when the elevator(a) is standing still.(b) is moving upward at constant velocity.(c) is accelerating upward.(d) is moving downward at constant velocity.(e) is accelerating downward.
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
A 0.140-kg baseball is dropped and reaches a speed of 1.20 m/s just before it hits the ground. It rebounds with a speed of 1.00 m/s. What is the change of the ball's momentum
Answer:
The change in momentum is Δp= 0.028 kg m/sExplanation:
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
A mass of 2.5 kg of saturated water vapor at 100 kPa is heated at constant pressure until the temperature reaches 200°C. Calculate the work done by the steam during this process. Use steam tables.
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
A virus has a diameter of 5.2×10−8m. What is the most appropriate prefix for reporting the diameter of the virus?
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.
The period of a simple pendulum is 8 s. If the same pendulum experiment is repeated on a plant of g = 1/4 gE, the new period is
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
To learm more about pendulum's visit: https://brainly.com/question/12495919
defenition of takes place in body cells
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.
Question 5 of 10
Which statement describes a characteristic of a question that can be
answered through scientific inquiry?
O A. It is constructed in such a way that possible answers can be
tested.
B. It must be related to something that benefits society.
O c. It can be answered using an ethical argument.
D. It can be answered by collecting votes from scientists.
Answer:
A
Explanation:
Ansthe answer is A
Explanation:
It is constructed in such a way that possible answers can be
tested.
Determine the weight in newtons of a woman whose weight in pounds is 157. Also, find her mass in slugs and in kilograms. Determine your own weight in newtons.
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]
Danielle exerts a 14.0 N force to compress a spring by a distance of 8.00 cm. What is the spring constant of this spring
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
A split highway has a number of lanes for traffic. For traffic going in one direction, the radius for the inside of the curve is half the radius for the outside. One car, car A, travels on the inside while another car, car B, travels at equal speed on the outside of the curve. Which statement about resultant accelerations of the cars is correct
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
Your friend asks you for a glass of water and you bring her 5 millilitersof water. Is this more or less than what she was probably expecting?Explain your reasoning
Pls help answer 7 and 8
Answer:
science is the knowledge gained through observations and experimentations
Characteristics
consistency
observability
predictability
testability
tentativeness
components of nature are soil,atmosphere and radiation
Sapphire has an index of refraction of 1.77. The critical angle for sapphire in air with an index of refraction of 1.0 is _____ degrees.
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.
A ball is thrown straight up in the air. For which situations are both the instantaneous velocity and the acceleration zero? (Select all that apply.)
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.
g A person walks 70 m west, then turns and walks 30 m east. Find the average speed and velocity if the time for the total trip is 45 seconds.
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
Which explanation is based on scientific evidence?
A. Observations made using microscopes reveal that all known
organisms are composed of tiny structures called cells.
B. Magnets have hidden powers that can have health effects.
C. Performing good deeds for other people will make a person happy.
D. illnesses are caused by bad smells in the air.
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.
What is the investigation?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.
To learn more about the investigation refer;
https://brainly.com/question/1191670
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A 0.450-kg ice puck, moving east with a speed of 5.34 m/s , has a head-on collision with a 0.990-kg puck initially at rest. Assume that the collision is perfectly elastic.1. What is the speed of the 0.450-kg puck after the collision?2. What is the direction of the velocity of the 0.450-kg puck after the collision?3. What ise the speed of the 0.990-kg puck after the collision?4. What is the direction of the velocity of the 0.990-kg puck after the collision?
(1) -2.0025m/s.
(2) It moves west.
(3) 3.3375m/s.
(4) It moves east.
Explanation:
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.
What is its inside radius, in centimeters, if it holds 360 g of coffee when filled to a depth of 8.5 cm
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
A wire is 24.5 m long at 4.00°C and is 1.40 cm longer at 34.0°C. Find the wire's coefficient of linear expansion (in (°C)−1)
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
Which is not an example of an external force acting on an object? (1 point)
• a meteor traveling unhindered through space
O a hockey puck striking the back of the net and coming to rest
O a billiard ball bouncing off the rail of a pool table
O a batter hitting a baseball
Answer:
A. a meteor traveling unhindered through space
Explanation:
Which question cannot be answered through making measurements?
A. Should wolves be reintroduced into national parks?
B. What is the birthrate for wolves in their natural habitats?
O c. How would reintroducing wolves into a national park affect the
deer population there?
D. Which species in a national park do wolves hunt?
"Should wolves be reintroduced into national parks" is a question that cannot be answered through making measurements, therefore the correct answer is option C.
What is a unit of measurement?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.
Learn more about the unit of measurement from here
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For small angles, does the pendulum's period of oscillation depend on initial angular displacement from equilibrium? Explain.
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.
At time t=0 , a cart is at x=10 m and has a velocity of 3 m/s in the −x -direction. The cart has a constant acceleration in the +x -direction with magnitude 3 m/s^2 < a < 6 m/s^2 . Which of the following gives the possible range of the position of the cart at t=1 s ?
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
Finding the cart's motion equations.
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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what is an atomic nucleus
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:
x rays with wavelength of 2.0nm scatter from a nacl crystal with plane spacing 0.281 nm find the scattering
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.
In a compound microscope, the objective has a focal length of 1.0 cm, the eyepiece has a focal length of 2.0 cm, and the tube length is 25 cm. What is the magnitude of the overall magnification of the microscope?
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.