Considering that the coefficient of friction between block and surface is 0.650, the speed of the clay immediately before impact is approximately 25.4 m/s.
To solve this problem, we can use the conservation of momentum and the work-energy principle. Let's denote the mass of clay as mc (11.0 g), the mass of the wooden block as mb (90 g), and the initial velocity of the clay as vc. After the impact, the clay and block will stick together and have a combined mass (mc + mb) and a common velocity (v).
First, let's use the conservation of momentum:
mc * vc = (mc + mb) * v
Now, we need to find v. To do this, we can use the work-energy principle. The work done by friction (Wf) equals the change in kinetic energy (ΔK):
Wf = μ * m_total * g * d = ΔK = 0.5 * m_total * (v² - 0)
where μ is the coefficient of friction (0.650), g is the acceleration due to gravity (9.81 m/s^2), and d is the distance the block slides (7.50 m). Note that we need to convert the masses from grams to kilograms:
mc = 0.011 kg, mb = 0.090 kg, m_total = mc + mb = 0.101 kg
Now, solve for v:
0.650 * 0.101 * 9.81 * 7.50 = 0.5 * 0.101 * v²
v ≈ 2.74 m/s
Finally, substitute this value back into the conservation of momentum equation and solve for vc:
0.011 * vc = (0.101) * 2.74
vc ≈ 25.4 m/s
So, the speed of the clay immediately before impact was approximately 25.4 m/s.
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1. you examine a test instrument commonly used to measure insulation resistance on equipment rated 600v or lower. the output of the test instrument is 1000 volts and the lead connections are?
The test instrument commonly used to measure insulation resistance on equipment rated 600V or lower has an output of 1000 volts and uses lead connections.
The test instrument being described is likely a megohmmeter or insulation resistance tester. These instruments are used to measure the insulation resistance of electrical equipment, which is important for ensuring the safety and proper functioning of the equipment.
The output voltage of 1000 volts is necessary to generate enough current through the insulation to accurately measure its resistance. The lead connections are used to connect the instrument to the equipment being tested, and they typically consist of two probes with insulated handles that are connected to the instrument by wires. The leads are carefully designed to minimize leakage current and ensure accurate measurements. Overall, these instruments play a crucial role in maintaining electrical safety and reliability.
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a descending elevator moves downward at 5 m/s. 10 m from the ground floor, it begins decelerating to come to rest when it reaches that floor. if the mass of the elevator car is 1000 kg and the mass of its occupants is 500 kg, what net upward force acted on the elevator during its deceleration?
A net upward force of 1875 N acted on the elevator during its deceleration.
The net upward force on the descending elevator during deceleration, and to determine its acceleration kinematic equation is used:
[tex]v^{2}[/tex] =[tex]u^{2}[/tex] + 2as
where v is the final velocity (0 m/s), u is the initial velocity (-5 m/s, negative because it's downward), a is the acceleration, and s is the distance (10 m), Here, acceleration
0 =[tex]-5^{2}[/tex] + 2a(10)
0 = 25 - 20a
20a = 25
a = 1.25 [tex]m/s^{2}[/tex] (upward, so it's positive)
Calculate the net upward force (F_net) using Newton's second law, F_net = m_total * a. The total mass (m_total) of the elevator and occupants is 1000 kg + 500 kg = 1500 kg. Therefore, the net upward force is:
F_net = 1500 kg * 1.25 [tex]m/s^{2}[/tex]
F_net = 1875 N
So, the net upward force that acted on the elevator during its deceleration is 1875 N.
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Which of these objects is an insulator?
b. copper coin
d. steel fork
a. gold ring
C. glass rod
Answer:
C
Explanation:
Glass is one of the objects included in an insular so glass rod will be the final ans.
A car with a mass of 1000 kg is traveling east at 4 m/s. Another car with a mass of 500 kg is traveling west at a speed of 3 m/s. The two cars collide. After the collision, the 1000 kg car has a velocity of 1 m/s east. What is the velocity of the 500 kg car after the collision?
Answer: the velocity of the 500 kg car after the collision is 3 m/s to the east.
Explanation:
Initial momentum = (mass of car 1 x velocity of car 1) + (mass of car 2 x velocity of car 2)
Initial momentum = (1000 kg x 4 m/s) + (500 kg x -3 m/s) (Note that we use a negative velocity for car 2 because it is traveling in the opposite direction)
Initial momentum = 4000 kg m/s - 1500 kg m/s = 2500 kg m/s
After the collision, the total mass and total momentum of the system remain the same.
Final momentum = (mass of car 1 x velocity of car 1) + (mass of car 2 x velocity of car 2)
Final momentum = (1000 kg x 1 m/s) + (500 kg x v) (where v is the velocity of the 500 kg car after the collision)
Final momentum = 1000 kg m/s + 500v
Since the total momentum is conserved, we can set the initial momentum equal to the final momentum:
Initial momentum = Final momentum
2500 kg m/s = 1000 kg m/s + 500v
Solving for v, we get:
v = (2500 kg m/s - 1000 kg m/s) / 500 kg
v = 3 m/s
??
Forces and Motion:Question 5 A force of 20 N acts upon a 5 kg block. Calculate the acceleration of the object
The acceleration of the 5 Kg object, given that a force of 20 N acts upon it, is 4 m/s²
How do i determine the acceleration of the objectFirst, we shall list out the given parameters from the question. This is shown below:
Force acting on object (F) = 20 NMass of object (m) = 5 KgAcceleration of object (a) =?The acceleration of the object can be obtained as illustrated below
Force = mass × acceleration
Divide both side by mass
Acceleration = Force / mass
Inputting the value of force and mass, we have:
Acceleration = 20 / 5
Acceleration = 4 m/s²
Thus, the acceleration of the object is 4 m/s²
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A student on a piano stool rotates freely with an angular speed of 3. 05 rev/s. The student holds a 1. 05kg mass in each outstretched arm 0. 789m from the axis of rotation. The combined momment of inertia of the student and the stool, ignoring the two masses, is 5. 33kg*m^2, a value that remains constant. As the student pulls his arms inward, his angular speed increases to 3. 54 rev/s. A) How far are the masses from the axis of rotation at this time considering the masses to be points
b) calculate the initial and final kinetic energies of the system
a) The distance of the masses from the axis of rotation is 0.620 m.
b) The initial kinetic energy of the system is 1.680 x 10² J and the final kinetic energy of the system is 2.020 x 10² J.
a) According to the law of conservation of angular momentum, the initial angular momentum of the system is equal to the final angular momentum. Therefore, (I1ω1) = (I2ω2), where I1 is the initial moment of inertia, ω1 is the initial angular velocity, I2 is the final moment of inertia, and ω2 is the final angular velocity.
Since the moment of inertia of the two masses is (2mr²), where m is the mass of each mass and r is the distance of each mass from the axis of rotation, the final moment of inertia is (5.33 + 2m(0.620)²) kg*m². Solving for r, we get r = 0.620 m.
b) The initial kinetic energy of the system is (1/2)I1ω1² + (1/2)mv1², where m is the mass of each mass and v1 is the initial tangential velocity. The final kinetic energy of the system is (1/2)I2ω2² + (1/2)mv2², where v2 is the final tangential velocity.
Since the work done by the student in pulling the masses inward is equal to the change in kinetic energy of the system, we have W = (1/2)mv2² - (1/2)mv1². Solving for the initial and final kinetic energies, we get KE1 = 1.680 x 10² J and KE2 = 2.020 x 10² J.
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when a high voltage is applied to a low-pressure gas, causing it to glow, it will emit what type of spectrum? a. li
When a high voltage is applied to a low-pressure gas and it starts to glow, it will emit an emission line spectrum.
This spectrum consists of bright, narrow lines at specific wavelengths, which are characteristic of the element or molecules in the gas. This is due to the electrons in the gas being excited to higher energy levels and then falling back down to lower energy levels, emitting photons of light at specific wavelengths corresponding to the energy differences between the levels. The resulting emission spectrum can be used to identify the elements or molecules present in the gas.
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a 1 meter long solenoid with 200 turns carries 2a of current . calculate the magnetic field on axis.
The magnetic field on the axis of the solenoid is 5.03 × 10⁻⁴ T.
The magnetic field on the axis of a solenoid can be calculated using the formula:
B = μ₀ * n * I
Where B denotes the intensity of the magnetic field, 0 denotes the permeability of empty space, n denotes the number of turns per unit length, and I is the current flowing through the solenoid.
In this case, the solenoid is 1 meter long and has 200 turns, so n = 200 turns / 1 meter = 200 turns/meter. The solenoid is delivering 2A of current.
The value of μ₀ is a constant, equal to 4π × 10⁻⁷ T·m/A
When we enter these values into the formula, we get:
B = μ₀ * n * I
= 4π × 10⁻⁷ T·m/A * 200 turns/m * 2A
= 5.03 × 10⁻⁴ T
Therefore, the magnetic field on the axis of the solenoid is 5.03 × 10⁻⁴ T.
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magnetic field on the axis of the solenoid is approximately 0.005 T
Solution - Hi! To calculate the magnetic field on the axis of a solenoid, you can use the formula:
Magnetic field (B) = μ₀ * n * I . (applicable for ideal long solenoid)
where μ₀ is the permeability of free space (approximately 4π x 10^-7 Tm/A), n is the number of turns per unit length, and I is the current.
In your case, the solenoid is 1 meter long with 200 turns and carries a 2 A current. To find n, divide the number of turns by the length:
n = 200 turns / 1 m = 200 turns/m
Now, plug the values into the formula:
B = (4π x 10^-7 Tm/A) * (200 turns/m) * (2 A)
B ≈ 0.005 T
The magnetic field on the axis of the solenoid is approximately 0.005 T (Tesla).
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a motorcycle passing by your apartment emits a sound with an intensity level of 70 db. if two identical motorcycles passed by together, what would be the intensity level of the resulting sound?
The intensity level of the resulting sound is approximately 73 dB, the correct option is (e)
To calculate the intensity level of the resulting sound, we use the formula:
L = 10 log(I ÷ I0)
where L is the intensity level in decibels, I is the intensity of the sound wave in watts per square meter, and I0 is the reference intensity, which is equal to 1 x 10⁻¹² watts per square meter.
Since the motorcycles emit identical sound waves, the intensity of each wave is the same. We can calculate the intensity of a single motorcycle's sound wave using the formula:
I = [tex](10^{L/10} )[/tex] x I0
where L is the intensity level of the sound wave in decibels. Substituting L = 70 dB and I0 = 1 x 10⁻¹² watts per square meter, we get:
I = (10⁷) x 1 x 10⁻¹²
= 1 x 10⁻⁵ watts per square meter
To calculate the intensity level of the resulting sound, we use the formula:
L = 10 log(2I ÷ I0)
where 2I is the intensity of the sound waves produced by two identical motorcycles. Substituting I = 1 x 10⁻⁵ watts per square meter and I0 = 1 x 10⁻¹² watts per square meter, we get:
2I = 2 x 1 x 10⁻⁵
= 2 x 10⁻⁵ watts per square meter
L = 10 log(2 x 10⁻⁵ ÷ 1 x 10⁻¹²)
= 10 log(2 x 10⁷)
= 10 (7.301)
= 73.01 dB
Therefore, the correct option is (e)
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The complete question is:
A motorcycle passing by your apartment emits a sound with an intensity level of 70 dB. If two identical motorcycles passed by together, what would be the intensity level of the resulting sound?
a. 80 dB
b. 140 dB
c. 103 dB
d. 70 dB
e. 73 dB
the fundamental, resonant wavelength of a pipe open at both ends that is 1 m long and 0.1 m in diameter is:
The fundamental resonant wavelength of a 1-meter long pipe open at both ends is 2 meters.
To find the fundamental resonant wavelength of a pipe open at both ends, we can use the formula:
Wavelength = 2 * Length of the pipe / Harmonic number
Since you're looking for the fundamental resonant wavelength, the harmonic number (n) is 1.
Given that the length of the pipe (L) is 1 meter:
Wavelength = 2 * 1 / 1
Wavelength = 2 meters
So, the fundamental resonant wavelength of a 1-meter long pipe open at both ends is 2 meters. The diameter of the pipe (0.1 meters) doesn't affect the wavelength in this case.
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a student is designing an investigation of the distribution of charges in conductors. she will use two conducting spheres mounted on insulating stands in the investigation. the conducting spheres are shown. the student wants to separate the charges of the spheres as shown. what should the student do in her investigation to produce these results? responses she should place a positively charged rod near the left sphere. she should place a positively charged rod near the left sphere. she should place two positively charged rods near each sphere. she should place two positively charged rods near each sphere. she should place two negatively charged rods near each sphere. she should place two negatively charged rods near each sphere. she should place a negatively charged rod near the left sphere.
The correct response would be: "She should place a positively charged rod near the left sphere."
What is Charges?
In physics, charges refer to the fundamental property of matter that gives rise to electric interactions. Charges can be positive or negative, and they are responsible for the phenomenon of electric force, which is the force that acts between charged objects.
By bringing a positively charged rod near the left sphere, it will induce a redistribution of charges in the conductive sphere. The positive charges in the left sphere will repel the positive charges in the rod, causing the electrons in the left sphere to move away from the rod and distribute themselves more evenly across the surface of the sphere, leaving the side facing the rod with a net positive charge.
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imagne that your friends cat was cloned. would it be the same
If my friend's cat was cloned, the resulting cat would be genetically identical to the original cat. However, this does not mean that the cloned cat would be exactly the same as the original cat in terms of its behavior, personality, or even appearance.
Environmental factors and experiences can have a significant impact on an animal's development and behavior, so even genetically identical cats can have differences in their behavior and personality. Additionally, the cloning process itself can introduce some genetic and epigenetic changes that may affect the cloned cat's development and behavior. Therefore, while the cloned cat may look and behave similarly to the original cat, it would not be exactly the same.
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what planet can come closest to the earth in its orbit and look brightest in our skies? a. none of the above b. venus c. mercury d. jupiter e. mars
Answer: B Venus
Explanation:
what is the wavelength of a radio photon from an am radio station that broadcasts at 1270 kilohertz? express your answer to three significant figures and include the appropriate units.
The wavelength of a radio photon from an AM radio station broadcasting at 1270 kilohertz is 236 meters.
To find the wavelength of a radio photon from an AM radio station broadcasting at 1270 kilohertz, we can use the formula:
wavelength (λ) = speed of light (c) / frequency (f)
1. First, we need to convert the frequency from kilohertz to hertz:
1270 kilohertz = 1270 * 10³ hertz = 1,270,000 hertz
2. Next, we will use the speed of light, which is approximately 3.00 * 10⁸ meters per second (m/s).
3. Now, we can plug in the values into the formula:
wavelength (λ) = (3.00 * 10⁸ m/s) / (1,270,000 Hz)
4. Calculate the wavelength:
λ ≈ 236.22 meters
5. Finally, express the answer to three significant figures and include the appropriate units:
λ ≈ 236 meters
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PLEASE ANSWER ASAP
1. How many atoms are present in 8.500 mole of chlorine atoms?
2. Determine the mass (g) of 15.50 mole of oxygen.
3. Determine the number of moles of helium in 1.953 x 108 g of helium.
4. Calculate the number of atoms in 147.82 g of sulfur.
5. Determine the molar mass of Co.
6. Determine the formula mass of Ca3(PO4)2.
IT WOULD BE HELPFUL
The number of atoms in 147.82 g of sulphur is 2.772 x 10²⁴. In 1.953 x 10⁸ g of helium, there are 4.883 × 10⁷ moles of helium. 15.50 moles of oxygen weigh 248 g. Calcium phosphate's formula mass would be 310.18 g/mol.
How many atoms make up 1 gramme?The quantity of atoms or molecules per gramme of atomic weight is known as Avogadro's number, which is 6.022 × 10²³/mole. One mole of hydrogen comprises 6.022 × 10²³ hydrogen atoms for one gramme of hydrogen with an atomic weight of one gramme.
The Avogadro's number states that 1 mole of any substance contains 6.022 x 10²³ particles. Therefore, 8.500 moles of chlorine atoms would contain:
8.500 moles * 6.022 x 10²³ atoms/mole = 5.1167 x 10²⁴ atoms of chlorine.
The molar mass of oxygen is 16.00 g/mol. Therefore, 15.50 moles of oxygen would have a mass of:
15.50 moles * 16.00 g/mol = 248 g
So the mass of 15.50 mole of oxygen is 248 g.
The molar mass of helium is 4.00 g/mol. Therefore, 1.953 x 10⁸ g of helium would contain:
1.953 x 10⁸ g / 4.00 g/mol = 4.883 x 10⁷ moles of helium.
The molar mass of sulfur is 32.06 g/mol. Therefore, 147.82 g of sulfur would contain:
147.82 g / 32.06 g/mol = 4.6055 moles of sulfur. Therefore, the formula mass of Calcium phosphate would be:
(340.08 g/mol) + (230.97 g/mol) + (8*16.00 g/mol) = 310.18 g/mol.
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a resistance r and a 3.2 h inductance are in series across a 60-hz ac voltage. the voltage across the resistor is 29 v and the voltage across the inductor is 33 v. assume that all voltages in this problem are rms voltages. (a) what is the resistance r?
The Resistance r is 56.97 ohms
To solve this problem, we can use Ohm's Law and the equation for the voltage across an inductor in an AC circuit.
First, let's find the current in the circuit. We know that the voltage across the series combination of the resistor and inductor is the sum of the voltage across the resistor (29 V) and the voltage across the inductor (33 V):
V_total = V_R + V_L
V_total = IR + IXL
where I is the current in the circuit, X_L is the inductive reactance (which depends on the frequency and inductance of the inductor), and R is the resistance.
Since the circuit is operating at a frequency of 60 Hz and the inductance is 3.2 H, we can find the inductive reactance using the formula:
X_L = 2πfL
X_L = 2π(60)(3.2)
X_L ≈ 120.96 Ω
Now we can solve the current:
V_total = IR + IXL
62 = I(R + 120.96)
I ≈ 0.509 A
Next, we can use Ohm's Law to solve for the resistance:
V_R = IR
29 = (0.509)R
R ≈ 56.97 Ω
Therefore, the resistance in the circuit is approximately 56.97 ohms.
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what is the cost of operating a 64.21-watt freezer for a month if the cost of electricity is $ 0.02 per kwh? assume we take a month as 30 days.
The operating cost is approximately $0.93.
How much does it cost to run a 64.21-watt freezer for 30 days, given that electricity costs $0.02 per kilowatt-hour (kWh)?First, we need to calculate the energy consumption of the freezer in kilowatt-hours (kWh) per month. We can use the following formula:
[tex]Energy (kWh) = Power (W) x Time (h) / 1000[/tex]
where the power of the freezer is 64.21 watts, and the time it runs is 30 days x 24 hours/day = 720 hours.
[tex]Energy (kWh) = 64.21 W x 720 h / 1000 = 46.3152 kWh[/tex]
Therefore, the energy consumption of the freezer in one month is 46.3152 kWh.
To find the cost of operating the freezer for a month, we can multiply the energy consumption by the cost per kWh:
[tex]Cost = Energy (kWh) x Cost per kWh[/tex]
[tex]Cost = 46.3152 kWh x $0.02/kWh = $0.926304[/tex]
Therefore, the cost of operating a 64.21-watt freezer for a month, assuming the cost of electricity is $0.02 per kWh, is approximately $0.93.
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two objects collide under conditions where total momentum is conserved. is the momentum conserved for each object?
Yes, the momentum is conserved for each object in a collision where total momentum is conserved.
This means that the momentum of each individual object before the collision will equal the momentum of that same object after the collision, but in the opposite direction. This conservation of momentum is a fundamental law of physics, stating that in a closed system, the total momentum remains constant unless acted upon by an external force. Yes, each object in the impact maintains its momentum. This is due to the law of conservation of momentum, which stipulates that the overall momentum of a closed system—in this case, the collision of the two objects—remains constant before and after the collision. Every object must conserve its momentum because it is a component of the closed system and is part of the overall momentum. As a result, in the collision, each object's momentum is preserved.
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Yes, the momentum is conserved for each object in a collision where total momentum is conserved.
This means that the momentum of each individual object before the collision will equal the momentum of that same object after the collision, but in the opposite direction. This conservation of momentum is a fundamental law of physics, stating that in a closed system, the total momentum remains constant unless acted upon by an external force. Yes, each object in the impact maintains its momentum
. This is due to the law of conservation of momentum, which stipulates that the overall momentum of a closed system—in this case, the collision of the two objects—remains constant before and after the collision. Every object must conserve its momentum because it is a component of the closed system and is part of the overall momentum. As a result, in the collision, each object's momentum is preserved.
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four weightlifters a through d enter a competition. the mass and distance that each lifts are shown in the table. which weightlifter does the least work? responses
From these calculations, we can see that weightlifter C does 3 x 10^3 J of work, as their work value is the closest to this value. Therefore, weightlifter C does 3 x 10^3 J of work.
Add gravity (9.81) to the weight, then multiply by the distance:
A) [tex]100 * 9.81 * 2.25 = 2207.25 = 2.2 \times 10^3[/tex]
B) [tex]150 * 9.81 * 1.76 = 2589.84 = 2.6 \times 10^3[/tex]
C) [tex]200 * 9.81 * 1.50 = 2943 = 2.9 \times 10^3[/tex] ( Can round to [tex]3.0 \times 10^3[/tex])
D) [tex]275 * 9.81 * 1.25 = 3372.18 = 3.4 \times 10^3[/tex]
Weightlifters are athletes who take part in the weightlifting sport, which entails performing precise movements with a barbell loaded with weights to ascertain the highest weight that can be lifted. The snatch and the clean are the primary competitions in weightlifting, which has been a part of the Olympic Games since 1896.
Weightlifters require strength, power, and explosive energy to perform the lifts correctly and maximize their potential. They often train with heavy weights to build their muscles and improve their technique. Weightlifting competitions are categorized by weight class, with athletes competing against others in their respective weight divisions. Weightlifting is a difficult and rewarding sport that calls for commitment, self-control, and perseverance to excel.
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Complete Question:-
Four weightlifters A through D enter a competition. Their mass and distance that each lifts are shown in the table.
Weighlifter Mass(kg) Distance(m)
A 100.0 2.25
B 150.0 1.76
C 200 1.50
D 275 1.25
Which weightlifter does 3 x 10^3 J of work?
Ben and Jerry are standing on an ice rink discussing who has the best skates. Ben says he will go faster due to his superior skates and gives Jerry a shove to prove his point. Ben has a mass of 150 kg and a velocity of 11 m/s after he pushed Jerry. What was Jerry's mass if he has a velocity of 15 m/s>
Therefore, Jerry's mass is approximately 118.4 kg.
What does mass mean in plain terms?It is the most fundamental characteristic of matter and one of the fundamental quantities in physics. Mass is a term used to describe how much matter is there in a body. (kg). The mass of a body is constant over time.
The following is the equation for momentum conservation:
m1v1 + m2v2 = m1v1' + m2v2'
We are aware of Ben's 150 kg mass and 11 m/s post-push velocity. Additionally, we are aware of Jerry's post-push velocity, which is 15 m/s. To find Jerry's mass, we can rewrite the equation as follows:
m2 = (m1v1 + m1v1' - m2v2') / v2
Substituting in the known values:
m2 = (150 kg * 0 m/s + 150 kg * 11 m/s - m2 * 15 m/s) / 15 m/s
Simplifying and solving for m2:
m2 = (150 kg * 11 m/s) / (15 m/s + 1) ≈ 118.4 kg
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what focal length of corrective lens should this person use to make the far point distance infinite?
To determine the focal length of a corrective lens required to make the far point distance infinite, we need to follow these steps:
1) Measure the person's far point distance: This can be done by having the person read letters on an eye chart or by using a refractometer.
Let's assume the person's far point distance is 3 meters.
2) Determine the person's current corrective lens prescription: If the person already wears corrective lenses, their current prescription can be used to calculate the required focal length of the corrective lens.
If they do not wear corrective lenses, this step can be skipped.
3) calculate the person's current refractive error: This can be done by subtracting the measured far point distance from infinity (1/∞) and converting the result to diopters.
For example, if the person's far point distance is 3 meters, their refractive error would be -0.33 diopters (1/3m = 0.33 D).
4) Determine the focal length of the corrective lens required to make the far point distance infinite: This can be done by adding the person's refractive error to the desired focal length of infinity (1/0 = 0 D).
For example, if the person's refractive error is -0.33 diopters, the required focal length of the corrective lens would be 0.33 meters or 33 centimeters.
Therefore, the person would need a corrective lens with a focal length of 33 centimeters to make their far point distance infinite.
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a cassegrain telescope like that shown in (figure 1) has a primary mirror with 1.0-m focal length, and its convex secondary mirror is located 0.85 m from the primary. what should be the focal length of the secondary in order to put the final image 0.12 m behind the front surface of the primary mirror?
The focal length of the secondary mirror should be 0.187 m.
In a Cassegrain telescope, the final image is formed at the point where the parallel rays of light converge after reflecting off the secondary mirror and the primary mirror. Using the mirror equation 1/f = 1/p + 1/q, where f is the focal length, p is the distance of the object from the mirror, and q is the distance of the image from the mirror, we can calculate the distance of the image from the primary mirror.
Given: f_primary = 1.0 m, p = 1.85 m (0.85 m distance from primary to secondary + 1.0 m focal length of primary), and q = 0.12 m (distance of final image from the front surface of the primary mirror).
Solving for f_secondary: 1/1.0 = 1/1.85 + 1/f_secondary + 1/0.12
f_secondary = 0.187 m.
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a 11-kg cart moving to the right with a speed of 15 m/s collides with a concrete wall and rebounds with a speed of 5 m/s. what is the change in momentum of the cart?
The change in momentum of the cart is -110 kg m/s. This means that the momentum of the cart decreased by 110 kg m/s as a result of the collision with the concrete wall.
The change in momentum of the cart can be calculated using the formula Δp = mΔv, where Δp is the change in momentum, m is the mass of the cart, and Δv is the change in velocity. In this case, the mass of the cart is 11 kg and the initial velocity is 15 m/s to the right, while the final velocity is 5 m/s in the opposite direction.
So, the change in velocity (Δv) is calculated by subtracting the final velocity from the initial velocity: Δv = 5 m/s - 15 m/s = -10 m/s.
Now, we can calculate the change in momentum (Δp) by multiplying the mass and change in velocity: Δp = 11 kg x (-10 m/s) = -110 kg m/s.
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a longitudinal wave is passing through the newly discovered element belmontium at 380 m/s when it encounters another longitudinal wave coming from the other direction. how fast is the other wave moving? express your answer with the appropriate mks units.
The other longitudinal wave moving through belmontium should also have a speed of 380 m/s.
In a longitudinal wave, particles of the medium oscillate parallel to the direction of the wave's propagation. When two longitudinal waves meet, they undergo a process called interference, which can be constructive or destructive depending on their phase relationship.
Belmontium, the newly discovered element, is the medium through which the first longitudinal wave is passing at a speed of 380 m/s. When this wave encounters another longitudinal wave coming from the opposite direction, they interact with each other.
In this scenario, the speed of the second longitudinal wave can be determined by the principle of superposition. According to this principle, the displacement of particles in the medium at any point in time is the algebraic sum of the displacements due to individual waves.
Since the medium is the same for both waves (belmontium), their speeds should also be the same. This is because the speed of a wave in a given medium is determined by the properties of that medium, such as its density and elasticity. In the case of longitudinal waves, the speed depends on the medium's bulk modulus and its mass density.
Therefore, the other longitudinal wave moving through belmontium should also have a speed of 380 m/s. The speed is expressed using the appropriate MKS (meter-kilogram-second) units as 380 meters per second (m/s).
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To stretch pizza dough into a perfect shape a chef throws the dough spinning around its symmetry axis with a rotational speed of 0. 42 rad/s. At the end of this process the pizza dough has a shape of a disk of radius r equal to 0. 23 m and a mass of 0. 34 kg. The pizza has a thicker circular rim of mass 0. 16 kg. What is the total rotational inertia of the pizza dough? (Hint : the rim can be approximated as a circular ring)
The total rotational inertia of the pizza dough is 0.0146 kg·m^2.
The rotational inertia of the dough can be calculated using the formula for the rotational inertia of a solid disk rotating around its axis:
I_dough = (1/2) * m_dough * r^2
Substituting the given values, we get:
I_dough = (1/2) * 0.34 kg * (0.23 m)^2 = 0.0105 kg·m^2
The rotational inertia of the rim can be approximated as that of a circular ring rotating around its axis:
I_rim = m_rim * (r_outer^2 + r_inner^2)/2
Substituting the given values:
I_rim = 0.16 kg * ((0.23 m)^2 + (0.02 m)^2)/2 = 0.0041 kg·m^2
Therefore, total rotational inertia of pizza dough:
I_total = 0.0105 kg·m^2 + 0.0041 kg·m^2 = 0.0146 kg·m^2
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a workman carries some lumber up a staircase. the workman moves 9.6 m vertically and 22 m horizontally. if the lumber weighs 45 n, how much work was done by the workman?
The total work done by the workman was 432 joules
The workman lifted the lumber a vertical distance of 9.6 m, which means he did work against gravity. The amount of work done is equal to the force (weight of the lumber) multiplied by the distance it was lifted:
Work = force x distance
Work = 45 N x 9.6 m
Work = 432 joules
In addition to lifting the lumber, the workman also moved it horizontally a distance of 22 m. However, since the lumber was not lifted or lowered during this movement, no work was done against gravity.
Therefore, this distance does not affect the amount of work done by the workman.
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if the human body has an average density of 983 kg/m3 , what fraction of a person is submerged when floating gently in fresh water?
Roughly half of a person's body is submerged when they are floating gently in fresh water.
When an object is floating in water, it displaces an amount of water equal to its weight. If the weight of the displaced water is greater than the weight of the object, the object will float, and if it is less, the object will sink.
The fraction of a person that is submerged while floating in fresh water depends on the ratio of their weight to the weight of the water displaced by their body.
Assuming that the volume of a person is constant, we can calculate the weight of a person as:
Weight = density x volume x gravity
where:
density = 983 [tex]kg/m^3[/tex] (average density of human body)
volume = the volume of a person (assumed to be constant)
gravity = 9.81 [tex]m/s^2[/tex] (acceleration due to gravity)
Let's assume the weight of a person is 70 kg, then their volume would be:
Volume = Weight / (density x gravity)
Volume = 70 / (983 x 9.81)
Volume = 0.00716 [tex]m^3[/tex]
Now, let's consider the weight of the water displaced by the person's body. The weight of the water displaced is equal to the weight of the person, which is 70 kg.
Therefore, the fraction of the person's body that is submerged in water is:
Fraction submerged = Weight of water displaced / Total weight
Fraction submerged = 70 / (70 + weight of water in the submerged part of the body)
Since the person is floating gently in water, we can assume that only a small part of their body is submerged, and we can neglect the weight of water in the submerged part of the body.
Thus, we can approximate the fraction submerged as:
Fraction submerged ≈ Weight of water displaced / Total weight
Fraction submerged ≈ 70 / (70 + 70)
Fraction submerged ≈ 0.5 or 50%
Therefore, roughly half of a person's body is submerged when they are floating gently in fresh water.
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What specific evidence does Norton offer for her
belief?
sunlight shining through a thin, cool gas produces a(n) continuous spectrum. emission line spectrum. absorption line spectrum.
Sunlight shining through a thin, cool gas produces an absorption line spectrum.
Which spectrum does sunlight shining through a thin, cool gas produces?When white light passes through a thin, cool gas, some of the light is absorbed by the gas atoms, causing dark lines to appear in the spectrum known as an absorption spectrum. These dark lines represent the wavelengths of light that were absorbed by the gas. This type of spectrum is known as an absorption line spectrum. In the case of sunlight passing through Earth's atmosphere, the gases in the atmosphere absorb specific wavelengths of light, creating a series of dark lines in the spectrum. These dark lines are called Fraunhofer lines and are used to identify the chemical composition of the Sun and other stars.
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what is the distance the masses on the right of the fulcrum need to be to balance with the two masses on the left?
Distance the masses on the right of the fulcrum need to be to balance with the two masses on the left is (3.5kgm - x kg * d m) / 1kg
In order for a lever to be balanced, the moments on either side of the fulcrum need to be equal. The moment is calculated by multiplying the distance from the fulcrum by the mass of the object. Therefore, to balance the two masses on the left of the fulcrum with the masses on the right, we need to calculate the moment on each side and make them equal.
Let's assume the masses on the left of the fulcrum are 2kg and 3kg, and the masses on the right are x kg and y kg, respectively. If the distance between the fulcrum and the 2kg mass is 1m, and the distance between the fulcrum and the 3kg mass is 0.5m.
we can calculate the moments on each side as follows:
Moment on the left side = 2kg x 1m + 3kg x 0.5m = 2kg + 1.5kg = 3.5kgm
Moment on the right side = x kg * d m + y kg * e m
where d and e are the distances between the fulcrum and the masses on the right.
To make the moments equal, we can set them equal to each other:
3.5kgm = x kg * d m + y kg * e m
If we know the mass of one of the objects on the right, we can solve for the distance needed for the other mass to balance the lever. For example, if we know the mass of the object closest to the fulcrum is 1kg.
we can rearrange the equation to solve for e:
e = (3.5kgm - x kg * d m) / 1kg
Once we know the distance needed for the other mass, we can set up the lever accordingly and it should be balanced.
The Question was Incomplete, Find the full content below :
A balanced lever has two weights on it, the masses on the left of the fulcrum are 2kg and 3kg, and the masses on the right are x kg and y kg. If the distance between the fulcrum and the 2kg mass is 1m, and the distance between the fulcrum and the 3kg mass is 0.5m.what is the distance the masses on the right of the fulcrum need to be to balance with the two masses on the left?
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