Answer:
Approximately [tex]0.97\; \rm N[/tex]. This force would point away from the center of the square (to the left at [tex]45^\circ[/tex] above the horizontal direction.)
Explanation:
Coulomb's constant: [tex]k \approx 8.98755 \times 10^{-9}\; \rm N \cdot m^{2} \cdot C^{-2}[/tex].
By Coulomb's Law, the electrostatic force between two point charges [tex]q_1[/tex] and [tex]q_2[/tex] that are separated by [tex]r[/tex] (vacuum) would be:
[tex]\displaystyle F = \frac{k \cdot q_1 \cdot q_2}{r^2}[/tex].
Consider the charge on the top-left corner of this square.
Apply Coulomb's Law to find the electrostatic force between this charge and the charge on the lower-left corner.
Convert quantities to standard units:
[tex]q_1 = q_2 = 3 \times 10^{-6}\; \rm C[/tex].
[tex]r = 0.40\; \rm m[/tex].
[tex]\begin{aligned}F &= \frac{k \cdot q_1 \cdot q_2}{r^2} \\ &\approx \frac{8.98755 \times 10^{-9}\; \rm N \cdot m^{2} \cdot C^{-2} \times (3 \times 10^{-6}\; \rm C)^{2}}{(0.40\; \rm m)^{2}} \\ &\approx 0.506\; \rm N\end{aligned}[/tex].
As the two charges are of the same sign, the electrostatic force on each charge would point away from the other charge. Hence, for the charge on the top-left corner of the square, the electrostatic force from the charge below it would point upwards.
Similarly, the charge to the right of this charge would exert an electrostatic force with the same magnitude (approximately [tex]0.506\; \rm N[/tex]) that points leftwards.
For the charge to the lower-right of the top-left charge, [tex]r = \sqrt{2} \times 0.40\; \rm m[/tex]. Therefore:
[tex]\begin{aligned}F &= \frac{k \cdot q_1 \cdot q_2}{r^2} \\ &\approx \frac{8.98755 \times 10^{-9}\; \rm N \cdot m^{2} \cdot C^{-2} \times (3 \times 10^{-6}\; \rm C)^{2}}{(\sqrt{2} \times 0.40\; \rm m)^{2}} \\ &\approx 0.253 \; \rm N\end{aligned}[/tex].
This force would point to the top-left of the top-left charge, which is [tex]45^\circ[/tex] above the horizontal direction. Decompose this force into two components that are normal to one another:
Horizontal component: approximately [tex]\sin(45^\circ) \times 0.253\; \rm N \approx 0.179\; \rm N[/tex].Vertical component: approximately [tex]\cos(45^\circ) \times 0.253\; \rm N \approx 0.179\; \rm N[/tex]Consider the net force on the top-left charge in two components:
Horizontal component: approximately [tex]0.506\; \rm N[/tex] from the charge on the top-right corner and approximately [tex]0.179\; \rm N[/tex] from the charge on the lower-right corner. Both components point to the left-hand side. [tex]F_x \approx 0.506\; \rm N + 0.179\; \rm N = 0.685\;\rm N[/tex] (to the left).Vertical component: approximately [tex]0.506\; \rm N[/tex] from the charge on the lower-left corner and approximately [tex]0.179\; \rm N[/tex] from the charge on the lower-right corner. Both components point upwards. [tex]F_y \approx 0.506\; \rm N + 0.179\; \rm N = 0.685\;\rm N[/tex] (upward).Combine these two components to find the magnitude of the net force on this charge:
[tex]\begin{aligned}F &= \sqrt{{F_x}^{2} + {F_y}^{2}} \\ &\approx \sqrt{0.685^2 + 0.685^2 }\; \rm N \\ &\approx 0.97\; \rm N\end{aligned}[/tex].
This force would point to the top-left of this charge (also at [tex]45^\circ[/tex] above the horizontal direction, away from the center of the square) because its horizontal and vertical components have the same magnitude.
tìm thời điểm vật đạt tốc độ 25\pi cm/s lần thứ 2021
Answer:
una ufx vek cintos kavres millianto
Explanation:
vekas moriqn5o siveria il a ola ola micanese ma n8 aou ko sevyaera
A steel cable with Cross Sectional Area 3.00cm² has an elastic limit of 2.40 x 10^8pascals. Find the maximum upward acceleration that can be given a 1200kg elevated supported by the cable if the stress is not to exceed one-third of the elastic limit.
Answer:
Stress = F / A force per unit area
A = 3.00 cm^2 = 3 E-4 m^2
F = 2.4E8 N/m^2 * 3E-4 m^2 = 7.2E4 N max force applied
F/3 = 2.4E4 N if force not to exceed limit (= f)
f = M a
a = 2.4 E4 N / 1.2 E3 kg = 20 m / s^2 about 2 g
two objects A and B vertically thrown up with velocities 80m/s and 100m/s at two sec interval.where and when will they meet each other?
Answer:
hcbvdgsyyvjusvbxjxu usbsbhsi
Explanation:
ysggsghxuxgscsixigdvgsibxhdhshshjf
Partial tides _______. Question 7 options: represent various components of local tides that are resolved mathematically are predicted individually are added together to predict the height and timing of astronomical tides All of the above are correct. Only a and c are correct.
Complete Question
Partial tides __________.
Question 7 options:
a. represent various components of local tides that are resolved mathematically
b. are added together to predict the height and timing of astronomical tides
c. consist of 4 components due to the influence of celestial bodies
d. consist of up to 60 components due to astronomical and non-astronomical factors
e. All of the above except c are correct.
Answer:
Option E
Explanation:
Generally
Partial tides represent various components of local tides that are resolved mathematically
Partial tides are added together to predict the height and timing of astronomical tides
Partial tides consist of up to 60 components due to astronomical and non-astronomical factors
But Partial tides do not consist of 4 components due to the influence of celestial bodies
Therefore
All of the above except c are correct.
Option E
The first law of motion describes the principle of __________
Answer:
The first law of motion describes the principle of law of inertia.
Why we use semiconductor instead of metal in thermopile.
Answer:
Semiconductors are not normal materials. They have special properties which conductors/metals cannot exhibit. The main reason for the behavior of semiconductors is that they have paired charge carriers-the electron-hole pair. This is not available in metals.
If a negatively charged particle is placed inside a uniform electric field the electric force that will act on that particle points in what direction in reference to the electric field lines?
Answer:
opposite direction
Explanation:
An electric field is defined as a physical field which surrounds the electrically charged particles that exerts force on the other particles on the field.
Now when an electron or a negatively charged particle enters a uniform electric field, the electric forces acts on the negatively charged particles and it forces the particle to move in the direction which is opposite to the direction of the field. In an uniform electric field, the field lines are parallel.
Answer:
Explanation:
negatively charged particle is placed inside uniform electric field
The force on the charge due to the electric field is
F = q E
when the charge is negative so the force on the charge is opposite to the direction of electric field.
The electric field is opposite to the force.
A 13.6 kg block is tied at the top of an incline to a tree. If the incline is 35.5 degrees and the coefficient of friction between the sled and the incline is .45, What is the tension force between the block and the tree
Answer:
Explanation:
ASSUMING that block = sled AND that the rope is parallel to the slope.
The force acting parallel due to the weight is
13.6(9.81)sin35.5 = 77.475 N
The maximum friction force is
(0.45)13.6(9.81)cos35.5 = 48.877 N
If rope tension is T
77.475 - 48.877 < T < 77.475 + 48.877
28.6 N < T < 126 N
28.6 N will occur if the block is on the verge of sliding downhill
126 N will occur if the block is on the verge of sliding uphill
Could be any value between them.
What is a measure of how hard it is to stop a moving object?
25.
A. gravity
B. weight
C.
inertia
D. momentum
Answer:
C. inertia
Explanation:
inertia describes an object’s resistance to change in motion (or to get in motion due to a lack of motion), and momentum describes how much motion it has.
both are connected, as inertia depends on the object's momentum, but the answer here is inertia.
Consider a box with two gases separated by an impermeable membrane. The membrane can move back and forth, but the gases cannot penetrate the membrane. The left side is filled with gas A and the right side is filled with gas B. We will assume that equipartition applies to both gases, but gas A has an excluded volume due to large molecules so its entropy has a different formula.
SA=NAkln(VA+ bNA)+f(UA,NA)
SB=NBkln(VB)+f(UB,NB)
Required:
If NA= 1 moles, NB = 2 moles, the total volume of the box is 1 m3, and b= 4 × 10-4 m3/mole, then find the equilibrium value of VA by maximizing the total entropy.
Answer:
The answer is "[tex]0.3336\ m^3[/tex]"
Explanation:
Using the Promideal gas law:
[tex]P_A=P_B\\\\P_A(V_A-\eta_A b)= \eta_A RT......(1)\\\\P_B V_B=\eta_B \bar{R}T........(2)\\\\From (1) \zeta (2)\\\\[/tex]
[tex]\frac{\eta_A}{V_A-\eta_A b}=\frac{\eta B}{V B}\\\\ \frac{V A- \eta_A b}{V B}=\frac{\eta A}{\eta B }\\\\ \frac{V A-b}{V B}=\frac{1}{2}\\\\V A+V B=1\\\\V B =1- V A\\\\\frac{V A-b}{1-V A}=\frac{1}{2}\\\\2V A-2b=1-V A\\\\3 V A=1+2b\\\\V A=\frac{1+2b}{3}\\\\[/tex]
[tex]=\frac{1+2(4\times 10^{-4})}{3}\\\\=0.3336\ m^3[/tex]
The equilibrium value of Va is 0.3336 m³.
Ideal gas lawThe equilibrium value of Va is determine by applying ideal gas law as shown below;
Pressure of gas A = Pressure of gas B
Pa = Pb
Pa(Va - nab) = naRT----(1)
PbVb = nbRT -----(2)
Solve equation (1) and (2)
[tex]\frac{P_b}{RT} = \frac{n_b}{V_b} \\\\\frac{P_b}{P_a(V_a- n_ab)/n_a} = \frac{n_b}{V_b}\\\\\frac{n_a}{V_a - n_ab} = \frac{n_b}{V_b} \\\\\frac{V_a - n_ab}{V_b} = \frac{n_a}{n_b} \\\\\frac{V_a - b}{V_b} = \frac{1}{2}[/tex]
Va + Vb = 1
Vb = 1 - Va
[tex]\frac{V_a - b}{1 - V_a} = \frac{1}{2}[/tex]
2Va - 2b = 1 - Va
3Va = 1 + 2b
[tex]V_ a = \frac{1 + 2b}{3} \\\\V_a = \frac{1 + (2 \times 4\times 10^{-4})}{3} \\\\V_a = 0.3336 \ m^3[/tex]
Thus, the equilibrium value of Va is 0.3336 m³.
Learn more about equilibrium value here: https://brainly.com/question/22569960
A block with a mass of 0.26 kg is attached to a horizontal spring. The block is pulled back from its equilibrium position until the spring exerts a force of 1.2 N on the block. When the block is released, it oscillates with a frequency of 1.4 Hz. How far was the block pulled back before being released?
Answer:
2
Explanation:
pulling force because of it force
Answer:
5.9 cm
Explanation:
f: frequency of oscillation
frequency of oscillationk: spring constant
frequency of oscillationk: spring constantm: the mass
[tex]f = \frac{1}{2\pi} \sqrt{ \frac{k}{m} } [/tex]
in this problem we know,
F= 1.4 Hz
m= 0.26 kg
By re-arranging the formula we get
[tex]k = {(2\pi \: f )}^{2} m = {(2\pi(1.4hz))}^{2} 0.26kg = 20.1 \frac{n}{m} [/tex]
The restoring force of the spring is:
F= kx
where
F= 1.2 N
k= 20.1 N/m
x: the displacement of the block
[tex]x = \frac{f}{k} = \frac{1.2 \: n}{20.1 \frac{n}{m} } = 0.059m \: = 5.9 \: cm[/tex]
Determine the acceleration of a pendulum bob as it passes through an angle of 15 degrees to the right of the equilibrium point.
Answer:
Explanation:
Since energy is conserved:
2
mu
2
=
2
mv
2
+mgh
⇒u
2
=v
2
+2gh
⇒(3)
2
=v
2
+2(9.8)(0.5−0.5cos60)
⇒v=2m/s
Acceleration of the simple pendulum is 2.62 m/s².
What is meant by a simple pendulum ?When a point mass is suspended from a fixed support by a light, non-extensible string, the instrument is said to be a simple pendulum.
Here,
Let the mass of the bob be m. The simple pendulum is attached to the fixed support with a string having length l. The pendulum makes an angle of 15° with the vertical from the equilibrium point.
Let T be the tension acting on the string.
As, the bob passes through the angle,
The weight of the bob becomes equal to the vertical component of the tension.
mg = T cos15°
Also, the horizontal component of the tension,
T sin15° = ma
By solving these two equations, we get that,
Acceleration of the simple pendulum,
a = g tan15°
a = 9.8 x 0.267
a = 2.62 m/s²
Hence,
Acceleration of the simple pendulum is 2.62 m/s².
To learn more about simple pendulum, click:
https://brainly.com/question/31816771
#SPJ3
MULTIPLE CHOICE
What is the role of the Sun in a forest ecosystem?
What is the Role of the sun in a forest ecosystem?
Answer:
It is to produce sunlight in the forest plants
A 0.3 kg mass attached to a 1.5 m long string is whirled in a horizontal circle at a speed of 6.0 m/s. What is the tension in the string? (neglect gfavity)
Answer:
Hi I hope this is correct!
Explanation:
You can use this formula to solve this question T = mv^2/R
m = 0.3 kg , v = 6.0 m/s , R = 1.5 m
T = (0.3 kg)(6.0 m/s)^2 / 1.5 m
= 7.2 Newtons
Hope this helps! Best of luck <3
Can someone please help!!!
Answer:
W = F • ∆x
so for work to be done, a force and displacement has to be in the same direction. (Ex: a box is being pushed forward and it's also moving forward.)
Ashley, a psychology major, remarks that she has become interested in the study of intelligence. In other words, Ashley is interested in?
Group of answer choices.
a) the capacity to learn from experience, solve problems, and to adapt to new situations.
b) how behavior changes as a result of experience.
c) the factors directing behavior toward a goal.
d) the ability to generate novel
Answer:
a) the capacity to understand the world, think rationally, and use resources effectively.
Explanation:
Psychology can be defined as the scientific study of both the consciousness and unconsciousness of the human mind such as feelings, emotions and thoughts, so as to understand how it functions and affect human behaviors in contextual terms.
This ultimately implies that, psychology focuses on studying behaviors and the mind that controls it.
In this scenario, Ashley who is a psychology major, stated that she's interested in the study of intelligence.
Intelligence can be defined as a measure of the ability of an individual to think, learn, proffer solutions to day-to-day life problems and effectively make informed decisions.
In other words, Ashley is interested in the capacity of humans to understand the world, think rationally, and use resources effectively to produce goods and services that meet the unending requirements, needs or wants of the people (consumers or end users) living around the world.
A parallel plate capacitor is constructed using two square metal sheets, each of side L = 10 cm. The plates are separated by a distance d = 2 mm and a voltage applied between the plates. The electric field strength within the plates is E = 4000 V/m. The energy stored in the capacitor is
Answer:
The energy stored is 1.4 x 10^-9 J.
Explanation:
Side of square, L = 10 cm = 0.1 m
Distance, d = 2 mm = 0.002 m
Electric field, E = 4000 V/m
The energy stored in the capacitor is
[tex]U = 0.5 C V^2[/tex]
The capacitance is given by
[tex]C = \frac{\varepsilon o A}{d}\\\\So \\\\U = 0.5\frac{\varepsilon o A}{d}\times E^2 d^2\\\\U = 0.5\times 8.85\times 10^{-12}\times 0.1\times 0.1\times 4000\times 4000\times 0.002\\\\U = 1.4\times10^{-9} J[/tex]
A load of 25 kg is applied to the lower end and of a steal wire of length 25 m and thickness 3.0mm .The other end of wire is suspeded from a rigid support calculate strain and stress produced in the wire
Answer:
the weight of the wire + 25kg
Explanation:
ASK YOUR TEACHER An oil slick on water is 99.8 nm thick and illuminated by white light incident perpendicular to its surface. What color does the oil appear (what is the most constructively reflected wavelength, in nanometers), given its index of refraction is 1.38
Answer:
There will be a phase change at the 1-1.38 interface and no phase change at the 1.38-1.33 interface.
At a thickness of lambda / 4 (y/4) one should get constructive interference for the reflected light.
y = 4 * 99.8 * 10E-9 m = 400 nm (about) = 4 * 10E-7 m
The color of this light will be violet or blue
which of the following can not happen when a light ray strikes a new medium
Answer:
amplification
Explanation:
reflection can happen
some amount of lighr get absorbed
something gets refracted
but amplification cant
the rate of cooling determines ....... and ......
Answer:
freezing point and melting point
4. A diver is 20 m underwater and they are startled by a shark. They are tempted to take a big breath of air, drop their gear, and swim to the surface while holding their breath. Explain why this is dangerous g
Answer:
Explanation:
The air enters their lungs at the same pressure as the water at that depth.
If they hold their breath as they rise to atmospheric pressure, the expanding volume of air (due to decreasing pressure) trapped in their lungs will hyperextend the alveoli in their lungs, likely tearing blood lines and risking death by drowning in their own blood.
Good morning 2 all ,What is mechanical advantage write its formula. Have a good day thank you ✌
The ratio of foort dustance to load distance in a simple machine is called mechanical advantage or MA.
MA= Effort Distance / Load Distance
What is the maximum speed at which a car can round a curve of 25-m radius on a level road if the coefficient of static friction between the tires and road is 0.80?
I assume the curve is flat and not banked. A car making a turn on the curve has 3 forces acting on it:
• its weight, mg, pulling it downward
• the normal force from contact with the road, n, pushing upward
• static friction, f = µn, directed toward the center of the curve (where µ is the coefficient of static friction)
By Newton's second law, the net forces on the car in either the vertical or horizontal directions are
∑ F (vertical) = n - mg = 0
∑ F (horizontal) = f = ma
where a is the car's centripetal acceleration, given by
a = v ²/r
and where v is the maximum speed you want to find and r = 25 m.
From the first equation, we have n = mg, and so f = µmg. Then in the second equation, we have
µmg = mv ²/r ==> v ² = µgr ==> v = √(µgr )
So the maximum speed at which the car can make the turn without sliding off the road is
v = √(0.80 (9.80 m/s²) (25 m)) = 14 m/s
Four identical metallic objects carry the following charges 1.08 6.74 4.61 and 9.41 C The objects are brought simultaneously into contact so that each touches the others Then they are separated a What is the final charge on each object b How many electrons or protons make up the final charge on each object
Answer:
(a) 5.46 C
(b) 3.4125 x 10^19
Explanation:
q' = 1.08 C, q'' = 6.74 C, q''' = 4.61 C, q'''' = 9.41 C
When the charges are in contact to each other.
(a) So, the net charge is
[tex]q = \frac{q' + q'' + q''' + q''''}{4}[/tex]
[tex]q = \frac{1.08+6.74+4.61+9.41}{4}\\\\q = 5.46 C[/tex]
(b) As the charge is positive in nature, so the protons are there. The number of protons is
[tex]n = \frac{q}{e}\\\\n = \frac{5.46}{1.6\times 10^{-19}}\\\\n = 3.4125\times 10^{19}[/tex]
i don't understand this, can someone help please??
Explanation:
N2 + H2 --> NH3
balance them:
N2 + 3 H2 --> 2 NH3
so if 6 moles of N2 react, 12 moles of NH3 will form.
(you have to look at the big number in front, in this case its N2 and 2 NH3, therefore the amount of N2 will produce double the amount of NH3 )
Proper physical exercise makes bones _[blank 1]_.
People with stronger muscles and bones have better _[blank 2]_.
Which option shows the words that correctly fill in blank 1 and blank 2, in that order?
longer, flexibilitylonger, flexibility , ,
stronger, posturestronger, posture , ,
longer, posturelonger, posture , ,
stronger, flexibility
stronger, posturestronger, posture
hope that helped
How can I solve the following?
In (Figure 1), let V = 15.0 V and C1=C2=C3= 24.2 μF.
Part A: How much energy is stored in the capacitor network as shown in (Figure 1)?
Part B: How much energy would be stored in the capacitor network if the capacitors were all in series?
Part C: How much energy would be stored in the capacitor network if the capacitors were all in parallel?
Answer:
Part A - 4.084 mJ
Part B - 0.908 mJ
Part C - 8.168 mJ
Explanation:
Part A: How much energy is stored in the capacitor network as shown in (Figure 1)?
Since capacitors C₂ and C₃ are in series, their equivalent capacitance is C',
1/C' = 1/C₂ + 1/C₃ (Since C₁ = C₂ = C₃ = C)
1/C' = 1/C + 1/C
1/C' = 2/C
C' = C/2
Since C' is in parallel with C₁, the equivalent capacitance for the circuit is C" = C₁ + C' = C + C/2 = 3C/2
C" = 3C/2
The energy stored in the circuit, W = 1/2C"V² where C" = equivalent capacitance = 3C/2 and V = voltage = 15.0 V
W = 1/2C"V²
W = 1/2(3C/2)V²
W = 3CV²/4
since C = 24.2 μF = 24.2 × 10⁻⁶ F
W = 3CV²/4
W = 3 × 24.2 × 10⁻⁶ F (15.0 V)²/4
W = 3 × 24.2 × 10⁻⁶ F × 225 V²/4
W = 16335/4 × 10⁻⁶ FV²
W = 4083.75 × 10⁻⁶ J
W = 4.08375 × 10⁻³ J
W = 4.08375 mJ
W ≅ 4.084 mJ
Part B: How much energy would be stored in the capacitor network if the capacitors were all in series?
If the capacitors are connected in series, their equivalent resistance is C'
and 1/C' = 1/C₁ + 1/C₂ + 1/C₃
Since C₁ = C₂ = C₃ = C
1/C' = 1/C + 1/C + 1/C
1/C' = 3/C
C' = C/3
The energy stored in the circuit, W = 1/2C'V² where C' = equivalent capacitance = C/3 and V = voltage = 15.0 V
W = 1/2C'V²
W = 1/2(C/3)V²
W = CV²/6
since C = 24.2 μF = 24.2 × 10⁻⁶ F
W = CV²/6
W = 24.2 × 10⁻⁶ F (15.0 V)²/6
W = 24.2 × 10⁻⁶ F × 225 V²/6
W = 5445/6 × 10⁻⁶ FV²
W = 907.5 × 10⁻⁶ J
W = 0.9075 × 10⁻³ J
W = 0.9075 mJ
W ≅ 0.908 mJ
Part C: How much energy would be stored in the capacitor network if the capacitors were all in parallel?
If the capacitors are connected in parallel, their equivalent resistance is C'
and C' = C₁ + C₂ + C₃
Since C₁ = C₂ = C₃ = C
C' = C + C + C
C' = 3C
The energy stored in the capacitor network, W = 1/2C'V² where C' = equivalent capacitance = 3C and V = voltage = 15.0 V
W = 1/2C'V²
W = 1/2(3C)V²
W = 3CV²/2
since C = 24.2 μF = 24.2 × 10⁻⁶ F
W = 3CV²/2
W = 3 × 24.2 × 10⁻⁶ F (15.0 V)²/2
W = 3 × 24.2 × 10⁻⁶ F × 225 V²/2
W = 16335/2 × 10⁻⁶ FV²
W = 8167.5 × 10⁻⁶ J
W = 8.1675 × 10⁻³ J
W = 8.1675 mJ
W ≅ 8.168 mJ
A motor is designed to operate on 117 V and draws a current of 17.7 A when it first starts up. At its normal operating speed, the motor draws a current of 2.78 A. Obtain (a) the resistance of the armature coil, (b) the back emf developed at normal speed, and (c) the current drawn by the motor at one-third normal speed.
Answer:
Resistance of the armature coil = 6.61 ohms
Back emf developed at normal speed = 98.62 V (Approx.)
Current drawn by the motor at one-third normal speed = 12.73 A
Explanation:
Given:
Potential difference V = 117 V
Current = 17.7 A
Motor drawn current = 2.78 A
Find:
Resistance of the armature coil
Back emf developed at normal speed
Current drawn by the motor at one-third normal speed
Computation:
A] Resistance of the armature coil R = V/ I
Resistance of the armature coil = 117 / 17.7
Resistance of the armature coil = 6.61 ohms
B] Back emf developed at normal speed = V- IR
Back emf developed at normal speed = 117 V - (2.78 A)(6.61 ohms)
Back emf developed at normal speed = 117 V - 18.37
Back emf developed at normal speed = 98.62 V (Approx.)
C] Current drawn by the motor at one-third normal speed = 17.7 A - (98.62/3)/(6.61 ohms)
Current drawn by the motor at one-third normal speed = 17.7 - 4.97
Current drawn by the motor at one-third normal speed = 12.73 A
The propeller on a boat motor is initially rotating at 8 revolutions per second. As the boat captain reduces the boat speed, the propeller SLOWS at a steady rate of 0.9 revolutions per second per second. After 17 revolutions, how fast is the propeller spinning in revolutions per second
Answer: [tex]5.77\ rps[/tex]
Explanation:
Given
Initial angular velocity is [tex]\omega_i=8\ rps[/tex]
rate of reduction [tex]\alpha=0.9 rev/s^2[/tex]
after 17 revolution i.e. [tex]\theta =17\ rev[/tex]
using [tex]\Rightarrow \omega_f^2-\omega_i^2=2\alpha\theta[/tex]
Insert the values
[tex]\Rightarrow \omega_f^2=8^2-2\times (0.9)\times17\\\Rightarrow \omega_f^2=33.4\\\Rightarrow \omega_f=5.77\ rps[/tex]
