Answer:
W = 29.06 KJ
Explanation:
The work done while stretching the leash can be calculated by the following formula:
[tex]W = \int\limits^b_a {F_{x}} \, dx \\[/tex]
whee,
W = Work Done = ?
Fₓ = Forcing Function = (-5.7 N/m)x - (78 N/m²)x²
a = starting point of x = 0 m
b = end point of x = 22 m
Therefore,
[tex]W = \int\limits^{22\ m}_{0\ m} {(-(5.7\ N/m)x - (7.8\ N/m^{2})x^{2}}) \, dx \\Integrating\ we\ get:\\W = -\frac{(5.7\ N/m)x^{2}}{2} - \frac{(7.8\ N/m^{2})x^{3}}{3}\\Applying\ limits:\\W = -\frac{(5.7\ N/m)(22\ m)^{2}}{2} - \frac{(7.8\ N/m^{2})(22\ m)^{3}}{3} - 0\\W = - 1379.4\ J - 27684.8\ J\\W = 29064.2\ J[/tex]
W = 29.06 KJ
Light with a wavelength of 560.0 nm is incident on a pair of slits with a separation of 0.380 mm. (a) Find the angles corresponding to the locations of the first three orders of bright fringes away from the central bright fringe
Answer:
Angles corresponding to the locations of the first three orders of bright fringes away from the central bright fringe are;
∅₁ = 0.8439°
∅₂ = 0.1688°
∅₃ = 0.2533°
Explanation:
Given that;
wavelength λ = 560 nm = 560 × 10⁻⁹
Separation between slits d = 0.380 mm = 0.00038
n = first three orders = 1st order, 2nd order and 3rd oder.
we know that for constructive interference;
λn = dsin∅
sin∅ = λn/d
∅ = sin⁻¹ ( λn/d )
where λ is wavelength, ∅ is the angle, d is the distance between slits, n is the order of constructive interference.
now;
-First order; n = 1
∅₁ = sin⁻¹(λn/d) = sin⁻¹( (560 × 10⁻⁹)×(1) /0.00038 )
∅₁ = sin⁻¹( 0.001473) = 0.8439°
-2nd order; n = 2
∅₂ = sin⁻¹(λn/d) = sin⁻¹( (560 × 10⁻⁹)×(2) /0.00038 ) =
∅₂ = sin⁻¹( 0.002947) = 0.1688°
-3rd order; n = 3
∅₃ = sin⁻¹(λn/d) = sin⁻¹( (560 × 10⁻⁹)×(3) /0.00038 ) =
∅₃ = sin⁻¹( 0.004421) = 0.2533°
Therefore, angles corresponding to the locations of the first three orders of bright fringes away from the central bright fringe are;
∅₁ = 0.8439°
∅₂ = 0.1688°
∅₃ = 0.2533°
A force of 60 N is applied to a skier to pull him along a horizontal surface so that his speed remains constant. If the coefficient of friction of the skis on snow is 0.05, then what is the weight of the skier?
Answer:
[tex]1200\ \text{N}[/tex]
Explanation:
F = Force on the skier = 60 N
[tex]\mu[/tex] = Coefficient of friction = 0.05
w = Weight of skier
Force is given by
[tex]F=\mu w[/tex]
[tex]\Rightarrow w=\dfrac{F}{\mu}[/tex]
[tex]\Rightarrow w=\dfrac{60}{0.05}=\dfrac{6000}{5}[/tex]
[tex]\Rightarrow w=1200\ \text{N}[/tex]
Weight of the skier on which the force is being applied is [tex]1200\ \text{N}[/tex] .
Blue ran 100 m south then 50 m north
all togather becomes 150 m
or 150 ×100cm = 15000cm
What happens to plankton during the spring bloom?Which organisms are consumers? (Select all that apply.) coyote, snail ,green algae, or bacteria
Answer:
See explanation
Explanation:
Plankton refers to the small and microscopic organisms drifting or floating in the sea or fresh water, consisting chiefly of diatoms, protozoans, small crustaceans, and the eggs and larval stages of larger animals(Oxford dictionary).
The spring bloom is a sudden growth or increase in plankton abundance. It begins around the early spring and continues until late in the spring or sometimes even early in the summer.
One organism that is a consumer of plankton are the snails. One of the commonest snails that eat plankton are the Nerite Snails.
PLEASE ANSWER 50 points
A car manufacturer wants to change its car’s design to increase the car’s acceleration. Which changes should the engineers consider making to the design?
O increase the force that the engine provides
O decrease the force that the engine provides
O increase the mass of the car
O decrease the mass of the car
O increase the top velocity the car can travel
O decrease the top velocity the car can travel
Abunai Hana is standing atop a hill and fires her crossbow perfectly horizontally. If the crossbow bolt begins
moving with a speed of 35 m/s, then at what height does the bolt land if it hits the ground 150 m horizontally
away from her?
Answer:
h = 90.09 m
Explanation:
First, we consider the horizontal motion of the crossbow. Considering air friction to be negligible we can use the following equation:
[tex]X = V_{x}t[/tex]
where,
X = horizontal distance covered = 150 m
Vₓ = Horizontal component of velocity = 35 m/s
t = time taken during the motion = ?
Therefore,
[tex]150\ m = (35\ m/s)t\\\\t = \frac{150\ m}{35\ m/s}\\\\t = 4.28\ s[/tex]
Now, we consider the vertical motion of the crossbow. Using second equation of motion:
[tex]h = V_{i}t + \frac{1}{2}gt^{2}\\\\[/tex]
where,
h = the height the bolt fell = ?
Vi = Vertical component of initial velocity = 0 m/s (since the crossbow was fired horizontally)
g = acceleration due to gravity = 9.81 m/s²
Therefore,
[tex]h = (0\ m/s)(4.28\ s) + \frac{1}{2}(9.81\ m/s^2)(4.28\ s)^{2}\\[/tex]
h = 90.09 m
Please help if giving 20 points and brainliest
You have designed a prototype of a new, lighter material. What should be the
next step in your process?
O A. Figure out what problems people want to solve.
B. Update your initial design for the new type of material.
O c. Test to see whether your material is strong and works well.
D. Brainstorm new ways to design materials.
Answer:
O
Explanation:
Because your product will not work well so people will not buy it and it could be a defect and explode
Answer:
c
Explanation:
electric heater carries a current of 18.0 A when operating at a voltage of 120 V. What is the resistance of the heater
Answer:
R = 6.67 ohms
Explanation:
Given that,
The current carried in the heater, I = 18 A
Voltage, V = 120 V
We need to find the resistance of the heater. Let the resistance be R.
We can use Ohm's law to find R.
V = IR
[tex]R=\dfrac{V}{I}\\\\R=\dfrac{120}{18}\\\\R=6.67\ \Omega[/tex]
So, the resistance of the heater is 6.67 ohms.
Find the power of a force F~ = (8 N)ˆı + (−4 N) ˆ if the velocity ~v = (−7 m/s)ˆı + (1 m/s) ˆ. Answer in units of W
Answer:
[tex]P=-60W[/tex]
Explanation:
From the question we are told that
Force of power [tex]F=8Ni+-4Nj[/tex]
Velocity of power [tex]V=-7m/si+1m/sj[/tex]
Generally the equation for power is mathematically represented as
[tex]Power=Force *Velocity[/tex]
[tex]P=F *V[/tex]
Generally the dot product of F and V is mathematically given as
[tex]P=[/tex] [tex]\begin{vmatrix}8 & -4\end{vmatrix} .[/tex][tex]\begin{vmatrix}-7 & 1\end{vmatrix}[/tex] [tex]=-56-4[/tex]
[tex]P=-60W[/tex]
6. What is the complete spectrum of all forms of light?
a. galaxy
b. electromagnetic spectrum
C. energy
d. system
Answer:
b. the electromagnetic spectrum
Explanation:
the electromagnetic spectrum contains all the forms of light, including gamma rays, x-rays, ultraviolet radiation, visible light, infrared, radio waves, microwaves, etc
1.
Which of the following best explains the
relationship between molecules and atoms?
A
Atoms are molecules that have a charge.
B
Atoms have smaller parts, called
molecules.
С
Molecules are made up of two or more
atoms.
D
Molecules are atoms that have no mass.
Answer:
С . Molecules are made up of two or more atoms.
Explanation:
The relationship between molecules and atoms is that molecules are made up of two or more atoms.
Molecules are made up of atoms.
A molecule is the smallest particle of a substance element or compound capable of independent existence.
A molecule could be monoatomic, diatomic or polyatomic.
Monoatomic molecules are made up of one atom
Diatomic are made up of two different atoms
Polyatomic substances are made up of more than two kinds of atoms.
A small car with a mass of 800kg moving with a velocity of 27.8 m/s. The car stops at a yellow light in 3.9 seconds. What force did it take for the car to stop?
Answer:
F = 5702.56 N
Explanation:
Given that,
Mass of a small car, m = 800 kg
Initial speed of the car, u = 27.8 m/s
Final speed, v = 0
Time, t = 3.9 s
We need to find the force did it take for the car to stop.
The force acting on an object is given by :
[tex]F=ma\\\\F=\dfrac{m(v-u)}{t}\\\\F=\dfrac{800\times (0-27.8)}{3.9}\\\\F=-5702.56\ N[/tex]
So, the magnitude of force acting on the car to stop is 5702.56 N.
At a certain location, wind is blowing steadily at 10 m/s. Determine the mechanical energy of air per unit mass and the power generation potential of a wind turbine with 90-m-diameter (D) blades at that location. Take the air density to be 1.25 kg/m3. The mechanical energy of air per unit mass is .05 Numeric ResponseEdit Unavailable. .05 correct.kJ/kg. The power generation potential of the wind turbine is
Answer:
[tex]X=3976.078202kW \approx 3976kW[/tex]
Explanation:
From the question we are told that
Wind speed[tex]V_w=10m/s[/tex]
Turbine blade diameter [tex]D=90m[/tex]
Air density [tex]\tau=1.25kg/m^3[/tex]
Mechanical energy [tex]K.E =0.05kJ/kg[/tex]
Generally the power generation potential of the wind turbine X is mathematically given as
[tex]X=m'*K.E[/tex]
Where
[tex]m'=\tau *\pi*D^2/4*V[/tex]
[tex]m'=1.25 *\pi*90^2/4*10[/tex]
[tex]m'=79521.56404kg/s \approx 79521.5kg/s[/tex]
Therefore
[tex]X=m'*K.E[/tex]
[tex]X=79521.56404*0.05[/tex]
[tex]X=3976.078202kW \approx 3976kW[/tex]
[tex]X=4.0MW[/tex]
A student drops an object from rest above a force plate that records information about the force exerted on the object as a function of time during the time interval in which the object is in contact with the force plate. Which of the following measurements should the student take, in addition to the measurements from the force plate, to determine the change in momentum of the object from immediately before the collision to immediately after the collision?
a. The mass of the object.
b. The final speed of the object MOH 5000
c. The distance fallen by the object
d. The student has enough information to make the determination
Answer:
D
Explanation:
The student has enough information to make the determination
Measurements should the student take, in addition to the measurements from the force plate, to determine the change in momentum of the object from immediately before the collision to immediately after the collision the student has enough information to make the determination. Thus, option D is correct.
What happens during the experiment?A student drops an object from rest above a force plate that records information about the force exerted on the object as a function of time during the time interval in which the object is in contact with the force plate.
Momentum has the measure of motion of the object. Momentum is given by the product of mass and the velocity of the object. The law of conservation of momentum states that the momentum before the collision is equal to the momentum after the collision. It also states that the total momentum of a system or a body remains constant.
Therefore, Measurements should the student take, in addition to the measurements from the force plate, to determine the change in momentum of the object from immediately before the collision to immediately after the collision the student has enough information to make the determination. Thus, option D is correct.
Learn more about Measurements on:
https://brainly.com/question/2107310
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a bag of cement is pulled along a horizontal plane by a constant force of 15n calculate the work done in moving the bag through a distance of 20m
Answer:
300J
Explanation:
Given parameters:
Constant force = 15N
Distance = 20m
Unknown:
Work done = ?
Solution:
Work done is the force applied to move a body through a particular distance.
Work done = Force x distance
So;
Work done = 15 x 20 = 300J
Do this for alot of points
1. A complete fitness and exercise program should incorporate three basic components: Endurance (Aerobic), Flexibility, and Strength. Each of these components has specific guidelines, which govern their effectiveness
4.Jessica Diggins a US world champion cross country skier is participating in the winter Olympic games. Over a 200m stretch in her race she increases her speed with a constant acceleration from 5.1 m/s to 6.2 m/s over a period of 25 seconds. What is her acceleration
Answer:
[tex]a=0.044\ m/s^2[/tex]
Explanation:
Given that,
Initial speed, u = 5.1 m/s
Final speed, v = 6.2 m/s
Time, t = 25 s
We need to find acceleration. We know that,
acceleration = rate of change of velocity
[tex]a=\dfrac{v-u}{t}\\\\a=\dfrac{6.2-5.1}{25}\\\\a=0.044\ m/s^2[/tex]
So, her acceleration is [tex]0.044\ m/s^2[/tex].
Suppose that the voltage is reduced by 10 percent (to 90 V). By what percentage is the power reduced
Answer:
percent decrease in power = 20 % .
Explanation:
Power P = v² / R where v is voltage and R is resistance which is constant .
taking log on both sides
log P = 2 log v - log R
differentiating on both sides
dP/P = 2 dv/v
-dP/P x 100 = 2 x -dv/v x 100
percent decrease in power = 2 x percent decrease in v ( voltage )
percent decrease in power = 2 x 10 = 20 %
Consider a space shuttle which has a mass of about 1.0 x 105 kg and circles the Earth at an altitude of about 200.0 km. Calculate the force of gravity that the space shuttle experiences
Answer:
1.6675×10^-16N
Explanation:
The force of gravity that the space shuttle experiences is expressed as;
g = GM/r²
G is the gravitational constant
M is the mass = 1.0 x 10^5 kg
r is the altitude = 200km = 200,000m
Substitute into the formula
g = 6.67×10^-11 × 1.0×10^5/(2×10^5)²
g = 6.67×10^-6/4×10^10
g = 1.6675×10^{-6-10}
g = 1.6675×10^-16N
Hence the force of gravity experienced by the shuttle is 1.6675×10^-16N
a railway train 100m long passes over a bridge 400m long at 20ms.1 how long will it take to pass over the bridge
Total length to be covered=400+100=500mts
time =distance/speed
=500/20
=25 sec
What distance does a plate with an average speed of 1.95 cm/year move in 1000 years? help pls
Answer:
1950cm
Explanation:
You should multiply 1.95 cm by 1000. This will result in the answer.
How many significant figures are in 20,000?
Answer:
4
Explanation:
Which type of electromagnetic radiation is useful in communications
technology?
ANSWER : RADIO WAVES
Explanation:
radio wave: Electromagnetic radiation having a wavelength between about.5 centimeters and 30,000 meters; used for the broadcasting of radio and television signals.
What is the relationship among the potential drops across each resistor when the resistors are in series
Answer:
V = V₁ + V₂ + V₃ + ... + Vₙ
Explanation:
When the resistors are connected end to end such that there is only one path for the current to follow, it is called a series arrangement of resistors. In the series arrangement of the resistors, the current across each resistor is the same as the current applied across the circuit.
The potential difference across each resistor is different in the series arrangement of the resistors. But the sum of potential differences across each of the resistors in the series arrangement of resistors is equal to the total potential difference applied by the battery or source. Therefore, if n number of resistors are connected in a series arrangement with a source of potential V, the:
V = V₁ + V₂ + V₃ + ... + Vₙ
Help!!
A stationary hockey puck has a mass of 0.18 kg. A hockey player uses her stick to apply a 11 N force over a distance of 0.56 m.
How much work does this force do on the puck?
A 20j
B 0.10j
C 2.0j
D 6.2j
E 34j
Answer:
6.2j
Explanation:
work done=force × displacement
wd=11N×0.56m
wd=6.16N/m~6.2j
An airplane flies eastward and always accelerates at a constant rate. At one position along its path, it has a velocity of 34.5 m/s . It then flies a further distance of 46100 m , and afterwards, its velocity is 40.7 m/s . Find the airplane's acceleration.
Answer:
the acceleration of the airplane is 5.06 x 10⁻³ m/s²
Explanation:
Given;
initial velocity of the airplane. u = 34.5 m/s
distance traveled by the airplane, s = 46,100 m
final velocity of the airplane, v = 40.7 m/s
The acceleration of the airplane is calculated from the following kinematic equation;
v² = u² + 2as
[tex]2as= v^2 - u^2\\\\a = \frac{v^2 - u^2}{2s} \\\\a = \frac{(40.7)^2 -(34.5)^2}{2 \times 46,100} \\\\a = 5.06 \ \times \ 10^{-3} \ m/s^2[/tex]
Therefore, the acceleration of the airplane is 5.06 x 10⁻³ m/s²
a 4.0x 10^3 watt motor applies a force of 8.0 x 10^2 newtons to move a boat at constant speed. ow far does the boat move in 16 seconds
Answer:
80 m
Explanation:
From the question,
Power(P) = Force(F) × Velocity (V)
P = FV..................... Equation 1
V = P/F.................... Equation 2
Given: P = 4.0×10³ W, F = 8.0×10² N.
Substitute into equation 2
V = 4.0×10³/(8.0×10²)
V = 5 m/s.
Applying,
S = Vt............................ Equation 3
Where S = distance move by the boat, t = time.
Given: t = 16 s, V = 5 m/s
Substitute into equation 3
s = 16(5)
s = 80 m.
Hence the distance moved by the boat is 80 m
A 15.0 kg bowling ball rolling at 3 m/s is stopped by a constant force of 11.2 newtons. Calculate the time the force must act on the bowling ball to stop it.
Answer:
4.01 seconds
Explanation:
Given that:
Mass of ball = 15kg
Initial velocity, u = 3m/s
Final velocity, v = 0
Force, F= 11.2 N
Change in velocity, dv = 3 - 0 = 3
Time force must act on the ball before stopping it:
Using the relation :
F = ma
a = (v - u) / t
Ft = m(v - u)
11.2 * t = 15 * 3
11.2t = 45
11.2t = 45
t = -+¯ 45 / 11.2
t = 4.01
t = 4 seconds.
What is the electrical consumption in KVA of a motor powered by a 3-phase, 60 Hz, 460 VAC supply that continuously draws 17 A
Answer:
15.34 kVA
Explanation:
A motor is a device that converts electrical energy into mechanical energy. It takes in electrical energy at the input and produce torque (motion) at the output.
The power consumption for a three phase motor is the product of voltage and current and √3. The √3 is because it is a three phase supply.
Hence Power (P) =√3 × voltage (V) × current (I)
P = √3 × V × I
Given that voltage (V) = 460 V, current (I) = 17 A. Hence:
P = √3 × V × I = √3 × 460 × 17 = 13544.64 VA
But 1000 VA = 1 kVA. Hence:
[tex]P=13544.64\ VA*\frac{1\ kVA}{1000\ VA}=13.54\ kVA[/tex]
The current in a coil with a self inductance of 1.5 mH increases from 0 to 1.0 A in a tenth of a second. What is the induced emf in the coil
Answer:
the induced emf in the coil is 15 mV.
Explanation:
Given;
self inductance, L = 1.5 mH = 1.5 x 10⁻³ H
change in current = dI = 1.0 A
change in time, dt = 1/10 = 0.1
The induced emf is calculated as;
[tex]Induced \ EMF = L (\frac{dI}{dt} )\\\\Induced \ EMF = 1.5 \times 10^{-3}\ (\frac{1}{0.1} )\\\\Induced \ EMF = 1.5 \times 10^{-3} \ \times \ 10\\\\Induced \ EMF = 15 \times 10^{-3} \ V\\\\Induced \ EMF = 15 \ mV[/tex]
Therefore, the induced emf in the coil is 15 mV.
