Answer:
See below
Explanation:
When a cold alcohol thermometer is placed in a hot liquid, the following takes place.The glass of thermometer expands because of the heat so the column of alcohol goes down.After some time, the heat travels to alcohol and then alcohol expands.So, Reason why alcohol goes down first:Alcohol first goes slightly down because of the expansion of the glass of thermometer before doing up.
[tex]\rule[225]{225}{2}[/tex]
Using the terminal velocity from Q2 and the other necessary values given previously, calculate C for the coffee filter. Show all your work—you may use the equation editor or insert a picture of your handwritten work. What are the units for C?
terminal velocity from Q2 is 0.85 m/s
The drag coefficient (C) is determined from terminal velocity, density of the medium, projected area and mass of the object.
What is terminal velocity?
Terminal velocity is the constant speed of a freely falling object when the resistance of the medium through which it is falling prevents further acceleration.
The magnitude of terminal velocity is calculated as;
[tex]V_T = \sqrt{\frac{2mg}{\rho A C} }[/tex]
where;
m is mass of the objectg is acceleration due to gravityρ is the density of the medium (coffee)C is drag coefficientA is projected areaThus, the drag coefficient (C) is determined from terminal velocity, density of the medium, projected area and mass of the object.
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Which statement is a true catalyst in a reaction
Answer:
it alters the rate of chemical reaction
hope it is useful
A long thin solid rod lies along the positive x-axis. One end is at x = 1.80 m and the other at x = 3.40 m. The linear mass density is λ = a[tex]x^{3}[/tex] + bx, where λ is measured in kg/m, and the constants have the following values: a = 1.70 kg/[tex]m^{4}[/tex] and b = 2.20 kg/[tex]m^{2}[/tex].
1. Determine the total mass of the rod.
2. Calculate the x-coordinate of the center of the mass for this rod.
1. The total mass of the rod is 61.48 kg.
2. The x-coordinate of the center of the mass for this rod is 172.6021 m.
What is density?The density is the ratio of the mass and the volume of the object. It is denoted by ρ.
ρ = mass/Volume = m/V
Given a long thin solid rod lies along the positive x-axis. One end is at x = 1.80 m and the other at x = 3.40 m. The linear mass density is
λ = ax³ + bx,
where λ is measured in kg/m, and the constants have the following values: a = 1.70 kg/m⁴ and b = 2.20 kg/m²
So, λ = 1.70x³ + 2.20x
1. The total mass of the rod is
m =₁.₈³⁴ ∫ [1.70x³ + 2.20x] dx
m = [ 1.70x⁴/4 + 2.20x² /2 ]₁.₈³⁴
Putting the limits, we have
m = 69.51 - 8.02548
m = 61.48 kg
Thus, the total mass of the rod is 61.48 kg
2. The x-coordinate of the center of the mass for this rod
Xcm =∫ xλdx/m
Xcm =∫[ x ( 1.70x³ + 2.20x) /m ]dx
Xcm =∫[( 1.70x⁴ + 2.20x²) /m ]dx
On integrating and putting the limits x = 1.80 m to x = 3.40 m
Xcm = = [ {1.70(3.4)⁵/5 + 2.20(3.4)³ /3} - {1.70(1.8)⁵/5 + 2.20(1.8)³ /3} ]
Xcm = 183.3034 - 10.70133
Xcm = 172.6021 m
Thus, the x-coordinate of the center of the mass for this rod is 172.6021 m.
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a highway curve has a radius of 300 m. at what angle should it be banked for a traffic speed of 100 km/h
The angle at which it should be banked for a traffic speed of 100 km/h is
14.57°.
How do find the angle of Banking of road?Banking of roads is the practice of raising the outer borders of curving roads over the inner edge in order to give vehicles the necessary centripetal force to make a turn safely.Skidding can be prevented by banking.The banking of roadways aids in preventing toppling or overturning.To find the angle of banking following formula can be used,
[tex]tan \alpha = v^{2} /rg[/tex]
Given v = 100km/h or
= 100 x 1000 / 3600
= 27.7 m/s
Hence,
[tex]tan \alpha = (27.7)^{2} / 300 * 9.81[/tex]
[tex]tan\alpha = 0.26[/tex]
[tex]\alpha = tan^{-1} 0.26[/tex]
[tex]\alpha = 14.57[/tex]°
Hence, the angle of banking of the road will be 14.57°
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A certain spring has a spring constant k1 = 660 N/m as the spring is stretched from x = 0 to x1 = 35 cm. The spring constant then changes to k2 = 250 N/m as the spring is stretched to x2 = 65 cm. From x2 = 65 cm to x3 = 89 cm the spring force is constant at F3 = 105 N.
Write an equation for the work done in stretching the spring from x1 to x2.
Calculate the work done, in joules, in stretching the spring from x1 to x2.
Calculate the work, in joules, necessary to stretch the spring from x = 0 to x3.
(a) The equation for the work done in stretching the spring from x1 to x2 is ¹/₂K₂Δx².
(b) The work done, in stretching the spring from x1 to x2 is 11.25 J.
(c) The work, necessary to stretch the spring from x = 0 to x3 is 64.28 J.
Work done in the springThe work done in stretching the spring is calculated as follows;
W = ¹/₂kx²
W(1 to 2) = ¹/₂K₂Δx²
where;
k is spring constantΔx is compression of the springW(1 to 2) = ¹/₂(250)(0.65 - 0.35)²
W(1 to 2) = 11.25 J
W(0 to 3) = ¹/₂k₁x₁² + ¹/₂k₂x₂² + ¹/₂F₃x₃
where;
k₁ is first spring constantk₂ is second spring constantF₃ is third force applied to the springW(0 to 3) = ¹/₂(660)(0.35)² + ¹/₂(250)(0.65 - 0.35)² + ¹/₂(105)(0.89 - 0.65)
W(0 to 3) = 64.28 J
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A skateboarder starts from rest and maintains a constant acceleration of 0.50 m/s² for 8.4 s. What is the rider's displacement during this time
meters
Answer:
4.2m/s
Explanation:
0.50x8.4=4.2m/s
A 10 cm diameter pulley is used to lift a bucket of cement weighing 400 N. How much force must be applied to the rope to lift the bucket at the other end?
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[tex]\large \bold {ANSWER}[/tex]
Considering that the pulley is fixed, the force applied should be equal to the weight of the object - of 400N.
[tex]\large \bold {EXPLANATION}[/tex]
Pulleys or pulleys are mechanical tools used to assist in the movement of objects and bodies. There are two types of pulleys: fixed and movable. While the fixed pulley changes the direction of force, the moving pulley helps to decrease the force needed to move the object or body in question.
As the statement only tells us a pulley, we must consider that it is fixed, because generally when it is mobile, this information is highlighted in the question.
In this way, a fixed pulley only changes the direction of the applied force. Thus, the force must have the same magnitude as the weight of the object to be moved. If the bucket weighs 400N, the force applied to the pulley must be 400N.
Therefore, having a fixed pulley, the force applied must be equal to the weight of the object, and will be 400N.
A 2100-W hair dryer is operated on a 120-V
circuit for 12 min. If electricity
costs $0.25/kWh, what was the cost (in
cents) of using the blow dryer? Round final
answer to the nearest cent.
Answer:
cost=$15
Explanation:
given;
P= 2100 W
t= 12'= 720 sec=0.2h
V= 120 V
required;
Energy?
cost?
solution;
Energy(kWh) = power*time(in hour)
E=2100*0.2= 420 kWh
cost= 420 kWh* $0.25/kWh
cost= $15
since blow dryer use 120-V
(2.) Jerry first walks 5m to East, then 6m to N 60 E, then, she walks 16m to N30'W, 3 finally turns he face and moves 3V3m to south. What is her displacement and direction?
The displacement is determined to be 5.11 m after every direction is plotted on the page.
What is displacement?Displacement is defined as the shortest distance between the two points.
The steps in which Jerry walks;
5m to East
6m to N 60' E,
16m to N30'W,
Turn
3√3 m to the south.
Each and every direction is plotted on the page and obtained that the displacement is found as 5.11 m.
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A stone is dropped from the top of a tower which touches the ground after 2 seconds. Calculate the speed of the stone hitting the ground surface. (g = 9.8 m/s²)
Answer:
19.6 m/s
Explanation:
The velocity is the product of acceleration and time.
__
Here, the acceleration is due to gravity.
v = at
v = (9.8 m/s²)(2 s) = 19.6 m/s
The stone hits the ground with a speed of 19.6 m/s.
A stone is dropped from the top of a tower which touches the ground after 2 seconds.
Calculate the speed of the stone hitting the ground surface. (g = 9.8 m/s²).[tex] \mathbb{SOLUTION:} [/tex][tex]v = u + at[/tex][tex]v = 9.8 m/s² x 2sec[/tex][tex]v = 19.6 \: m/ {s}^{2} [/tex]••••••••••••••••••••••••••••••••••••••••••••Hence, The stone hit the ground with the velocity speed of 19m/s².
- When you're solving velocity, you're determining how fast an object moves from its original position, with respect to a frame of reference, and a function of time.
- That means an object's velocity will be equal to the object's speed and direction of motion.
"Problem has been solve"
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A cup of water is warmed from 21 °C to 85 °C. What is the difference between these two temperatures, in kelvins?
Answer:
337k
Explanation:
First, let us find the difference between the given two temperatures.
Difference = 85°C - 21°C
= 64°C
And now we have to write the temperature in kelvins.
To convert Celcius to Kelvins you can add 273 to the temperature in Celcius.
Let us find it now.
64°C + 273 = 337k
Therefore,
64°C ⇒ 337k
Two masses, m and 2m, approach each along a path at right angles to each other. After collision, they stick together and move of at 2m/s at angle 37⁰ to the original direction of the mass m. What where the initial speeds of the two particles?
The initial speed of the object with mass "m" is 4.79 m/s and the initial speed of the object with mass "2m" is 1.81 m/s.
Initial speed of the two massesThe initial speed of the two masses is calculated by applying the principle of conservation of linear momentum as follows;
m₁u₁ + m₂u₂ = v(m₁ + m₂)
let m be in horizontal directionlet 2m be in vertical directionangle between the two masses = 90 degreesin y - direction[tex]m_1u_1sin(\theta_1) + m_2u_2sin(\theta_2) = (m_1 + m_2)vsin(\theta_3)\\\\mu_1sin(0) + 2mu_2sin(90) = (m + 2m)(2)sin(37)\\\\2mu_2 = 3.61m\\\\u_2 = \frac{3.61 m}{2m} \\\\u_2 = 1.81 \ m/s[/tex]
in x - direction[tex]m_1u_1sin(\theta_1) + m_2u_2sin(\theta_2) = (m_1 + m_2)vsin(\theta_3)\\\\mu_1cos(0) + 2mu_2cos(90) = (m + 2m)(2)cos(37)\\\\mu_1 = 4.79 m\\\\u_1 = 4.79 \ m/s[/tex]
Thus, the initial speed of the object with mass "m" is 4.79 m/s and the initial speed of the object with mass "2m" is 1.81 m/s.
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A car is traveling along a straight road at a velocity of 30m/s when its engine cuts off. For the next ten seconds, the car slows down, and its average acceleration is a₁. For the next five seconds, the car slows down further, and its average acceleration is a₂. The ratio of the average acceleration values is a₁/a₂=1.5. Find the velocity of the car at the end of the initial ten-second interval.
The velocity of the car at the end of the initial ten-second interval is 15a₂ + 30.
Initial velocity of the carv = u + at
after 10 seconds;
v = 30 + 10a₁ --(1)
after 5 seconds
v₂ = v + 5a₂ ---- (2)
solve (1) and (2) together
v₂ = 30 + 10a₁ + 5a₂
but a₁/a₂=1.5
a₁ = 1.5a₂
v₂ = 30 + 10(1.5a₂) + 5a₂
v₂ = 30 + 15a₂ + 5a₂
v₂ = 30 + 20a₂
from equation (2), v₂ = v + 5a₂
v + 5a₂ = 30 + 20a₂
v = 15a₂ + 30
Thus, the velocity of the car at the end of the initial ten-second interval is 15a₂ + 30.
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A solenoid with 465 turns has a length of 8.00 cm and a cross-sectional area of 3.10 ✕ 10−9 m2. Find the solenoid's inductance and the average emf around the solenoid if the current changes from +3.50 A to −3.50 A in 7.83 ✕ 10−3 s
The solenoid's inductance and the average emf around the solenoid if the current changes from +3.50 A to −3.50 A in 7.83 ✕ 10−3 s will be 1.01 ×10⁻⁸ H and 9.02 × 10⁻² V.
What is a solenoid?A coil of wire that carries an electric current is a solenoid. A solenoid is an electromagnet formed by a helical coil of wire.
Which generates a magnetic field when an electric current is passed through the coil.
A solenoid is a form of coil that produces a magnetic field when the electric current is passed through it. A solenoid is created when a conductive wire is used to make a loop.
Given data;
Turns ,N = 465
Length,L= 8.00 cm
Cross-sectional area,A = 3.10 ✕ 10−9 m2.
Solenoid's inductance, L=?
The average emf around the solenoid, E=?
Time of flow,t= 7.83 ✕ 10−3 s
Current changes from +3.50 A to −3.50 A
The inductance of the solenoid is found as;
[tex]\rm L = \frac{\mu_0 AN^2}{L} \\\\ \rm L = \frac{4 \times \pi \times 10^{-7}\times 3.0 \times 10^{-9} \times (465)^2 }{8.00 \times 10^{-2}} \\\\ L= 1.01 \times 10^{-8} \ H[/tex]
The average emf around the solenoid is found as;
[tex]\rm e = L \frac{I_2-I_1}{t} \\\\ \rm e = 1.01 \times 10^{-8} \times \frac{3.50-(-3.50)}{7.83 \times 10^{-3}} \\\\ e =9.02 \times 10^{-12} \ V[/tex]
Hence, the solenoid's inductance will be 1.01× 10⁻⁸ H.
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An upward force is applied to a 6.0–kilogram box. This force displaces the box upward by 10.00 meters. What is the work done by the force on the box?
The work done by the force on the box 588 Joule.
What is Potential energy ?It is the energy that is stored in an object due to its position relative to some zero position.
According to the question,
Given mass of the box (m) = 6.0 kg
Given displacement of the box = 10.00 m
Hence , the height of the box (h) = 10.00 m
Acceleration due to gravity (g) = 9.8 m/s²
Since ,
The upward force was applied to the box, the box moves up to the height.
Therefore, the work done by the ball is the potential energy gained by the ball.
By using the formula of potential energy
P.E. = mgh
= 6 × 9.8 × 10 Joule = 588 Joule
As we know .
Work done (W) = Potential energy (P.E.)
Work done (W) = 588 Joule
Thus, 588 Joule is the work done by the force on the box.
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what is the output voltage of a transformer if the input is 240volts, and the number of turns on the primary coil is 1200 and on the secondary coil is 200.
The output voltage of a transformer is 40V.
What is an output voltage?An output voltage is the voltage released by a device, such as a voltage regulator or a generator.
The formula to calculate Output voltage of transformer is:
[tex]\frac{V_{s} }{V_{p} } = \frac{N_{s} }{N_{p} }[/tex]
here, [tex]V_{s}[/tex] is the secondary voltage, [tex]V_{p}[/tex] is the primary voltage, [tex]N_{s}[/tex] is the number of secondary windings and [tex]N_{p}[/tex] is the number of primary windings.
According to the question.
[tex]N_{p}[/tex] =1200 , [tex]N_{s}[/tex]=200 , [tex]V_{p}[/tex]=240V ,[tex]V_{s}[/tex]= ?
By using the formula of Output voltage,
[tex]{V_{s} } = \frac{V_{p}N_{s} }{N_{p} }[/tex]
=[tex]\frac{240*200}{1200}[/tex]
[tex]=40V[/tex]
Therefore, 40V is the output voltage of a transformer.
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A uniform, 255 N rod that is 1.80 m long carries a 225 N weight at its right end and an unknown weight W toward the left end. When W is placed 60.0 cm from the left end of the rod, the system just balances horizontally when the fulcrum is located 75.0 cm from the right end.
Part a) Find W.
Part b) If W is now moved 20.0 cm to the right, how far must the fulcrum be moved to restore balance? Δx = ?
Part c) If W is now moved 20.0 cm to the right, in what direction must the fulcrum be moved to restore balance?
(a)The value of W for the given condition will be 237.3 N.
(b)The distance must the fulcrum be moved to restore balance will be 0.070 m.
What is the center of mass?A location is established in relation to an object or set of objects in the center of mass. It is the system's average position across all of its components.
Given data;
Weight is applied to the right end of the rod, W₁= 225 N
Rod's weight,W₂ = 255
W₃ is the Weight at "x" distance from the left end.
x1 is the location of W₁ with respect to the left end, where L = 1.80 m
m is the location of the rod's center of mass from the left end.
The position of W from the left end; x₃ = 50 cm = 0.50 m
Xcm is the position of the center of gravity of the rod at the fulcrum from the left end;
Given that the fulcrum is balanced in this situation, the rod's center of gravity will be there.
Xcm= L - 75 cm
Xcm=1.80 m - 0.75 m
Xcm= 1.05 m
The value of x₂
x₂= 1.80 m/2 = 0.90 m
Currently, the horizontal center of gravity is determined by
[tex]\rm X_{cm} =\frac{ (W_1x_1 + W_2x_2 + W_3*x_3)}{(W_1 + W_2 + W_3)}[/tex]
Substitute the values we get;
[tex]\rm 1.05 = \fraca{ (225 \times 1.80 + 255\times 0.90 + W\times 0.50)}{(225 + 255 + W)}\\\\ W = \frac{ (225\times 1.80 + 255\times 0.90 - 480 \times 1.05)}{(1.05 - 0.50)}\\\\ W = 237.3 \ N[/tex]
After moving the fulcrum 20.0 cm to the right,
The location of the W from the left end;
x₃ = .50 cm + 20 cm
x₃ = 70 cm
x₃ = 0.70 m
W₁, W₂, W, x₁, and x₂ have fixed values. Therefore, based on these values, the new center of gravity will be:
[tex]\rm X_{cm} =\frac{ (W_1x_1 + W_2x_2 + W_3*x_3)}{(W_1 + W_2 + W_3)}[/tex]
[tex]\rm X_{cm} = \frac{(225\times 1.80 + 255\times 0.90 + 237.3\times 0.70)}{(225 + 255 + 237.3)}\\\\ X_{cm} = 1.12 m[/tex]
Fulcrum must be shifted by;
Y = (1.12 - 1.05)
Y= 0.070 meters.
W has been moved in the appropriate direction, thus the fulcrum should likewise be moved in the appropriate direction.
Hence, the value of W for the given condition will be 237.3 N. and the distance must the fulcrum be moved to restore balance will be 0.070 m.
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The practice of science can answer only scientific questions. And scientific
questions guide the design of investigations. What must be true of the
possible answers to a scientific question?
OA. They could be shown to be false by evidence.
B. They are at odds with established scientific theories.
C. They support an established scientific theory.
OD. They do not require the use of physical measurements.
SUBMIT
Evidence might be used to demonstrate their falsity. must apply to all potential solutions to a scientific topic.Option A is correct.
What is a Scientific hypothesis?A scientific hypothesis is the main element in the scientific method and experiment.
It is said that a hypothesis is a scientific hypothesis. The majority must agree on it, or it must be done after thorough experimentation.
Only scientific inquiries can have their answers provided by scientific endeavor. Scientific concerns have an impact on the research's design as well.
Evidence might be used to demonstrate their falsity. must apply to all potential solutions to a scientific question.
Hence option A is correct.
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Which two of the following statements best describe the similarity between elements and compounds? 1. Elements and compounds are listed in the periodic table. 2. Elements and compounds are both pure substances. 3. Elements and compounds are both made of different kinds of atoms. 4. Elements and compounds cannot be broken down by physical changes.
In infrared satellite images, land appears _________ and clouds appear _________. A. red, yellow B. white, black C. black, white D. yellow, red
In infrared satellite images, land appears black and clouds appear white. C
What are infrared satellite images?Infrared satellite images are images produced as a result of electromagnetic radiations reflected or emitted from a target surface in the infrared position of the electromagnetic spectrum.
On infrared images, the clouds emit very bright white color because of the low temperature and the land appears to be black because of the hot temperature.
Therefore, in infrared satellite images, land appears black and clouds appear white. C
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A ball is projected with initial velocity 50m/s at an angle of elevation of 37 degrees from the top of a cliff 55 m high. Calculate the total time the ball is in the air and the maximum horizontal distance covered.
The total time the ball is in the air is 1.47 s and the maximum horizontal distance covered is 58.7 m.
Time of motion of the ball
The time of motion of the ball is calculated as follows;
h = vt + ¹/₂gt²
55 = (50sin37)t + ¹/₂(9.8)t²
55 = 30.1t + 4.9t²
4.9t² + 30.1t - 55 = 0
Solve using formula method;
t = 1.47 s
Horizontal distance of the ballX = vxt
where;
vx is the horizontal velocityt is time of motionX = (50 x cos37) x 1.47
X = 58.7 m
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Question 2 of 10
Which two types of energy does a book have as it falls to the floor?
what is the formula for finding balance length
Answer:
Case 1: Balancing length when cell is shunted l1 = 150 cm = 1.5 m, Value of shunt = R = 5 ohm. Case 2: Balancing length when cell is shunted l1 = 175 cm = 1.75 m, Value of shunt = R = 10 ohm. Example 06: A cell balances against a length of 250 cm on potentiometer wire when it is shunted by a resistance of 10 ohms
An object weighs 200N, what is its mass?
Answer:
kg
Explanation:
the highr and jebad to kilogram mizans
Answer:
w=m×g
Explanation:
w is given and take g as 9.8m/s^2
While a substance is heated it reaches its boiling point. What happens if heating continues while it is boiling?
Answer:
liquid turns into vapor when the liquid molecules achieves the energy to break down the form or when gets highly excited. The temp required for this is called latent heat of vaporization. As the liquid molecules attain this energy through heat it suddenly changes form into vapor , and when the heat is continued , molecule after molecule receives this energy and changes to vapor .So if you continue heating the liquid all the liquid will change form to vapor state leaving residue , ie the dissolved particles .
liquid turns into vapor when the liquid molecules achieves the energy to break down the form or when gets highly excited. The temp required for this is called latent heat of vaporization. As the liquid molecules attain this energy through heat it suddenly changes form into vapor , and when the heat is continued , molecule after molecule receives this energy and changes to vapor .So if you continue heating the liquid all the liquid will change form to vapor state leaving residue , ie the dissolved particles .I’m no expert but this is what i think happens …
After the terrorist attacks of September 11th, 2001, the National Center on the Psychology of Terrorism was founded to research psychological aspects of terrorism. This is an example of how __________ affect theories and perspectives in psychology.
A.
current events
B.
new discoveries
C.
oppositions
D.
personal ideologies
A satellite circles the Earth in an orbit whose radius is twice the Earth’s radius. The Earth’s mass is 5.98 x 1024 kg, and its radius is 6.38 x 106 m. What is the period of the satellite?
Hello!
Recall the period of an orbit is how long it takes the satellite to make a complete orbit around the earth. Essentially, this is the same as 'time' in the distance = speed * time equation. For an orbit, we can define these quantities:
[tex]d = 2\pi r[/tex] ← The circumference of the orbit
speed = orbital speed, we will solve for this later
time = period
Therefore:
[tex]T = \frac{2\pi r}{v}[/tex]
Where 'r' is the orbital radius of the satellite.
First, let's solve for 'v' assuming a uniform orbit using the equation:
[tex]v = \sqrt{\frac{Gm}{r}}[/tex]
G = Gravitational Constant (6.67 × 10⁻¹¹ Nm²/kg²)
m = mass of the earth (5.98 × 10²⁴ kg)
r = radius of orbit (1.276 × 10⁷ m)
Plug in the givens:
[tex]v = \sqrt{\frac{(6.67*10^{-11})(5.98*10^{24})}{(1.276*10^7)}} = 5590.983 m/s[/tex]
Now, we can solve for the period:
[tex]T = \frac{2\pi (1.276*10^7)}{5590.983} =\boxed{ 14339.776 s}[/tex]
2. Two small (green) objects, each of mass m, are separated by a solid, massless rod of length L. They are located so that one of the objects is located at a distance of r away from the center of a uniform spherical planet with mass M (see figure). M r m L m Assume that m is very small so that you can ignore the gravitational force between the two small (green) objects. Is the rod being compressed, stretched, or neither? If compressed/stretched, calculate the magnitude of this deformation force on the rod. If neither, explain clearly why.
The rod is stretched due to the force of gravitational attraction.
The magnitude of the deformation force on the rod is -GMm×((1/r² + 1/(L+r)²)
What is gravity?The force of attraction felt by a person which is directed at the center of a planet or Earth is called as the gravity.
The force of attraction is directly proportional to the product of masses of the object and inversely proportional to the square of distance between them.
F = GMm/R²
Given are two small (green) objects, each of mass m, are separated by a solid, massless rod of length L. They are located so that one of the objects is located at a distance of r away from the center of a uniform spherical planet with mass M. Assume that m is very small so that you can ignore the gravitational force between the two small (green) objects.
Let the mass closer to the planet is A and the other is B
FA = Force on planet A = -GMm/r²
FB = Force on planet B = -GMm/(L+r)²
Net Force on the rod is given by the addition of the individual forces.
Fnet= FA + FB = -GMm/r² -GMm/(L+r)²
Fnet = -GMm×((1/r² + 1/(L+r)²)
Thus, the magnitude of the deformation force on the rod is derived above.
A experience more force than B, so A will stretch out from B. Hence the force is stretching the rod.
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Suppose a piano tuner stretches a steel piano wire 7.5 mm. The wire was originally 0.975 mm in diameter, 1.45 m long, and has a Young's modulus of 2.10 × 1011 N/m2. Calculate the force a piano tuner applies to stretch the steel piano wire in Newtons.
The forces a piano tuner applies to stretch the steel piano wire willl be 1.4 × 10¹¹ N.
What is force?Force is defined as the push or pulls applied to the body. Sometimes it is used to change the shape, size, and direction of the body. Force is defined as the product of mass and acceleration. Its unit is Newton.
The application of a force may be used to describe the steel as an elastic element within a certain range of applied force.
Given data;
Young modulus, E=2.10 × 10¹¹ N/m²
Cross-sectional area,A
Final length,[tex]\rm L_f = 1.45 m = 1450 \ mm[/tex]
Initial length,[tex]\rm L_i = 7.5 mm[/tex]
[tex]\rm F = \frac{(L_f-L_i)(E)(A)}{L_1} \\\\ \rm F = \frac{(1450 - 7.5)(2.0 \times 0^{11})(0.746)}{1450} \\\\ F = 1.4 \times 10^{11} \ N[/tex]
Hence, the force a piano tuner applies to stretch the steel piano wire willl be 1.4 × 10¹¹ N.
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Question 2 of 25
What is the term for a pair of forces described by Newton's third law?
A.
Normal-friction pair
B.
Action-reaction pair
C.
Kinetic-static pair
D.
Inertia-movement pair
The term for a pair of forces described by Newton's third law is action-reaction pair. Details about Newton's law can be found below.
What does Newton's third law state?Newton's third law of motion states that for every action, there is an equal and opposite reaction.
This law proposed that when an object 1 acts on object 2 with a force of a particular magnitude, object 2 also acts on object 1 with an opposite force of same magnitude.
Therefore, it can be said that the term for a pair of forces described by Newton's third law is action-reaction pair.
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