1.) Calculate the mass of a solid gold rectangular bar that has dimensions lwh = 4.30 cm ✕ 14.0 cm ✕ 27.0 cm. (The density of gold is 19.3 ✕ 103 kg/m3.)
kg
2.)A brass ring of diameter 10.00 cm at 17.3°C is heated and slipped over an aluminum rod of diameter 10.01 cm at 17.3°C. Assume the average coefficients of linear expansion are constant.
(a) To what temperature must the combination be cooled to separate the two metals?
(b) What if the aluminum rod were 10.06 cm in diameter?
Answers
Answer:
1) m = 0.3137 kg
2a)T_f = -181.7°C
2b) T_f = -1176.97°C
Explanation:
1) We are given;
Length; l = 4.30 cm = 0.043 m
Width; w = 14.0 cm = 0.014 m
height; h = 27.0 cm = 0.027 m
density of gold; ρ = 19.3 × 10³ kg/m³
Formula for the density is known as;
ρ = mass/volume
Thus;
m =ρV
m = 19.3 × 10³ × (lwh)
m = 19.3 × 10³ × (0.043 × 0.014 × 0.027)
m = 0.3137 kg
2a) We are given;
Diameter of brass; L_br = 10 cm
Diameter of aluminum; L_al = 10.01 cm
Now, to some for change in temperature we will use the formula;
L_f = L_i + αL_i(Δt)
Where α is coefficient of expansion.
Now, for the ring to be removed from the rod, the final diameter of the brass has to be same as the aluminium.
Thus;
L_f(brass) = L_f(aluminium)
From table attached, α_brass ≈ 19 × 10^(-6) /°C
Also, α_aluminium ≈ 24 × 10^(-6) /°C
Thus;
L_f(brass) = 10 + (19 × 10^(-6) × 10 × (Δt))
Similarly,
L_f(aluminium) = 10.01 + (24 × 10^(-6) × 10.01 × (Δt))
Since L_f(brass) = L_f(aluminium), then;
10 + (19 × 10^(-6) × 10 × (Δt)) = 10.01 + (24 × 10^(-6) × 10.01 × (Δt))
Rearranging, we have;
10.01 - 10 = (19 × 10^(-6) × 10 × (Δt)) - (24 × 10^(-6) × 10.01 × (Δt))
0.01 = Δt(-50.24 × 10^(-6))
Δt = 0.01/(-50.24 × 10^(-6))
Δt ≈ -199°C
Thus, temperature at which the combination must be cooled to separate the two metals is;
T_f = T_i + Δt
T_f = 17.3 + (-199)
T_f = -181.7°C
2b) Diameter of aluminum is now;
L_al = 10.06 cm
Thus;
10.06 - 10 = (19 × 10^(-6) × 10 × (Δt)) - (24 × 10^(-6) × 10.01 × (Δt))
0.06 = Δt(-50.24 × 10^(-6))
Δt = 0.06/(-50.24 × 10^(-6))
Δt = -1194.27°C
T_f = 17.3 + (-1194.27)
T_f = -1176.97°C
Related Questions
the pygmy shrew has an average mass of 2.0 g if 49 of these shrew are placed on a spring scale with a spring constant of 24 N/m , what is the springs displacement
Answers
Answer:
Spring's displacement, x = -0.04 meters.
Explanation:
Let the spring's displacement be x.
Given the following data;
Mass of each shrew, m = 2.0 g to kilograms = 2/1000 = 0.002 kg
Number of shrews, n = 49
Spring constant, k = 24 N/m
We know that acceleration due to gravity, g is equal to 9.8 m/s².
To find the spring's displacement;
At equilibrium position:
Fnet = Felastic + Fg = 0
But, Felastic = -kx
Total mass, Mt = nm
Fg = -Mt = -nmg
-kx -nmg = 0
Rearranging, we have;
kx = -nmg
Making x the subject of formula, we have;
[tex] x = \frac {-nmg}{k} [/tex]
Substituting into the formula, we have;
[tex] x = \frac {-49*0.002*9.8}{24} [/tex]
[tex] x = \frac {-0.9604}{24} [/tex]
x = -0.04 m
Therefore, the spring's displacement is -0.04 meters.
What happens when Earth rotates on its axis and how long does it take
Answers
Answer:
You get Day and Night
It takes 24 hour
Answer:
Explanation:
The Earth's orbit makes a circle around the sun. At the same time the Earth orbits around the sun, it also spins.Since the Earth orbits the sun and rotates on its axis at the same time we experience seasons, day and night, and changing shadows throughout the day.It only takes 23 hours, 56 minutes and 4.0916 seconds for the Earth to turn once on its axis.
A ball is attached to one end of a wire, the other end being fastened to the ceiling. The wire is held horizontal, and the ball is released from rest. It swings downward and strikes a block initially at rest on a horizontal frictionless surface. Air resistance is negligible, and the collision is elastic. The masses of the ball and block are, respectively, 1.48 kg and 2.77 kg, and the length of the wire is 1.11 m. Find the velocity of the ball just after the collision.
Answers
Answer: Velocity of the ball just after the collision is -1.414 m/s.
Explanation:
As energy is conserved in a reaction so here, energy before collision will be equal to the energy after collision.
[tex]E_{before} = mgh = E_{after} = \frac{1}{2}mv_{o}^{2}[/tex]
where,
m = mass
g = gravitational energy = [tex]9.8 m/s^{2}[/tex]
h = height or length
[tex]v_{o}[/tex] = initial velocity
Also here, height is the length of wire. Let the height be denoted by 'L'. Therefore,
[tex]\frac{1}{2}mv_{o}^{2} = mgL\\v_{o}^{2} = 2gL\\v_{o} = \sqrt{2gL}\\= \sqrt{2 \times 9.8 m/s^{2} \times 1.11 m}\\= 4.66 m/s[/tex]
Formula used to calculate velocity after the collision is as follows.
[tex]v_{f ball} = v_{o} [\frac{m_{ball} - m_{block}}{m_{ball} + m_{block}}][/tex]
where,
[tex]v_{f ball}[/tex] = final velocity of ball after collision
[tex]m_{ball}[/tex] = masses of ball
[tex]m_{block}[/tex] = masses of block
Substitute the values into above formula as follows.
[tex]v_{f ball} = v_{o} [\frac{m_{ball} - m_{block}}{m_{ball} + m_{block}}]\\= 4.66 m/s [\frac{1.48 kg - 2.77 kg}{1.48 kg + 2.77 kg}]\\= 4.66 m/s \times (-0.303)\\= -1.414 m/s[/tex]
Thus, we can conclude that velocity of the ball just after the collision is -1.414 m/s.
The law of conservation of angular momentum states that if no external force acts on an object, then its angular momentum does not change. true or false
Answers
Answer:
the answer is false.
Explanation:
i took the test and it is false trust me!!!!!!!!!
In a physics lab experiment for the determination of moment of inertia, a team weighs an object and finds a mass of 4.07 kg. They then hang the object on a pivot located 0.155 m from the object's center of mass and set it swinging at a small amplitude. As two of the team members carefully count 113 cycles of oscillation, the third member measures a duration of 247 s. What is the moment of inertia of the object with respect to its center of mass about an axis parallel to the pivot axis
Answers
Answer:
I = 0.65 kgm²
Explanation:
Since the mass is an inertial pendulum, we use the formula for the period, T of an inertial pendulum.
T = 2π√(I/mgh) where I = moment of inertia of object about pivot point, m = mass of object5 = 4.07 kg, g = acceleration due to gravity = 9.8 m/s² and h = distance of center of mass of object from pivot point = 0.155 m.
Given that the team measures 113 cycles of oscillation in 247 s, the period, T = time of oscillations/total number of oscillations = 247 s/113 oscillations = 2.186 s/oscillation
So, T = 2.186 s
We now find I by making it subject of the formula in the equation for T.
So,
T = 2π√(I/mgh)
dividing both sides by 2π, we have
T/2π = √(I/mgh)
squaring both sides, we have
(T/2π)² = [√(I/mgh)]²
T²/4π² = I/mgh
multiplying both sides by mgh, we have
T²mgh/4π² = I
I = T²mgh/4π²
substituting the values of the variables into the equation, we have
I = T²mgh/4π²
I = (2.186 s)² × 4.07 kg × 9.8 m/s² × 0.155 m/4π²
I = 4.778 s² × 4.07 kg × 9.8 m/s² × 0.155 m/4π²
I = 29.539 kgm²/4π²
I = 0.748 kgm²
Now I = I' + mh² (parallel axis theorem) where I' = moment of inertia of object about its center of mass, m = mass of object = 4.07 kg and h = distance of center of mass object from pivot point.
So, I' = I - mh²
Substituting the values of the variables into the equation, we have
I' = I - mh²
I' = 0.748 kgm² - 4.07 kg × (0.155 m)²
I' = 0.748 kgm² - 4.07 kg × 0.02403 m²
I' = 0.748 kgm² - 0.098 kgm²
I = 0.65 kgm²
Application question: In Lancaster county, Pennsylvania, it is common for members of the Amish community to use windmills to pump water from underground to fill a tank for drinking water. The wind causes the turbine blades to spin, rotating a shaft, which is transferred through some gears to operate a pump, which pumps water up from deep below the ground to fill an above ground tank. Identify the energy conversions happening at each step below.
Wind blows______causing the turbine to turn, rotating shaft works pump_____energy.
Motion of water moving up from well______energy.
Water in tank which is positioned 5 feet above the ground level______potential energy.
Answers
Answer:
Wind blows__wind energy ____causing the turbine to turn, rotating shaft works pump__mechanical___energy.
Motion of water moving up from well___kinetic energy___energy.
Water in tank which is positioned 5 feet above the ground level______potential energy
Explanation:
Wind has in it wind energy which is then used to rotate the turbine shaft which is a form of mechanical work and hence possess mechanical energy
Moving water posses kinetic energy and when this water is kept at some height it possess potential energy
What are applications of zeroth law of thermodynamics?
Answers
Answer:
Applications of zeroth law of thermodynamics:
1. When we get very hot food, we wait to make it normal. In this case, hot food exchanges heat with surrounding and brings equilibrium.
2. We keep things in the fridge and those things come equilibrium with fridge temperature.
3. Temperature measurement with a thermometer or another device.
4. In the HVAC system, sensors or thermostats are used to indicate temperature. It always comes in a thermal equilibrium with room temperature.
5. If you and the swimming pool you’re in are at the same temperature, no heat is flowing from you to it or from it to you (although the possibility is there). You’re in thermal equilibrium.
A turbo molecular pump has rapidly rotating blades which hit the molecules of gas in the coating chamber. This collision transfers some momentum to the particles. This process of momentum transfer is more efficient if the average linear velocity of a molecule is less than the linear velocity of the blade tip. Assuming that a particular pump has a linear blade tip velocity of 400 m/s, (a) calculate the ratio of the average room temperature (say, 27 0 C) molecular velocity to blade tip velocity for the gases such as hydrogen, nitrogen and xenon having molar masses of 2, 28 and 131 g/mol, respectively. (b) Is the turbo molecular pump better for pumping heavy element or light element?
Answers
Answer:
heavy molecules are pumped much more efficiently than light molecules. Most gases are heavy enough to be well pumped but it is difficult to pump hydrogen and helium efficiently.
g An airplane is flying through a thundercloud at a height of 1500 m. (This is a very dangerous thing to do because of updrafts, turbulence, and the possibility of electric discharge.) If a charge concentration of 25.0 C is above the plane at a height of 3000 m within the cloud and a charge concentration of -40.0 C is at height 850 m, what is the electric field at the aircraft
Answers
Answer:
[tex]523269.9\ \text{N/m}[/tex]
Explanation:
q = Charge
r = Distance
[tex]q_1=25\ \text{C}[/tex]
[tex]r_1=3000\ \text{m}[/tex]
[tex]q_2=40\ \text{C}[/tex]
[tex]r_2=850\ \text{m}[/tex]
The electric field is given by
[tex]E=E_1+E_1\\\Rightarrow E=k(\dfrac{q_1}{r_1^2}+\dfrac{q_2}{r_2^2})\\\Rightarrow E=9\times 10^9\times (\dfrac{25}{3000^2}+\dfrac{40}{850^2})\\\Rightarrow E=523269.9\ \text{N/m}[/tex]
The electric field at the aircraft is [tex]523269.9\ \text{N/m}[/tex]
You and a friend are playing with a Coke can that you froze so it's solid to demonstrate some ideas of Rotational Physics. First, though, you want to calculate the Rotational Kinetic Energy of the can as it rolls down a sidewalk without slipping. This means it has both linear kinetic energy and rotational kinetic energy. [The freezing only matters because if there is liquid inside, the calculation for the Moment of inertia becomes more complicated]. A Coke can can be modeled as a solid cylinder rotating about its axis through the center of the cylinder. This can has a mass of 0.33 kg and a radius of 3.20 cm. You'll need to look up the equation for the Moment of Inertia in your textbook. It is rotating with a linear velocity of 6.00 meters / second in the counter-clockwise (or positive) direction. You can use this to determine the angular velocity of the can (since it is rolling without slipping). What is the Total Kinetic Energy of the Coke can
Answers
Answer:
K_{total} = 8.91 J
Explanation:
In this exercise you are asked to find the kinetic energy of the can of coca-cola
K_total = K_ {Translation} + K_ {rotation}
the translational kinetic energy is
K_ {translation} = ½ m v²
the kinetic energy of rotation is
K_ {rotation} = ½ I w²
The moment of inertia of a cylinder is
I = ½ m r²
we substitute
K_ {total} = ½ m v² + ½ (½ m r²) w²
angular and linear velocity are related
v = w r
we substitute
K_ {total} = ½ m v² + ¼ m r² v² / r²
K_ {total} = m v² (½ + ¼)
K_ {total} = ¾ m v²
let's calculate
K_ {total} = ¾ 0.33 6.00²
K_{total} = 8.91 J
To determine the muzzle velocity of a bullet fired from a rifle, you shoot the 2.47-g bullet into a 2.43-kg wooden block. The block is suspended by wires from the ceiling and is initially at rest. After the bullet is embedded in the block, the block swings up to a maximum height of 0.295 cm above its initial position. What is the velocity of the bullet on leaving the gun's barrel
Answers
Answer:
The velocity of the bullet on leaving the gun's barrel is 236.36 m/s.
Explanation:
Given;
mass of the bullet, m₁ = 2.47 g = 0.00247 kg
mass of the wooden block, m₂ = 2.43 kg
initial velocity of the wooden block, u₂ = 0
height reached by the bullet-block system after collision = 0.295 cm = 0.00295 m
let the initial velocity of the bullet on leaving the gun's barrel = v₁
let final velocity of the bullet-wooden block system after collision = v₂
Apply the principle of conservation of linear momentum;
Total initial momentum = Total final momentum
m₁v₁ + m₂u₂ = v₂(m₁ + m₂)
0.00247v₁ + 2.43 x 0 = v₂(2.43 + 0.00247)
0.00247v₁ = 2.4325v₂ -------(1)
The kinetic energy of the bullet-block system after collision;
K.E = ¹/₂(m₁ + m₂)v₂²
K.E = ¹/₂ (2.4325)v₂²
The potential energy of the bullet-block system after collision;
P.E = mgh
P.E = (2.4325)(9.8)(0.00295)
P.E = 0.07032
Apply the principle of conservation of mechanical energy;
K.E = P.E
¹/₂ (2.4325)v₂² = 0.07032
1.21625 v₂² = 0.07032
v₂² = 0.07032 / 1.21625
v₂² = 0.0578
v₂ = √0.0578
v₂ = 0.24 m/s
Substitute v₂ in equation (1), to obtain the initial velocity of the bullet;
0.00247v₁ = 2.4325v₂
0.00247v₁ = 2.4325 (0.24)
0.00247v₁ = 0.5838
v₁ = 0.5838 / 0.00247
v₁ = 236.36 m/s
Therefore, the velocity of the bullet on leaving the gun's barrel is 236.36 m/s.
An object changes velocity from 100m/s
to 76m/s in 6 seconds. If it has a mass of
20kg, what is the net force?
Answers
Answer:
1-1=0
Explanation:
ahriqqwertyuioo
If the acceleration of the body is towards the center, what is the direction of the unbalanced force ? Using a complete sentence , describe the direction of the net force that causes the body to travel in a circle at a constant speed.
Answers
Accelerating objects are changing their velocity. Velocity is often thought of as an object's speed with a direction. Thus, objects which are accelerating are either changing their speed or changing their direction. They are either speeding up, slowing down or changing directions. Changing the velocity in any one of these three ways would be an example of an accelerated motion.
An ideal horizontal spring-mass system has a mass of 1.0 kg and a spring with constant 78 N/m. It oscillates with a period of 0.71 seconds. When this same spring-mass system oscillates vertically instead, the period is _______ seconds. Enter 2 significant figures (a total of three digits) and use g = 10.0 m/s2 if necessary.
Answers
Answer:
T = 0.71 seconds
Explanation:
Given data:
mass m = 1Kg, spring constant K = 78 N/m, time period of oscillation T = 0.71 seconds.
We have to calculate time period when this same spring-mass system oscillates vertically.
As we know
[tex]T = 2\pi \sqrt{\frac{m}{K} }[/tex]
This relation of time period is true under every orientation of the spring-mass system, whether horizontal, vertical, angled or inclined. Therefore, time period of the same spring-mass system oscillating vertically too remains the same.
Therefore, T = 0.71 seconds
What is the chemical formula for the molecule modeled?
Answers
Answer:
What is the chemical fórmula For the molecule modeled?
Explanation:
C6H12O2
The unit of work done is called derived unit why
Answers
Question 2 of 20 :
Select the best answer for the question.
2. Which of the following is considered to be a vector?
A. Velocity
B. Time
C. Temperature
D. Mass
Mark for review (Will be highlighted on the review page)
Answers
The answer is A. velocity .
Velocity is a vector quantity because it need magnitude as well as direction to be defined.
What are the similarities between a resultant force equilibrant force?
Answers
Answer:
Explanation:
Resultant is a single force that can replace the effect of a number of forces. "Equilibrant" is a force that is exactly opposite to a resultant. Equilibrant and resultant have equal magnitudes but opposite directions.
Can someone please help me on this?
Answers
An object is pushed with a force of 400 N for 20 meters; what is the work done on the object? Solve using W=F*d
Answers
Answer:
800joules
Explanation:
work is measured in joules
A rabbit dashes across a field in a zig-zag pattern trying to outrun a fox. If the rabbit’s average is speed is 9.8 m/s it reaches the hole in 8.5 s what is the total distance it ran?
Answers
Answer:
83.3 m
Explanation:
From the question,
Applying on of the formula of velocity
V = d/t.................. Equation 1
Where V = average velocity, d = distance, t = time.
make d the subject of the equation
d = V×t................. Equation 2
Given: V = 9.8 m/s, t = 8.5 s
Substitute these values into equation 2
d = 9.8×8.5
d = 83.3 m
Hence the total distance covered by the rabbit is 83.3 m
whem completing an emergency Roaside stop,it is necessary to put on your parking brake
A. True
B. False
Answers
Answer:
trueeeeeeee..........mmmm...........
When two substances that cannot dissolve each other are mixed, a ________ mixture is formed
Answers
Answer: hetero i think i dont know
Explanation:
Answer:
When two substances that cannot dissolve each other are mixed, a mixture is formed.
i hope this helps a little bit.
Describing a Wave
What does a wave carry?
Answers
Answer:
Waves carry energy from one place to another.
Explanation:
Because waves carry energy, some waves are used for communication, eg radio and television waves and mobile telephone signals.
A doorknob is a type of wheel and axle. In a doorknob, the door handle acts as the wheel. The handle is connected to a cylinder, called a spindle, which acts as the axle. When the handle turns, the spindle turns in the same direction. The spindle is located inside the handle and pulls the latch back and forth, allowing the door to open.
In the doorknob shown above, when the handle is rotated a distance of 84 millimeters, the spindle is rotated a distance of 14 millimeters. What is the mechanical advantage of this doorknob?
A. 504
B. 6
C. 84
D. 14
Answers
Can someone take there time and answer this :)
Answers
Answer: I think B.)
Explanation:
Carbon-14 is the typical radioisotope used to date materials; however, it has a limitation to 40,000 years. A scientist who wants to date materials older than 40,000 years would most likely use which radioisotope?
Answers
Answer:
the decay of uranium ending in lead, of potassium (40K) that becomes argon, the decay of rubidium
Explanation:
For the radioactive dating process, a material is needed that has a known average life time and that we can know the amount of material at a given moment,
In the case of carbon 14 (14C), living beings stop capturing it from the air and plants when they die, so knowing the amount they currently have, it is possible to calculate the time in which they stopped absorbing, but the life time average is 5730 years, the maximum time that can be used is up to about 10 average visa times
To analyze extra samples have high half-life times
* the decay of uranium ending in lead
* the decay of potassium (40K) that becomes argon T1 / 2 = 1,251 10⁹ years
* the decay of rubidium (87Ru) which becomes strontium T1 / 2 = 4.92 10¹⁰ years
(a) A simple pendulum oscillates back and forth on a space vehicle. An astronaut on the space vehicle measures the period of the pendulum to be 22.58 seconds (it is a big pendulum). A passing observer in another space ship measures the period to be 31.87 seconds. Determine the relative velocity between the two observers. Show all calculation steps.
Answers
Answer:
0.706
Explanation:
Since the other astronaut measures a longer time, this is a time dilation problem. So, our equation for time dilation is given by
T = T₀/√(1 - β²) where T = period on passing space ship = 31.87 s, T₀ = period on other space vehicle = proper time = 22.58 s and β = relative velocity of between the two observers.
T = T₀/√(1 - β²)
√(1 - β²) = T₀/T
squaring both sides, we have
[√(1 - β²)]² = (T₀/T)²
1 - β² = (T₀/T)²
β² = 1 - (T₀/T)²
taking square root of both sides, we have
√β² = √[1 - (T₀/T)²]
β = √[1 - (T₀/T)²]
substituting the values of the variables into the equation, we have
β = √[1 - (22.58 s/31.87 s)²]
β = √[1 - (0.7085)²]
β = √[1 - 0.502]
β = √0.498
β = 0.706
describe brefly how you can charge a body
Answers
Answer:
charge or change?
Explanation:
I'll write my answer in the comments when you reply
A geologist notices that a river is eroding its valley at a constant rate. Knowing the height of the valley walls, how could the geologist figure out when the river started carving the valley?
A.
Count growth rings of trees growing on the valley floor.
B.
Divide the height of the valley walls by the rate of erosion.
C.
Fill up the river valley with rocks, and time how long it takes the rocks to wash out.
D.
Sit and observe the river for a few hours until the valley walls double in height.
Answers
Answer:
B.
Divide the height of the valley walls by the rate of erosion.
Explanation:
There is a relationship between the rate of erosion and the hieght at which it is eroded according to Newton's law of motion. In the case of the scenario above, the best way to determine the time the river started carving the valley would be the division of the height of the valley walls by the rate of erosion.
