Answer:
work done is -2.8 × 10⁻⁶ J
Explanation:
Given the data in the question;
mass of the pendulum m = 6 kg
Length of core = 1.7 m
Now, case1, mass is pulled aside a small distance of 7.6 cm and released from rest. so let θ₁ be the angle made by mass with vertical axis.
so, θ₁ = ( 7.6 × 10⁻² m / 1.7 m ) = 0.045 rad
In case2, mass is pulled aside a small distance of 8 cm and released from rest. so let θ₁ be the angle made by mass with vertical axis.
so, θ₂ = ( 8 × 10⁻² m / 1.7 m ) = 0.047 rad.
Now, the required work done will be;
[tex]W = \int\limits^{\theta_2} _{\theta_1} {r} \, d\theta[/tex]
[tex]W = \int\limits^{\theta_2} _{\theta_1} {-mgl sin\theta } \, d\theta[/tex]
[tex]W = -mgl \int\limits^{0.047 } _{0.045 } {sin\theta } \, d\theta[/tex]
W = [tex]-mgl[[/tex] -cosθ [tex]]^{0.047}_{0.045 }[/tex]
W = 6 × 9.8 × 1.7 × [ cos( 0.047 ) - cos( 0.045 ) ]
W = 6 × 9.8 × 1.7 × [ -2.8 × 10⁻⁸ ]
W = -2.8 × 10⁻⁶ J
Therefore, work done is -2.8 × 10⁻⁶ J
A wire long and with mass is positioned horizontally near the earth's surface and perpendicular to a horizontal magnetic field of magnitude . What current I must flow through the wire in order that the wire accelerate neither upwards nor downwards
The question is incomplete. The complete question is :
A wire 0.6 m long and with mass m = 11 g is positioned horizontally near the earth's surface and perpendicular to a horizontal magnetic field of magnitude B = 0.4 T. What current I must flow through the wire in order that the wire accelerate neither upwards nor downwards? The magnetic field is directed into the page.
Solution :
Given :
Length of the wire, L = 0.6 m
Mass of the wire length, m = 11 g
= [tex]11 \times 10^{-3}[/tex] kg
Magnetic field , B = 0.4 T
Know we know that :
ILB = mg
or [tex]$I=\frac{mg}{BL}$[/tex]
[tex]$I= \frac{(11 \times 10^{-3})(9.81)}{(0.4)(0.6)}$[/tex]
[tex]I=0.44963\ A[/tex]
[tex]I = 449.63 \ mA[/tex]
System A consists of a mass m attached to a spring with a force constant k; system B has a mass 2m attached to a spring with a force constant k; system C has a mass 3m attached to a spring with a force constant 6k; and system D has a mass m attached to a spring with a force constant 4k. Rank these systems in order of decreasing period of oscillation.
Answer:
T₂ > T₁ > T₃ >T₄
Explanation:
In a simple harmonic motion the angular velocity is
w = [tex]\sqrt{\frac{k}{m} }[/tex]
angular velocity and period are related
w = 2π / T
we substitute
T = [tex]2 \pi \ \sqrt{\frac{m}{k} }[/tex]
let's find the period for each case
a) mass m
spring constant k
T₁ = 2π [tex]\sqrt{\frac{m}{k} }[/tex]
b) mass 2m
spring constant k
T₂ = 2π [tex]\sqrt{\frac{2m}{k} }[/tex]
T₂ = T₁ √2
T₂ = T₁ 1.41
c) masses 3m
spring constant 6k
T₃ = 2π [tex]\sqrt{\frac{3m}{6k} }[/tex]
T₃ = 2π [tex]\sqrt{\frac{m}{k} } \ \sqrt{0.5}[/tex]
T₃ = T₁ 0.707
d) mass m
spring constant 4k
T₄ = 2π [tex]\sqrt{ \frac{m}{4k} }[/tex]
T₄ = 2π [tex]\sqrt{\frac{m}{k} } \ \sqrt{0.25}[/tex]
T₄ = T₁ 0.5
now let's order the periods in decreasing order
T₂ > T₁ > T₃ >T₄
3. Some guitarists like the feel of a set of strings that all have the same tension. For such a guitar, the G string (196 Hz) has a mass density of 0.31 g/m. What is the mass density of the A string (110 Hz)
Answer:
0.98 g/m
Explanation:
Note: Since Tension and frequency are constant,
Applying,
F₁²M₁ = F₂²M₂............... Equation 1
Where F₁ = Frequency of the G string, F₂ = Frequency of the A string, M₁ = mass density of the G string, M₂ = mass density of the A string.
make M₂ the subject of the equation
M₂ = F₁²M₁/F₂²............... Equation 2
From the question,
Given: F₁ = 196 Hz, M₁ = 0.31 g/m, F₂ = 110 Hz
Substitute these values into equation 2
M₂ = 196²(0.31)/110²
M₂ = 0.98 g/m
1. To avoid getting hurt, do not play with sharp simple machines. The highlighted statements best reminds us about ____.
A. Safety measures in handling machines
B. Gentle reminders when playing
C. Benefits of using machines
D. Disadvantages of simple machines
2. Road signs are example of advertisements that play important role in the promotion of road safety. If you are going to make an advertisement, which do you think is appropriate to make part of a road is temporarily closed for repair or renovation?
A. End of 4 lanes
B. No Parking
C. One lane, follow the traffic signal
D. Stop, look and listen
3. Wherever you go, you see mountains, plains and volcanoes. Which among the given ideas is being supported by the highlighted statement?
A. Earth's landmasses before and at present are the same.
B. Earth's land features are not charging
C. Internal forces such as plate tectonic movements do not result to various surface features
D. Internal and external forces contribute to the formation of various surface features of earth
4. Landslides, avalanche, tsunami, seiche and fire are some effects of strong earthquakes. If the huge inland wave produced during an earthquake is known as SEICHE (SAYSH) then what refers to the huge underwater wave produced when an earthquake occurs under the sea?
A. Avalanche
B. Landslide
C. Seiche
D. Tsunami
Answer:
1. A. Safety measures in handling machines
2. C. One lane, follow the traffic signal
3. D. Internal and external forces contribute to the formation of various surface features of the earth.
4. D. Tsunami
Explanation:
1. Safety measures are precautions that must be taken to avoid injuries when handling some potentially dangerous equipment. They are meant to protect us from harm.
2. If a part of the road is to be sealed up temporarily, road users should be alerted that there is just one lane ahead. Therefore, they should follow the traffic signal.
3. The pressure exerted on the earth through phenomena like plate tectonics, earthquakes, etc., causes the eruption and formation of different features on the earth.
4. A tsunami is a giant ocean wave caused by earthquakes and volcanic eruptions that occur under the sea. They occur with a lot of speed and cause an overflow of water onto land.
A velocity of ship A relative to ship B is 10m/s in the direction N45E . If the velocity of B is 20m/s in the direction N60W . Find the velocity of ship A and direction.
Answer:
ewjefkljlajwawk;dlqa;wdka:WDKkjlhgzkljwidaJLdkjALIw
Explanation:
S.I unit for distance =______
(A) m (B)cm
(c) km (d) mm
Answer:
opinion a
Explanation:
the si units of distance is metre (m)
Answer:
A
Explanation:
Suppose your actual height is 5 feet and 5.2 inches. A tape measure which can be read tothe nearest 1/8 of an inch gives your height as 65 3/8 inches. The laser device at the clinic that givesreadings to the nearest hundredth of an inch says you are 65.31 inches.
Required:
a. Which measuring device is more accurate?
b. Which measuring device is more precise?
Answer:
a) The laser device
b) The tape
Explanation:
First, there is a need to understand what accuracy and precision mean.
Accuracy is the closeness of a measurement to its true (pre-determined) value.
Precision is the closeness of repeated measurements to each other.
Since 1 feet = 12 inches, then, 5 feet and 5.2 inches would be equivalent to 65.2 inches. This value represents the true value of my height.
The tape measured the height as 65 3/8, which is equivalent to 65.375 inches.
The laser device measured the height as 65.31.
Error = true value - measured value
Absolute error from the tape = 65.2 - 65.375
= -0.175 inches
Absolute error from laser device = 65.2 - 65.31
= -0.11
a) The magnitude of error from the tape is more than that of the laser device. Hence, the laser device is said to be more accurate.
b) Even though there were just single readings from both instruments, the tape can be read to the nearest 1/8 of an inch and as such, can give more precisive measurements than the laser device.
In a photoelectric effect experiment, it is observed that violet light does not eject electrons from a particular metal. Next, red light with the same intensity is incident on the same metal. Which result is possible
Answer:
No ejection of photo electron takes place.
Explanation:
When a photon of suitable energy falls on cathode, then the photoelectrons is emitted from the cathode. This phenomenon is called photo electric effect.
The minimum energy required to just eject an electron is called work function.
The photo electric equation is
E = W + KE
where, E is the incident energy, W is the work function and KE is the kinetic energy.
W = h f
where. h is the Plank's constant and f is the threshold frequency.
Now, when the violet light is falling, no electrons is ejected. When the red light is falling, whose frequency is less than the violet light, then again no photo electron is ejected from the metal surface.
There is given an ideal capacitor with two plates at a distance of 3 mm. The capacitor is connected to a voltage source with 12 V until it is loaded completely. Then the capacitor is disconnected from the voltage source. After this the two plates of the capacitor are driven apart until their distance is 5 mm. Now a positive test charge of 1 nC is brought from the positively charged plate to the negatively charges plate. How large is the kinetic energy of the test charge? The test charge of 1 nC can be regarded to be so small that it does not influence the electric field between the two plates of the capacitor.
Answer:
K = 2 10⁻⁸ J
Explanation:
Let's solve this exercise in parts, we start by finding the charge on each plate of the capacitor
C = Q / ΔV
C = ε₀ A / d
ε₀ A / d = Q / ΔV
Q = ε₀ A ΔV / d (1)
indicate the potential difference ΔV₁ = 12 V, the distance between the plates d₁ = 3 mm = 0.003 m,
as the power supply is disconnected and the capacitor is ideal the charge remains constant
in the second part we separate the plates at d₂ = 5 mm = 0.005 m, using equation 1
ΔV₂ = [tex]\frac{Q d_2}{ \epsilon_o A}[/tex]
we substitute the equation for Q
ΔV₂ = [tex]\frac{d_2}{\epsilon_o A} \ \frac{\epsilon_o A \Delta V }{d_1}[/tex]
ΔV₂ = [tex]\frac{d_2}{d_1} \ \Delta V_1[/tex]
in the third part we use the concepts of energy
starting point. Test charge near positive plate
Em₀ = U = q ΔV₂
final point. Test charge near negative plate
Em_f = K
energy is conserved
Em₀ = Em_f
q ΔV₂ = K
K = q ΔV₁ [tex]\frac{d_2}{d_1}[/tex]
we calculate
K = 1 10⁻⁹ 12 0.005/0.003
K = 2 10⁻⁸ J
Give reason why think before you use a simple cell ?
The disadvantages of simple cell are: It is not rechargeable. The battery needs to be disposed of after all the power has been used up. It can't produce electricity anymore. That is why, why think before you use a simple cell.
What are the benefits and drawbacks of simple cell?A battery designed to be used only once is called a simple cell. Small gadgets used in the house are frequently powered by simple cells.
The benefits of a simple cell include:
A simple cell can be used to power small electronic devices because of its modest size. (Games, lightsabers, radios on the go, cameras, hearing aids)Simple cell electrolyte is not very detrimental to the environment.Simple cells are reasonably priced.Among the drawbacks of a simple cell are:
The biggest drawback of a simple cell is that once it runs out of electricity, it cannot be replenished.Learn more about cell here:
https://brainly.com/question/30046049
#SPJ2
A ball is launched from the ground with a horizontal speed of 30 m/s and a vertical speed of 30 m/s. How far horizontally will it travel in 2 seconds?
A. 30 m
B. 90 m
C. 45 m
D. 60 m
Answer:
It will travel Vx * t = 30 m/s * 2 s = 60 m
Để sử dụng nguồn điện xoay chiều 220V/50Hz thắp sáng bóng đèn 12V/3W, ta chọn điện trở giảm áp có giá trị:
Explanation:
Hi Linda,
How's it going?
Sorry I haven't been in touch for such a long time but I've had exams so I've been studying every free minute. Anyway, I'd love to hear all your news and I'm hoping we can get together soon to catch up. We just moved to a bigger flat so maybe you can come and visit one weekend?
How's the new job?
Looking forward to hearing from you!
Helga
Two train 75 km apart approach each other on parallel tracks, each moving at
15km/h. A bird flies back and forth between the trains at 20km/h until the trains pass
each other. How far does the bird fly?
Answer:
The correct solution is "37.5 km".
Explanation:
Given:
Distance between the trains,
d = 75 km
Speed of each train,
= 15 km/h
The relative speed will be:
= [tex]15 + (-15)[/tex]
= [tex]30 \ km/h[/tex]
The speed of the bird,
V = 15 km/h
Now,
The time taken to meet will be:
[tex]t=\frac{Distance}{Relative \ speed}[/tex]
[tex]=\frac{75}{30}[/tex]
[tex]=2.5 \ h[/tex]
hence,
The distance travelled by the bird in 2.5 h will be:
⇒ [tex]D = V t[/tex]
[tex]=15\times 2.5[/tex]
[tex]=37.5 \ km[/tex]
A point charge of +35 nC is above a point charge of –35 nC on a vertical line. The distance between the charges is 4.0 mm. What are the magnitude and direction of the dipole moment ?
Answer:
Magnitude = 140 x 10⁻¹² Cm
Direction = upwards
Explanation:
A pair of two equal and opposite point charges forms an electric dipole.
The magnitude of the moment of such dipole is the product of the magnitude of any of the charges (since the charges are the same in magnitude) and the distance of separation between them. i.e
p = q x d ----------(i)
Where;
p = dipole moment
q = magnitude of any of the charges
d = distance between the charges.
The direction of the dipole moment is from the negative charge to the positive charge.
(a) From the question, the charges are +35 nC and -35 nC, and the distance between them is 4.00mm.
This implies that;
q = 35 nC = 35 x 10⁻⁹C
d = 4.00mm = 4.0 x 10⁻³ m
Substitute the values of q and d into equation (i) to give;
p = 35 x 10⁻⁹C x 4.00 x 10⁻³ m
p = (35 x 4.0) x (10⁻⁹ x 10⁻³) C m
p = 140 x 10⁻¹² Cm
The magnitude of the dipole moment is 140 x 10⁻¹² Cm
(b) From the question, the +35nC charge is above the -35nC charge on a vertical line as shown below;
o +35nC
|
|
|
|
|
|
o -35nC
Since the direction should point from the negative charge to the positive charge, this means that the direction of the dipole moment of the two charges is upwards (due North).
o +35nC
↑
|
|
|
|
|
|
o -35nC
You are asked to build an LC circuit that oscillates at 13 kHz. In addition, you are told that the maximum current in the circuit can be 0.14 A and the maximum energy stored in the capacitor must be 1.4x10-5 J. What value of inductor and capacitor should you choose
Answer:
a)[tex]L=0.00142H[/tex]
b) [tex]C=2.65*10^{-12}[/tex]
Explanation:
From the question we are told that:
Frequency[tex]F=13kHz[/tex]
Current [tex]I=0.14A[/tex]
Capacitor[tex]C_e=1.4*10^{-5}J[/tex]
Generally the equation for Energy in the inductor is mathematically given by
Where L is now subject
[tex]L=\frac{2C_e}{I^2}[/tex]
[tex]L=\frac{2*1.4*10^{-5}}{(0.14)^2}[/tex]
[tex]L=0.00142H[/tex]
Generally the equation for Value of Capacitor is mathematically given by
[tex]C=\frac{1}{(2 \pi f)^2} L[/tex]
[tex]C=\frac{1}{(2 3.142 13*10^3Hz)^2} *0.00142[/tex]
[tex]C=2.65*10^{-12}[/tex]
A meter stick has only two forces acting on it, of equal sizes at the ends that are in opposite directions. (I have magically turned gravity Off.) Is the stick in equilibrium? Explain your answer.
Answer:
Explanation:
Equilibrium is a state in which the algebraic sum of all forces acting on an object is zero. Thus the object has no force acting on it. The types are: stable, unstable and neutral equilibrium. While a torque is a turning force which are equal but acts in an opposite direction. When applied to on object, it constitute a turning effect. Example is the force applied on a tap, handle wheel of a car etc.
In the given question, the condition stated shows that the stick would experience a torque, thus not in equilibrium. Since the forces at its ends are in opposite directions, then it continues to rotate about its axis.
A string has its 4th harmonic at 31.5 Hz. What is the frequency of its third harmonic?
Answer:
The answer would be 7.5 Hz.
01.04 Law of Conservation of Energy
science question
Answer:
law of conservation of energy states that the total energy of an isolated system remains constant; it is said to be conserved over time.
(a) (1) What is meant by the term modern technology? Give three reasons for the lack of improvement of technology in Ghana.
Answer:
Modern technology is the advancement of old technology with adjustments.
1. Ghana is still developing economically and modern infrastructure is not yet well established.
2. Ghana has Environmental- health concerns which contribute to the lack of improvement of technology in Ghana.
3. Youth unemployment is prevalent therefore contributing to lack of improvement of technology in Ghana.
Explanation:
Ghana is a developing country with rising debt payments which could very well contribute as whole to the lack of improvement of technology in Ghana.
Which of the following behaviors would best describe someone who is listening and paying attention? a) Leaning toward the speaker O b) Interrupting the speaker to share their opinion c) Avoiding eye contact d) Asking questions to make sure they understand what's being said
Answer:
D
Explanation:
Anyone could be leaning forward toward the speaker but be distracted and I believe if you're paying attention to the speaker, you would ask questions to make sure you're understanding what they are speaking
Answer:
A
.............................
PLEASE ANSWER IF YOU CAN AND NOT FOR THE SAKE OF GAINING POINTS!
what do we mean by thrust?
Answer:
the answer is push example: she thrust her hand into her pocket
The cart travels the track again and now experiences a constant tangential acceleration from point A to point C. The speeds of the cart are 11.0 ft/s at point A and 18.0 ft/s at point C. The cart takes 5.00 s to go from point A to point C, and the cart takes 1.30 s to go from point B to point C. What is the cart's speed at point B
Answer:
The speed at B is 16.18 ft/s .
Explanation:
Speed at A, u = 11 ft/s
Speed at C, v' = 18 ft/s
Time from A to C = 5 s
Time from B to C = 1.3 s
Let the speed of car at B is v.
Let the acceleration is a.
From A to B
Use first equation of motion
v = u + a t
18 = 11 + a x 5
a = 1.4 ft/s^2
Let the time from A to B is t' .
t' = 5 - 1.3 = 3.7 s
Use first equation of motion from A to B
v = 11 + 1.4 x 3.7 = 16.18 ft/s
a cheetah running at a velocity of 18m/s accelerates at 1m/s² for 5sec what is the final velocity of the cheetah
state the laws of reflection
Answer:
Explanation:
The law of reflection says that the reflected angle (measured from a vertical line to the surface called the normal) is equal to the reflected angle measured from the same normal line.
All other properties of reflection flow from this one statement.
What is the principle of potentiometer?
Answer:
The principle of a potentiometer is that the potential dropped across a segment of a wire of uniform cross-section carrying a constant current is directly proportional to its length. The potentiometer is a simple device used to measure the electrical potentials (or compare the e.m.f of a cell).
Explanation:
I hope it will help you
An airplane propeller is 2.16 m in length (from tip to tip) with mass 100 kg and is rotating at 2900 rpm (rev/min) about an axis through its center. You can model the propeller as a slender rod. What is its rotational kinetic energy? Suppose that, due to weight constraints, you had to reduce the propeller's mass to 75.0% of its original mass, but you still needed to keep the same size and kinetic energy. What would its angular speed have to be, in rpm?
a) The rotational kinetic energy of the airplane propeller is 1792152.287 joules.
b) The angular speed of the airplane propeller is approximately 3348.631 revolutions per minute.
How to determine the angular speed of a airplane propeller
Let consider the airplane propeller a rigid body, the rotational kinetic energy of the propeller (K), in joules, is described by the following formula:
K = 0.5 · I · ω² (1)
Where:
I - Moment of inertia of the airplane propeller, in kilogram-square meters.ω - Angular speed, in radians per secondIn addition, the moment of inertia of a slender rod rotating around its center is:
I = 0.0833 · M · L² (2)
Where:
M - Mass of the propeller, in kilogramsL - Length of the propeller, in metersa) If we know that M = 100 kg, L = 2.16 m and ω = 303.687 rad/s, then the rotational kinetic energy of the propeller is:
K = 0.5 · [0.0833 · (100 kg) · (2.16 m)²] · (303.687 rad/s)²
K = 1792152.287 J
The rotational kinetic energy of the airplane propeller is 1792152.287 joules. [tex]\blacksquare[/tex]
b) By (1) and (2) we know that the mass of the propeller is inversely proportional to the square of the angular speed. Therefore, we have the following relationship:
[tex]M_{o}\cdot \omega_{o}^{2} = M_{f}\cdot \omega_{f}^{2}[/tex]
[tex]\omega_{f} = \sqrt{\frac{M_{o}}{M_{f}} }\cdot \omega_{o}[/tex] (3)
If we know that [tex]\omega_{o} = 2900\,\frac{rev}{min}[/tex], [tex]M_{o} = 100\,kg[/tex] and [tex]M_{f} = 75\,kg[/tex], then the angular speed of the airplane propeller is:
[tex]\omega_{f} = \left(2900\,\frac{rev}{min} \right)\cdot \sqrt{\frac{100\,kg}{75\,kg} }[/tex]
[tex]\omega_{f} \approx 3348.631\, \frac{rev}{min}[/tex]
The angular speed of the airplane propeller is approximately 3348.631 revolutions per minute. [tex]\blacksquare[/tex]
To learn more on rotational kinetic energy, we kindly invite to check this verified question: https://brainly.com/question/20261989
What is an internal resistance?
Explanation:
some thing inside a resistor
An observer on Earth sees spaceship 1 fly by at 0.80c. 6.0 years later, the observer on Earth sees spaceship 2 fly by at 0.80c, traveling in the same direction as the first. Both spaceships continue to travel with constant velocities. An observer in spaceship 1 observes Earth to pass spaceship 2 ____ years after Earth passed spaceship 1.
Answer:
[tex]t_2=10[/tex]
Explanation:
From the question we are told that:
Velocity of both spaceships [tex]V=0.8c[/tex]
Time [tex]t_1=6[/tex]
Generally the equation for time of spaceship 2 through earth is mathematically given by
[tex]t_2=\frac{t_1}{\sqrt{1-v^2}}[/tex]
[tex]t_2=\frac{6}{\sqrt{1-0.8^2}}[/tex]
[tex]t_2=10[/tex]
A nylon string on a tennis racket is under a tension of 285 N . If its diameter is 1.10 mm , by how much is it lengthened from its untensioned length of 29.0 cm ? Use ENylon=5.00×109N/m2.
Answer:
1.74×10⁻³ m
Explanation:
Applying,
ε = Stress/strain............. Equation 1
Where ε = Young's modulus
But,
Stress = F/A.............. Equation 2
Where F = Force, A = Area
Strain = e/L.............. Equation 3
e = extension, L = Length.
Substitute equation 2 and 3 into equation 1
ε = (F/A)/(e/L) = FL/eA............. Equation 4
From the question,
Given: F = 285 N, L = 29 cm = 0.29 m, ε = 5.00×10⁹ N/m²,
A = πd²/4 = 3.14(0.0011²)/4 = 9.4985×10⁻⁶ m²
Substitute these values into equation 4
5.00×10⁹ = (285×0.29)/(9.4985×10⁻⁶×e)
Solve for e
e = (285×0.29)/(5.00×10⁹×9.4985×10⁻⁶)
e = 82.65/4.74925×10⁴
e = 1.74×10⁻³ m
