The mass of the second skater is equal to 27 Kg, which acquires a speed of 3.81 m/s.
What is law of conservation of linear momentum?According to the law of conservation of momentum, the sum of the momentum of the two objects before and after the collision must be equal.
m₁ u₁ + m₂u₂ = m₁ v₁ + m₂ v₂
where m₁ and m₂ is the mass of the collided bodies, u₁ and u₂ are the initial speed while v₁ & v₂ is their final speed.
The linear momentum can be described as the product of the mass times the velocity of the object. Conservation of momentum is a characteristic held by an object where the total amount of momentum remains the same.
Given the initial speed of the skaters is equal to zero so u₁ = u₂ =0
The mass of the one skater, m₁ = 49 Kg
The first skater acquires the speed, v₁ = 2.10 m/s
The speed acquired by the second skater, v₂ = -3.81 m/s
From the law of conservation of momentum, we can find the mass of another skater:
m₁ u₁ + m₂ u₂ = m₁v₁ + m₂ v₂
49 × 0 + m₂ ×0 = 49 × (2.10) + m₂ × (- 3.81)
m₂ = -49 × (2.10)/ (- 3.81)
m₂ = 27 Kg
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Please answer 9 only. Simple answer and simple explanation is needed, thanks.
Answer:
a = -493.83 m/s²
Explanation:
The acceleration can be calculated as:
[tex]a=\frac{v_f-v_i}{t}[/tex]Where vf is the final velocity, vi is the initial velocity and t is the time.
Then, we need to convert 320 km/h to m/s as follows:
[tex]320\frac{\operatorname{km}}{h}\times\frac{1000m}{1\operatorname{km}}\times\frac{1h}{3600s}=88.89\text{ m/s}[/tex]Now, we can replace vf by 0 m/s, vi by 88.89 m/s, and t by 0.18 s to get an acceleration equal to:
[tex]\begin{gathered} a=\frac{0-88.89\text{ m/s}}{0.18s}=\frac{-88.89\text{ m/s}}{0.18s}=-493.83m/s^2 \\ \end{gathered}[/tex]Therefore, the acceleration that takes place in this time is equal to -493.83 m/s²
Find the equation of a line passing through (8, 43.6) and (4.5, 26.3)
5x + y = 3.6 equation of a line going between (8, 43.6) and (4.5, 26.3).
Write about a vector?Having independent properties for both size and direction, a quantity or phenomenon is referred to as a vector. The representation of a quantity in mathematics or geometry is another use of the term. In nature, vectors include things like force, momentum, weight, electromagnetic fields, and velocity.
Exactly what is a unit vector?Unit vectors are those that have a magnitude that is exactly one unit. They are quite useful for a variety of reasons. The unit vectors [0,1] and [1,0] in particular can be combined to create any other vector.
The slope of the line joining points A(8,43.6) and B(4.5,26.3) is given by the equation m= y2-y1/x2-x1=26.3-43.6/4.5-8 = 5.
Consequently, the equation for the line that is required is given by y-y1 = m. (x-x1)
y- 43.6 = 5(x-8) =5x + y = 3.6.
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The oscilloscope can be used to measure AC frequency by counting the number of _____________ per unit time.A. PeaksB. Complete wavesC. ValleysD. Partial wavesJust please give me the answer, no explanation.
The oscilloscope can be used to measure AC frequency by counting the number of complete waves (Option B).
What is an oscilloscope?An oscilloscope is a tool used to measure voltage by observing how the electrical signals from different types of waves may change over a given unit or period of time, which is useful to monitor a client's heartbeat and brain waves.
Therefore, with this data, we can see that an oscilloscope is a device used to measure waves (in this case brain waves) in order to indicate a given outcome associated with electrical signals.
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IfWhile shopping in England, Sally notices the cost of bananas is £2.10/kg. Sally isn't familiar with Great Britain Pounds (GBP) or kilograms, and needs to convert the unit price into dollars per pound. You may assume the conversion rate from dollars to GBP is $1 to £0.77, and there are 2.2lbs to 1kg. Round your answer to the nearest cent.
Each pound costs $1.2 in unit pricing.
Sally notes that the price of bananas in England is £2.10/kg.
Applying the exchange rate from dollars to British pounds (GBP), if $1 = £0.77, then £2.10 would be calculated as 2.10/0.77, or 2.72.
Using the pounds to kilograms conversion rate, 1 kilogram equals 2.2 pounds.
Consequently, the price per unit in dollars would be 2.72/2.2 = $1.236.
If we round to the nearest cent, the price per pound is $1.2.
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Consider a house with a floor space of 200 m2and anaverage height of 3 m at sea level, where thestandard atmosphericpressure is 101.3 kPa.Initially the house is at a uniformtemperature of 10°C.Now the electric heater is turned on, andthe heater runs until the air temperature in the house risesto anaverage value of 22°C. Determine how much heat is absorbedby the air assuming some airescapes through the cracks asthe heated air in the house expands at constant pressure. Also,determine the cost of this heat if the unit cost of electricity inthat area is $0.075/kWh.
9038 kJ of heat is absorbed by the air assuming some air escapes through the cracks as the heated air in the house expands at constant pressure, and cost of this heat if the unit cost of electricity in that area is $0.075/kWh is $0.19.
What is pressure?In the physical sciences, pressure is defined as the perpendicular force per unit area or the stress at a point within a confined fluid.
A 42-pound box with a bottom area of 84 square inches will press down on a surface with a pressure equal to the force divided by the area over which it is applied, or half a pound per square inch.
The specific heat of air at room temperature is
[tex]C_p[/tex] = 1.007 kJ/kg⋅°C
The volume and mass of the air in the house are
V = Floor space × height
= (200 m² )(3m)
= 600 m ³
Mass = PV/RT
= [tex]\frac{(1013 kPa)(600 m^3 )}{(0287 kPa.m/kg.K)(10+273.15 K)}[/tex]
= 7479 kg
The amount of heat that must be transferred to the air in the house as it is heated from 10 to 22°C is calculated, taking into account that the pressure in the house remains constant during heating, as follows:
Q = [tex]mC_p[/tex] [tex](T_2 - T_1)[/tex]
= (747.9 kg)(1.007 kJ/kg⋅ °C)(22 – 10) °C
= 9038 kJ
Noting that 1 kWh = 3600 kJ, the cost of this electrical energy at a unit cost of $0.075/kWh is
Enegy Cost = (Energy used)(Unit cost of energy)
= (9038/3600 kWh)($0.075/kWh)
= $0.19
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Dots sells a total of 266 T-shirts ($2) and shorts ($4). In April, total sales were $672.How many T-shirts and shorts did Dots sell? Hint: Let S = Shorts.
Let x be the number of t-shirts and y the number of shorts they sold. Since in total they sold 266 items we have the equation:
[tex]x+y=266[/tex]Now we know that each shirt cost $2 and each short cost $4 and that the total sales were $672 then we have the equation:
[tex]2x+4y=672[/tex]Hence we have the system of equations:
[tex]\begin{gathered} x+y=266 \\ 2x+4y=672 \end{gathered}[/tex]Solving for y from the first equation we have:
[tex]y=266-x[/tex]Plugging this in to the second equation we have:
[tex]\begin{gathered} 2x+4(266-x)=672 \\ 2x+1064-4x=672 \\ -2x=672-1064 \\ -2x=-392 \\ x=\frac{-392}{-2} \\ x=196 \end{gathered}[/tex]Plugging this value in the equation for y we have:
[tex]y=266-196=70[/tex]Therefore the sold 196 shirts and 70 shorts.
This defense mechanism offers self-justifying explanations in place of the real, more threatening, unconscious reasons for one's actions. This is known as:
This defense mechanism offers self-justifying explanations in place of the real, more threatening, unconscious reasons for one's actions. This is known as Rationalization.
According to the question, rationalization is a defense mechanism, and the phrase refers to the act of justifying through the creation of numerous sorts of justifications, explanations, and reasons for any behavior.
A coherent, logically ordered system that also serves to rationalize an individual's unconscious motivation for acting is referred to as a rationalization.
One method of reorganizing a business to improve operational effectiveness and alter organizational policy is rationalization.
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A box with a mass of 45.0 kg is pushed across a horizontal surface with a force of 19.0 N. What isthe acceleration of the box in meters per second squared?
Given data:
Mass of the box;
[tex]m=45.0\text{ kg}[/tex]Force;
[tex]F=19.0\text{ N}[/tex]The force is given as,
[tex]F=ma[/tex]Here, a is the acceleration of the box.
Rearraning the above equation to get an expression for acceleration,
[tex]a=\frac{F}{m}[/tex]Substituting all known values,
[tex]\begin{gathered} a=\frac{19\text{ N}}{45\text{ kg}} \\ =0.42\text{ m/s}^2 \end{gathered}[/tex]Therefore, the acceleration of the box is 0.42 meters per second squared.
Pls answer. Will rate 5 start and give a Thanks or Brainliest.
What are the characteristics of the Sun? (Select all that apply.)
Group of answer choices
The Sun is the center of our solar system and radiates energy.
The Sun is a medium-sized star compared to other stars in the universe.
The Sun has planets and dwarf planets that orbit it.
The Sun is composed of helium and hydrogen.
The Sun is near the end of its life.
The Sun is composed of helium and hydrogen. Option C.
The photosphere chromosphere and corona are all part of the Sun's atmosphere. Although the corona is sometimes called the solar atmosphere it is actually the sun's upper atmosphere. The sun's atmosphere includes features such as sunspots, coronal holes, and solar flares the sun is a star.
It's a huge spinning ball of hot gas. The sun is like a star in the night sky. Because we are so close it appears much larger and brighter than other stars. The sun is the center of the solar system and accounts for most of the mass of the solar system. Compared to the billions of other stars in the universe, the sun stands out. But for the Earth and the other planets orbiting around it, the Sun is a powerful focal point.
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Which of the following scenarios where a ball is in motion describes balanced forces? (choose only one answer choice) Select one or more: a. 2, 4, and 5 b. 1, 3, and 4 c. 2 and 4 d. 1, 2, and 5
The scenario where a ball in motion describes balanced forces is 1, 3, and 4. That is option B.
What is motion?Motion is defined as the movement of an object from one position to another with respect to time.
There are different type of motion which include the following:
linear motion,rotary motion,reciprocating motion, oscillating motion.Periodic motion, andCircular motion.When an object is in motion, the forces acting on them are said to be balanced when they are equal in magnitude and in opposite directions.
1N + 3N = 4N
This shows that the forces 1N + 3N which is equal to 4N are equal and opposite.
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A student made the table shown to list some contact and non-contact forces .
Examples of forces
Contact force - the upward force applied by a coach on a student sitting on it .
The force applied by a student in a box to move it .
Non- contact forces
The force applied by an electromagnetic on a wire
The force which opposes of an object on a ruff surface .
Which statement best explains why the table is incorrect?
A- Normal force is a force acting at a distance.
B- The student applies a non- contact force on the box .
C- The electromagnetic and wire have to be in contact to apply the force .
D- Frictional force acts between the object and the rough surface when they are In contact.
The statement that best explains why the table is incorrect is that frictional force acts between the object and the rough surface when they are In contact ( D ).
The statements in the table that describes contact forces are correct and one of the statements that describes a non-contact force is not correct. A contact force is a force applied by one mass on another due to being in contact with each other. A non contact force is the opposite of a contact force.
The force which opposes the motion of an object on a rough surface is frictional force. Frictional force is opposing between two surfaces in contact with each other. Since the two surfaces have to be in contact with each other it falls under the description of contact force.
Therefore, the statement that best explains why the table is incorrect is that frictional force acts between the object and the rough surface when they are in contact ( D ).
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Electronegativity can best be defined as a) relative measure showing how many bonds an atom will formb) a relative measure showing the degree to which electrons can be removed from an atom c) the degree to which an electron will leave an atom d) the degree to which an atom wants to gain more electrons
The electronegativity of an element is the tendency of an atom to attract electrons to itself in a chemical compound.
The electronegativity decreases down the group and increases from left to right across the period.
Therefore, electronegativity can best be defined as the degree to which an atom wants to gain more electrons. Hence, option (d) is the correct choice.
Solve for the impulse imparted on the golf ball.
t = 0.001 s
F = 2000 N
Answer:
2 N s
Explanation:
Impulse = force * time
= 2000 N * .001 s = 2 N s
A mosquito was accelerating from rest at a rate of 0.15 m/s'. If she flew for 12 meters, what was her final velocity?
The final velocity of the mosquito if it was accelerating from rest at a rate of 0.15 m/s² and flew for 12 meters, is 1.8 m/s
What is velocity?velocity is a term used to describe how quickly and in what direction a point is moving. A point always moves in a direction that is perpendicular to its path; in the case of a circular path, for instance, its direction is always perpendicular to a line connecting the point to the circle's centre (a radius).
The speed at which a point is moving along a path is measured by the magnitude of the velocity.
When a point moves a specific distance along its path in a predetermined amount of time, the distance travelled divided by the time required represents the point's average speed during that time. For instance, the average speed of a train travelling 100 km in two hours is 50 km/h.
The formula for final velocity is
v² - u² = 2as
where v is the final velocity,
u is initial velocity,
a the acceleration and
s the distance
Assuming initial velocity to be 0
Substituting the values
v² - (0)² = 2(0.15)(12)
v = 1.8
So, The final velocity of the mosquito if it was accelerating from rest at a rate of 0.15 m/s² and flew for 12 meters, is 1.8 m/s.
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A hockey stick 1.1 m long completes a swing in 0.15 seconds through a range of 85°. Assume a uniform angular velocity. What is the linear distance moved by the end of the stick? What is the tangential velocity of the end of the stick?
The linear distance and the tangential velocity of the end of the stick are 1.63 m and 10.9 m/s respectively.
What is rotational motion?Rotational motion is the motion of a body around a circular path, in a fixed orbit. The dynamics for rotational motion are entirely analogous to linear or translational dynamics. The equations for rotating objects are similar to the motion equations for linear motion.
Given, the length of the hockey stick, r = 1.1 m
The hockey stick completes one swing in time, t = 0.15 sec
The angle θ = 85° = 1.483 rad
The average angular velocity of the hockey stick,
ω = θ/t = 1.483rad/0.15s = 9.9 rad/s
The linear distance moved by the end of the hockey stick:
L = rθ = 1.1× 1.483 = 1.63 m
The tangential velocity of the end of the hockey stick:
v = rω = 1.1 × 9.9 = 10.9 m/s
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A net force of 20 Newtons acts on and object of mass 5.0 kilograms for 5.0 seconds. What is the magnitude of the impulse?
The impulse of the objects is N-s.
In physics, the term "impulse" is used to characterize or measure the impact of force operating gradually to alter an object's motion. It is often stated in Newton-seconds or kilograms per second and is denoted by the symbol J.
We are given that,
The net force acted on the object = F = 20 N
The mass of the object = m = 5.0kg
The total time taken = t = 5.0s
Therefore, the impulse of the object can be calculated by the formula,
J = F × t
Where, J is the impulse on the object, F is the force on the object , t is the total time taken ,
J = 20N × 5.0sec
J = 100 N-sec
Thus , the total impulse on the object would be 100N-sec.
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A box weighing 51.1 N is pulled horizontally until it slides uniformly over a level floor. If the applied force is 6.30 N, what is the coefficient of friction between the box and the floor?
Given data
*A box weighs is N = 51.1 N
*The applied force is F = 6.30 N
The formula for the coefficient of friction between the box and the floor is given as
[tex]\mu=\frac{F}{N}[/tex]Substitute the known values in the above expression as
[tex]\begin{gathered} \mu=\frac{6.30}{51.1} \\ =0.123 \end{gathered}[/tex]Hence, the coefficient of friction between the box and the floor is 0.123
A stone is thrown upword from the top of a 59.4m high cliff with an upword velocity component of 19.6m/s how long is stone in the air?
The time taken up to which the stone will be in the air is 4.01 seconds.
Here we are dealing with free falling which is referred to as A free falling object is an object that's falling beneath the sole impact of gravity. Any object that's being acted upon as it were by the force of gravity is said to be in a state of free fall. As we are given the velocity which is 19.6 m/s and the height which is 59.4 m.
So the in the first case when the stone travels for a certain distance until its velocity becomes zero.
The formula we are referring to for calculating the maximum height which is v² = u² - 2gh , where v is the final velocity , u is the intial velocity ,g is the acceleration due to gravity and h is the height.
So at v=0
=> h= u²/2g
=> h = (19.6)2/( 2*9.8)= 19.6 m
Whereas when the stone starts to freely fall, so
h = 1/2*gt², here the time taken will be, t = √(2h/g)
where h = sum of the height of the building and the height traveled after the throw
which is 19.6 m+59.4 =79
So , t = √(2h/g)
=>t = √2*(79) /9.8 = 4.01 second
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for equation solve for x given 0
x=2.61 radians
Explanation
[tex]2\cos (x)+\sqrt[]{3}=0[/tex]
Step 1
Let's isolate x
a)
[tex]\begin{gathered} 2\cos (x)+\sqrt[]{3}=0 \\ \text{subtract }\sqrt[]{3}\text{ in both sides} \\ 2\cos (x)+\sqrt[]{3}-\sqrt[]{3}=0-\sqrt[]{3} \\ 2\cos (x)=-\sqrt[]{3} \end{gathered}[/tex]
Step 2
b) now, divide both sides by 2
[tex]\begin{gathered} 2\cos (x)=-\sqrt[]{3} \\ \text{divide both sides by 2} \\ \frac{2\cos(x)}{2}=\frac{-\sqrt[]{3}}{2} \\ \cos (x)=\frac{-\sqrt[]{3}}{2} \\ \end{gathered}[/tex]Step 3
c) finally,Inverse cosine in both sides ( remember we are looking for an angle)
[tex]\begin{gathered} \cos (x)=\frac{-\sqrt[]{3}}{2} \\ \text{ Inverse cosine in both sides} \\ \cos ^{-1}(\cos (x))=\cos ^{-1}(\frac{-\sqrt[]{3}}{2}) \\ x=\cos ^{-1}(\frac{-\sqrt[]{3}}{2}) \\ x=\cos ^{-1}(-0.86) \\ x=2.61\text{ radians} \end{gathered}[/tex]therefore, the answer is
x=2.61 radians
I hope this helps you
Question 11 of 16 If a reaction occurs, what will be the products of the unbalanced reaction below? Zn(s) + HCl(aq) The Activity Series of Elements A. ZnH(s) + Cl2(9) OB. No reaction will occur. O C. HZnCl(s) O D. ZnCl2(s) + H2(9)
When zinc reacts with hydrochloric acid, zinc chloride and hydrogen gas will be produced.
i.e.,
[tex]Zn(s)+\text{HCl(aq)}\rightarrow ZnCl_2(s)+H_2(g)[/tex]Hence the correct answer is option D.
Julie flew 450 miles to Connecticut to visit her sister and then returned three days later. At the end of the trip, what was her displacement and distance traveled?
a. 450 miles; 0 miles
b. 900 miles; 0 miles
c. 0 miles; 900 miles
d. 450 miles, 450 miles
Submission
VIEW GRADE DETAILS
Julie travelled displacement of 0 miles distance of 900 miles. So the correct answer is option (C) 0 miles; 900 miles.
According to question, Julie travelled from Connecticut to visit her sister is 450 miles and return back to Connecticut .
Here, total journey = distance travelled by Julie = 450 + 450 = 900 miles.
Displacement is shortest distance from point one to other, but here Julie return back to her initial point. So, the displacement is zero.
Distance is the total journey travelled between two points from one point to other. Its magnitude cannot be zero. Its S.I. unit is meter.
Displacement is the shortest distance between two points. Its magnitude may be zero. Its S.I. unit is meter.
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. In one day, the temperatures of a desert range from 110°F in the afternoon to 55°F at night. What
is this temperature range on the Kelvin scale?
Answer:
30.5555°K
Can be rounded to 30.56°K
Explanation:
The relationship between °C and °K is
°K = °C + 273.15
To convert °F to °K, first convert °F to °C and then add 273.15
°C = (°F - 32) x 5/9
So combining the two conversions we get
°K = (°F - 32) x 5/9 + 273.15
55°F = (55-32) x 5/9 + 273.15 = 285.9278°K
110°F = (110-32) x 5/9 + 273.15 = 316.4833°K
Temperature range in Kelvin scale
= 316.4833°K - 285.9278°K = 30.5555°K
in order to you need to apply a force of 1700N to the baseball. How much work done on baseball to hit a distance of 110m? How much power is delivered to the baseball the hitter takes 0.35s to swing the bat?
F = 1700N
Work = ?
mass = 0.14kg
distance = 110m
Work = Force * distance = 1700N * 110 m = 187,000J
Power = Work/ time = 187000J/0.35 = 534,285.7 Watts
ㄱ Question 18 of 25 Studying the solar system helps scientists learn about the universe. Why might a scientist use a model to represent the solar system? O A. The actual solar system is too large. B. The actual solar system is too small. C. The actual solar system is too simple. D. The actual solar system moves too slowly. SUBMIT it's A
8. Climbing a mountain, your water bottle falls and hits the ground. If it is moving at 30m/s upon impact. how far did it fall?
Answer:
45.9 m
Explanation:
FIRST:
vf = a t
30 = 9.81 (t) shows t = 3.06 s
THEN:
df = 1/2 a t^2
= 1/2 ( 9.81)(3.06)^2 = 45.9 m
Which of the following statements about treating PTSD is true? a. By focusing on a person’s specific traumatic memory, trauma-focused therapy has been shown to be too narrow in scope to be helpful in treating PTSD. b. The American Psychological Association has issued guidelines to replace psychotropic interventions with trauma-focused therapy. c. The American Psychological Association has issued guidelines to replace cognitive-behavioral therapy with trauma-focused therapy. d. Trauma-focused therapy is gaining support as a first-line treatment showing longer-lasting results than psychotropic medication.
A person with PTSD has trouble bouncing back after experiencing or seeing a traumatic event.
With triggers producing intense emotional and physical reactions as well as memories of the incident, the syndrome can last for months or even years.
Affected individuals may experience nightmares or unwelcome recollections of the trauma, avoid situations that trigger those memories, have heightened reactions, experience anxiety, or experience depression.
Different forms of trauma-focused psychotherapy are utilized in treatment, along with drugs to treat symptoms.
Trauma-focused therapies maintain a constant focus on the trauma and its ensuing repercussions on the patient over the course of therapy. By exposing the patient to reminders of the traumatic incident, this method aids in the correction of incorrect cognitions and the reduction of symptoms.
"Trauma-focused treatment has been demonstrated to be too limited in scope to be effective in treating PTSD since it concentrates on a person's particular traumatic memory."
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How many hours would it take a plane to fly 1,500 miles if it was moving at a constant speed of 300 miles/hour? Include units!
Best answer gets brainliest!
Answer:
5 hours
Explanation:
distance/speed= time
1500/300= 5
what rays gives more heat from the sun?
ANSWER
Vertical rays
EXPLANATION
We have two types of rays from the sun: vertical rays (direct sunlight), which are those rays that hit the surface of Earth vertically, and slanted rays (indirect sunlight), which are those that hit the surface with an angle less than 90° with the surface. We can appreciate both in the following diagram,
As is shown in the diagram, direct sunlight hits the surface in a smaller area than indirect sunlight. This way, the vertical rays are more concentrated than slanted rays and, therefore, give more heat - note that the energy provided by those rays will be concentrated in a smaller area.
Hence, vertical rays give more heat from the sun.
Answer:
slanted rays that is correct
Oil having a density of 924 kg/m? floats onwater. A rectangular block of wood 3.59 cmhigh and with a density of 975 kg/m° floatspartly in the oil and partly in the water. Theoil completely covers the block.How far below the interface between thetwo liquids is the bottom of the block?Answer in units of m.
A diagram of the given problem is the following:
To determine the distance "x" from the interface between the water and the oil of the block we need to add the forces that are acting on the system. We have the following:
Where:
[tex]\begin{gathered} F_b=\text{ force of the block} \\ F_w=\text{ force of the water} \\ F_{o\text{ }}=\text{ force of the oil} \end{gathered}[/tex]Since the system is in equilibrium this means that the total sum of forces adds up to zero:
[tex]F_b-F_w-F_0=0[/tex]Now, the force is the product of the pressure by the area, therefore, we have:
[tex]P_bA-P_wA-P_0A=0[/tex]We can cancel out the area:
[tex]P_b-P_w-P_0=0[/tex]The pressure is the hydrostatic pressure and is given by:
[tex]P=\rho gh[/tex]Where:
[tex]\begin{gathered} \rho=\text{ density} \\ g=\text{ acceleration of gravity} \\ h=\text{ height} \end{gathered}[/tex]Substituting in the equation we get:
[tex]\rho_bgh_b-\rho_wgh_w-\rho_ogh_0=0_{}[/tex]Now, we substitute the values of the heights according to the first diagram:
[tex]\rho_bgh_b-\rho_wgx-\rho_og(h_b-x)=0_{}[/tex]Now, we solve for "x". To do that we will apply the distributive property on the parenthesis:
[tex]\rho_bgh_b-\rho_wgx-\rho_ogh_b+\rho_ogx=0_{}[/tex]Now we associate terms according to the value of the height:
[tex]\rho_bgh_b-\rho_ogh_b-\rho_wgx+\rho_ogx=0_{}[/tex]Now, we take common factors:
[tex](\rho_b-\rho_o)gh_b+(-\rho_w+\rho_o)gx=0_{}[/tex]We can cancel out the gravity:
[tex](\rho_b-\rho_o)h_b+(-\rho_w+\rho_o)x=0_{}[/tex]Now, we bring the terms with the height of the block to the right side:
[tex](-\rho_w+\rho_o)x=-(\rho_b-\rho_o)h_b[/tex]Now, we divide both sides by the factor of "x":
[tex]x=-\frac{(\rho_b-\rho_o)}{(-\rho_w+\rho_o)}h_b[/tex]Now, we plug in the values:
[tex]x=-\frac{(975\frac{kg}{m^3}-924\frac{kg}{m^3})}{(-1000\frac{kg}{m^3}+924\frac{kg}{m^3})}(0.0359m^)[/tex]We converted the height of the block using the following conversion factor:
[tex]100cm=1m[/tex]Now, we solve the operations, we get:
[tex]x=0.024m[/tex]Therefore, the distance between the interface and the bottom of the block is 0.024 meters.
How much work does a 12-V battery do in pushing 2 mC of charge through a circuit containing onelight bulb?
Given data:
[tex]\begin{gathered} V=12\text{ V} \\ Q=2\text{ mC} \end{gathered}[/tex]The work done is given as,
[tex]W=QV[/tex]Putting all known values,
[tex]\begin{gathered} W=2\times10^{-3}\text{ C}\times12\text{ V} \\ =24\text{ mJ} \end{gathered}[/tex]Therefore, 24 mJ of the work is done.