In order to find the direction of the initial velocity, first let's calculate the change in velocity caused by the acceleration:
\(\begin{gathered} F=m\cdot a\\ \\ 2655=15.5\cdot a\\ \\ a=171.29\text{ m/s^^b2}\\ \\ \\ \\ \Delta V=a\cdot t\\ \\ \Delta V=171.29\cdot0.05\\ \\ \Delta V=8.5645\text{ m/s} \end{gathered}\)Now, let's calculate the horizontal and vertical components of the final velocity.
The direction is N45W, therefore the angle is 90° + 45° = 135°:
\(\begin{gathered} V_x=V\cdot\cos135°=45\cdot(-\frac{\sqrt{2}}{2})=-31.82\text{ m/s}\\ \\ V_y=V\cdot\sin135°=45\cdot\frac{\sqrt{2}}{2}=31.82\text{ m/s} \end{gathered}\)The change in the velocity occurred in north direction, so let's calculate the initial vertical velocity:
\(V_{iy}=V_y-\Delta V=31.82-8.5645=23.2555\text{ m/s}\)Now, to calculate the direction, we can use the arc tangent below:
\(\theta=\tan^{-1}(\frac{V_{iy}}{V_{ix}})=\tan^{-1}(\frac{23.2555}{-31.82})=-36.16°\)Since the direction is between north and west, we need to add 180° to the result, so the angle will be 143.84°.
This angle is equal to the direction N 53.84° W.
a fixed amount of a monatomic ideal gas is taken through the following cyclic process. originally (a) it is near atmospheric pressure (100 kpa) with a volume of 0.50 m3 and a temperature of 375 k. then it is isothermally compressed to half its volume (b). then its volume triples (c) during an isobaric expansion.
The qualitative sketch of the process on the PV plane is attached below:
What is ideal gas equation?The ideal gas law (also called the perfect gas law), the relationship between pressure P, volume V, and temperature T of a gas in the boundary region between low pressure and high temperature. Gas molecules move almost independently. each other. In such cases, all gases obey an equation of state known as the ideal gas law.
PV = nRT, where n is the number of moles of gas and R is the universal (or complete) gas constant, 8.31446261815324 joules/kelvin/mol (the universal gas constant is defined as Avogadro's number NA multiplied by Boltzmann's constant k) . ) In the International System of Units, energy is measured in joules, volume in cubic meters (m3), force in newtons (N), and pressure in pascals (Pa). where 1 Pa = 1 N/m2. A force of 1 Newton moving a distance of 1 meter does 1 Joule of work. Therefore, the dimension of both products PV and nRT is work (energy).
The qualitative sketch of the process is drawn on the PV plane.
At A,
P₁ = 100 kPa
V₁ = 0.50 m³
T₁ = 375 K
At B,
T₂ = 375 K
V₂ = 0.25 m³
P₁V₁ = P₂V₂
So, P₂ = (100× 10³ ×0.50)/ 0.25
= 200 kPa
At C,
P₃ = 200 kPa
V₃ = 0.75 m³
We know, V₂/ T₂ = V₃/ T₃
So,
T₃ = V₃T₂/ V₂
= (0.75 × 375)/ 0.25
= 1125 K
At D,
P₄ = 100 kPa
T₄ = 1125 K
V₄ = P₃V₃/ P₄
= (200 × 0.75)/ 100
= 1.5 m³
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The complete question is:
Brendan Gan is about to drive to Kuala Lumpur from Johor Bahru. The distance from Johor Bahru to Kuala Lumpur is 330 km. Brendan's car can drive 60 miles using 1 gallon of petrol The current petrol costs are RM1.85 per liter.
Calculate the total petrol cost for Brendan to drive from Johor Bahru to Kuala Lumpur.
Use: 1 gallon = 4.5 liters
1 mile = 1.61 km
Round up answer to 2 decimal places (8 marks)
Answer:
The total cost in petrol will be: RM 28.43
Explanation:
The distance to be covered is: 330 km
The car does 60 mi per 1 gallon
so we convert this into km per liter as
60 mi/gal = 60 * 1.61 / 4.5 = 21.47 km/liter
Then, if 1 liter is needed to cover 21.47 km, then to cover 330 km one would need:
330 / 21.47 liters = 15.37 liters
Since each liter costs RM 1.85, then the cost in gas will be:
1.85 * 15.37 = RM 28.43
The two plates are now to be pushed together to a separation of d/2. The pushing together can be done either with the battery connected or with it disconnected. Which way would result in the greater electric field magnitude, and by what factor
Answer:
Electric field will be greater when the battery is connected by the factor of 2.
Explanation:
Solution:
I will be doing some algebraic calculations to answer this question:
As we know that,
Q = CV
and
C = \(\frac{AE_{0} }{d}\)
So, when separation = d/2, then,
\(C^{'}\) = \(\frac{AE_{0} }{d/2}\) by rearranging we get
So,
\(C^{'}\) = 2C
We further know that, Voltage will remain same if the battery is connected.
This further implies that,
Q = CV
So,
\(Q^{'}\) = \(C^{'}\)V
\(Q^{'}\) = 2CV
\(Q^{'}\) = 2Q
and we also know that,
Electric field E = \(\frac{Q}{AE_{0} }\)
So, the new E or \(E^{'}\) = \(\frac{Q^{'} }{AE_{0} }\)
Hence,
\(E^{'}\) = \(\frac{2Q}{AE_{0} }\) = 2E
\(E^{'}\) = 2E
when battery is disconnected, Q remain the same.
So,
When disconnected
E = E
E = \(\frac{Q}{AE_{0} }\) = Same
Hence, we can see that the magnitude of the electric does not depend upon the distance of separation. Instead it does depend upon the magnitude of charge.
So, when battery is disconnected, Q is same, so the Electric field.
But when it is connected, \(Q^{'}\) = 2Q and the \(E^{'}\) = 2E
So,
\(\frac{E connected}{E disconnected} = \frac{E^{'} }{E}\) = \(\frac{2E}{E}\) = 2
Electric field will be greater when the battery is connected by the factor of 2.
A golf ball has a mass of 45.6 grams. It rolls off a table at a height of 85.0 cm above the ground. As it bounces, 0.115 J of energy is lost. What maximum height does it travel to after the bounce? You may neglect air resistance.
The maximum height traveled by the ball of mass 45.6 grams is 0.593 m.
What it height?Height is the vertical distance between two points.
To calculate the maximum height the golf ball will travel to after the bounce, we use the formula below.
Formula:
h = (mgH-E')/mg......... Equation 1Where:
H = Height of the tableE' = Energy lost by the ballm = Mass of the ballh = Maximum height traveled by the ballg = Acceleration due to gravityFrom the question,
Given:
m = 45.6 g = 0.0456 kgH = 85 cm = 0.85 mE' = 0.115 Jg = 9.8 m/s²Substitute these value into equation 1
h = [(0.0456×0.85×9.8)-0.115]/(0.0456×9.8)h = 0.593 mHence, the maximum height traveled by the ball is 0.593 m.
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if the 52 lb bucket is released from rest, determine its velocity after it has fallen a distance of 12 ft . the windlass a can be considered as a 31 lb cylinder, while the spokes are slender rods, each having a weight of 2 lb . neglect the pulley's weight.(figure 1)
The velocity of the bucket after falling a distance of 12 ft is 7.54 m/s.
To determine the velocity of the bucket after it has fallen a distance of 12 ft, we need to use the equation of motion for an object falling under the influence of gravity:
v = √(2gh)
where v is the velocity of the object, g is the acceleration due to gravity (9.8 m/s²), h is the height the object has fallen, and h is the distance the object has fallen.
In this case, h = 12 ft = 3.66 m, so the velocity of the bucket after falling a distance of 12 ft is:
v = √(2 × 9.8 m/s² × 3.66 m) = 7.54 m/s
Note that this is the velocity of the bucket relative to the ground, and does not take into account any effects of the windlass or the spokes.
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817 cm3 at 80.8 kPa to 101.3 kPa
The volume of the gas at 101.3 kPa would be approximately 651.25 cm³.
To calculate the change in volume of a gas from an initial pressure to a final pressure, we can use Boyle's law, which states that the pressure and volume of a gas are inversely proportional at constant temperature.
Boyle's law can be expressed as:
P1 * V1 = P2 * V2
Where:
P1 = Initial pressure (80.8 kPa)
V1 = Initial volume (817 cm³)
P2 = Final pressure (101.3 kPa)
V2 = Final volume (to be calculated)
Let's plug in the values into the equation and solve for V2:
80.8 kPa * 817 cm³ = 101.3 kPa * V2
V2 = (80.8 kPa * 817 cm³) / 101.3 kPa
V2 ≈ 651.25 cm³
Therefore, the volume of the gas at 101.3 kPa would be approximately 651.25 cm³.
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how much metal is needed to cast a cubical metal box
If metal is required to cast the cubical metal box, it would require 784cm3 of solid static electricity iron.
What exactly is static electricity?Unbalanced electric charge on such a material's surface is known as static electricity. In contrast for dynamic (moving) electricity, which takes the shape of electric currents, static electricity is defined as being fixed or immovable. A typical atom is neutral, meaning it has an equal number of protons and electrons.
What effects does static electricity have on the body?Although static electricity does not directly endanger human life, it can nonetheless shock us and, if we were on an elevated surface, might inflict serious injuries.
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The push exerted on one object when it has a collision with another object is called
?
Your answer
The push exerted on one object when it has a collision with another object these forces are also referred to as force pairs, action forces, and reaction forces.
Collision: What is it?A collision, also known as an impact, occurs when two bodies, such as two pool cues, a golf club and a ball, a hammer and a nail, two railroad cars when joined, or a falling object and a floor, suddenly and violently collide. Collisions help physicists understand the characteristics of atomic and subatomic particles.
Collisions happen when two objects come into contact. In most cases, conservation of momentum and conservation of energy are used to solve collision-related problems. Collisions might be of two different types: Momentum is conserved in inelastic collisions, whereas it is also conserved in elastic collisions together with kinetic energy.
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A 1 000 kg car is pulling a 300 kg trailer. Together, the car and trailer move forward with an acceleration of 2. 15 m/s². Ignore any force of air drag on the car and all friction forces on the trailer. Determine (a) the net force on the car
(a) A 1 000 kg car is pulling a 300 kg trailer, together the car and trailer move forward with an acceleration of 2. 15 m/s² the net force acting on the car (and trailer) is approximately 2,795 Newtons (N).
To determine the net force on the car, we can use Newton's second law of motion, which states that the net force acting on an object is equal to the product of its mass and acceleration.
The total mass of the car and trailer combined is the sum of their individual masses: 1,000 kg + 300 kg = 1,300 kg.
The acceleration of the car and trailer system is given as 2.15 m/s².
Using Newton's second law:
Net force = mass × acceleration
Net force = 1,300 kg × 2.15 m/s²
Net force ≈ 2,795 N
Therefore, the net force acting on the car (and trailer) is approximately 2,795 Newtons (N).
This net force is responsible for accelerating the combined mass of the car and trailer in the forward direction. It represents the sum of all external forces acting on the system, such as the force exerted by the car's engine and the tension in the connection between the car and trailer.
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What is the Momentum of a ball that has a mass of 0.5 kg and a velocity of 20 m/s?
PLEASE HELP QUICKLY!!
Which of the following statements, about projectile motion is false.
Select one:
O a. How fast an object falls depends on its mass.
O b. The range of a projectile depends on the angle at which the projectile is fired.
O c.
The horizontal component of the acceleration is zero
O d. The acceleration due to gravity always acts downwards.
O e. The velocity in the x and y directions can be treated independently
у
Answer:
A
Explanation:
took the test today at school, got a 95.
O a. How fast an object falls depends on its mass.
IS FALSE
Explanation:
Mass does not affect the speed of falling objects, assuming there is only gravity acting on it.
If you pull with a constant force of 400n , how much mechanical work does it take to pull pinball launcher back 0.2meters
If you pull with a constant force of 400 N for 0.2 meters, then the work done will be equal to 80 J.
What is Work?In physics, the word "work" involves the measurement of energy transfer that takes place when an item is moved over a range by an externally applied, at least a portion of which is applied within the direction of the displacement.
The length of the path is multiplied by the element of a force acting all along the path to calculate work if the force is constant. The work W is theoretically equivalent towards the force f times the length d, or W = fd, to portray this concept.
As per the given information in the question,
Force, f = 400 N
Displacement, d = 0.2 meters
\(Work done(W)=Force(f)*Displacement(d)\)
W = 400 × 0.2
W = 80 J.
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why do we breath air?
Answer:
We breath air for us to supply oxygens in terms of functioning the circulatory system because oxygen can be transported as blood. We breath air because it has many minerals in it.
Explanation:
What is the best description of temperature?
O the same thing has heat energy
O the measurement of calories burned in a substance
O a measurement of the impact of heat energy
O an indirect measurement of Celsius
Explanation:
o has Celsius of indirect measurment
a mass of 20kg is held stationary by a rope passing over a frictionless pally. what is the tension T in the rope?
The tension in the rope is 196.2 N. The rope is exerting a force of 196.2 N on the object to keep it stationary.
Assuming that the mass is not accelerating, the tension in the rope must be equal to the weight of the mass. The weight of the mass can be found using the formula:
weight = mass x acceleration due to gravity
where acceleration due to gravity is approximately 9.81 m/s².
Therefore, the weight of the mass is:
weight = 20 kg x 9.81 m/s² = 196.2 N
Since the mass is held stationary, the tension in the rope must be equal to the weight of the mass, which is 196.2 N. So the tension T in the rope is 196.2 N.
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HELP ME ASAPPPPPPPPPPP
A penny sinks to the bottom of a wishing well
What type of frictional force is that?
The frictional force involved when a penny sinks to the bottom of a wishing well is primarily due to viscous drag or fluid friction. As the penny moves through the water, it experiences resistance from the surrounding fluid. This resistance is caused by the frictional forces between the water molecules and the penny's surface.
1. Two charges are separated by a distance of 1 cm. One charge has a value of 7 micro Coulombs. The other charge has a value of 10 micro Coulombs. What is the force between them, in pounds. Make sure to include the sign of the force which will be positive if the charges repel each other and negative if they attract each other.
2. 12 gauge copper wire is normally used in house wiring. When aluminum wire is used one needs to use a smaller gauge size to obtain the same resistance, 40 ft of 12 gauge copper wire was calculated. What would the resistance be if 10 gauge aluminum wire were used?
3. A 12 V automobile battery can supply 51 amps for one hour and cost $194. What is the cost of this electricity in cents per kWh?
4. Most of the body's resistance is in its skin. When wet, salts go into ion form, and the resistance is lowered. Thus, the resistance of the skin can go from 100,000 ohms when dry to 300 ohms when wet. What is the current that would be carried through the body, in milliAmperes, if you touched a 240 V power line while dry? Currents over 10 mA are almost always deadly.
1. The force between the two charges is 1.78 × 10⁻⁵ pounds, with opposite signs indicating attraction between the charges.
2. The resistance of 10 gauge aluminum wire over a 40 ft distance would be 0.506 ohms.
3. The cost of electricity from the automobile battery is 38.6 cents per kWh.
4. The current that would be carried through the body is 0.8 mA if dry.
1. The force between two point charges can be calculated using Coulomb's law, which states that the force is proportional to the product of the charges and inversely proportional to the square of the distance between them.
Using the values given, the force can be calculated as F = (k * q1 * q2) / r², where k is Coulomb's constant, q1 and q2 are the charges, and r is the distance between them. Plugging in the values, the force can be calculated as 1.78 × 10⁻⁵ pounds, with opposite signs indicating attraction between the charges.
2. The resistance of a wire is determined by its length, cross-sectional area, and resistivity. The resistivity of aluminum is higher than that of copper, so a larger cross-sectional area is required to achieve the same resistance. Using the gauge size conversion chart, 10 gauge aluminum wire has a cross-sectional area of 5.26 mm², which is approximately 83% of the cross-sectional area of 12 gauge copper wire.
Thus, the resistance of 10 gauge aluminum wire over a 40 ft distance can be calculated as R = (rho * L) / A, where rho is the resistivity of aluminum, L is the length, and A is the cross-sectional area. Plugging in the values, the resistance can be calculated as 0.506 ohms.
3. To calculate the cost of electricity per kWh, the total cost and the total amount of energy supplied must be known. Since the battery supplies 12 V and 51 A for one hour, the total energy supplied can be calculated as E = V * I * t, where V is the voltage, I is the current, and t is the time.
Plugging in the values, the total energy supplied can be calculated as 612 watt-hours (Wh). Since one kWh is equal to 1000 Wh, the total energy supplied can be converted to 0.612 kWh. Dividing the total cost by the total energy supplied gives the cost per kWh, which is 38.6 cents.
4. The current through the body can be calculated using Ohm's law, which states that current is equal to voltage divided by resistance. Using the values given, the resistance can be either 100,000 ohms or 300 ohms depending on whether the skin is dry or wet.
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A 200 kg bumper car travelling at 1 m/s hits a 300 kg bumper car travelling at "-2" m/s. If the velocity of 200 kg bumper car after the collision is "-3" m/s and the force exerted on the 200 kg bumper car was 500 N, what was the magnitude of the force exerted on the 300 kg bumper car?
A.) 200 N
B.) 500 N
C.) 750 N
D.) 333N
The magnitude of the force exerted on the 300 kg bumper car is 500 N.
option B.
What is Newton's third law of motion?
Newton's third law of motion states that for every action force, there is an equal and opposite reaction force. That is action force and reaction force are equal in magnitude but opposite in direction.
Mathematically, the formula for Newton's third law of motion is given as;
Fa = - Fb
where;
Fa is the force exerted on 200 kg bumperFb is the reaction force of 300 kg bumperFb = - 500 N
| Fb | = 500 N
Thus, the force exerted by 200 kg bumper is to the force exerted by 300 kg bumper.
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A spring stretches 0.294-m when a 0.360-kg mass is gently suspended from it as in Fig. 11–3b. The spring is then set up horizontally with the 0.431-kg mass resting on a frictionless table as in Fig. 11–5. The mass is pulled so that the spring is stretched 0.250-m from the equilibrium point, and released from rest.
Determine:
(a) the spring stiffness constant k.
The spring constant k based on the information is 12.0 N/m.
How to calculate the valueFrom the information, a spring stretches 0.294-m when a 0.360-kg mass is gently suspended from it as in Fig. 11–3b. The spring is then set up horizontally with the 0.431-kg mass resting on a frictionless table.
The spring constant k is the force required to stretch or compress the spring by a unit distance. In this case, the spring is stretched by 0.294 m when a 0.360 kg mass is suspended from it.
This means that the force exerted by the spring is equal to the weight of the mass, which is 0.360 kg x 9.8 m/s^2 = 3.53 N.
Therefore, the spring constant k is:
= 3.53 N/0.294 m
= 12.0 N/m.
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what is the mass of a 50 kg person on earth?
a) 50 kg
b) 490 kg
c) 5.1 kg
d) 0.19 kg
Answer:
a. 50 Kg hope it helps :)
Am arrow of mass 1000kg is shot into a wooden block of mass 5000lg lying at rest in a smooth surface.If the arrow travels 15m/s horizontally at the moment of impact,Calculate the common velocity after the impact
Answer:
Vf=3
Explanation:
you must first write your data
data before impact
M1=1000 M2=5000
V1=0 m/s V2 =0m/s
data after impact
M1=1000 M2=5000
V1=15m/s V2=?
M1V1 +M2V2=M1V1 +M2V2f
(1000)(0)+(5000)(0)=(1000)(15)+(5000)Vf
0=15000+5000Vf
- 15000÷5000=5000Vf÷5000
Vf= -3
Vf =3
The total momentum during a collision is conserved. Using this concept, the final velocity for the combined mass after the impact will be 2.4 m/s.
What is momentum?Momentum of a moving body is the product of its mass and velocity. The momentum during a collision is conserved. Thus, the sum of initial momentum of each body will be equal to the sum of final momentum of the two bodies.
Thus, m1u1 + m2 u2 = m1 v1 + m2v2.
Where u and v be the initial and final velocities respectively.
Given that, mass of arrow = 1000 kg
velocity = 15 m/s
initial momentum = 1000 × 15 = 15000 kg m/s.
mass of wooden black = 5000 kg
initial velocity = 0
thus, initial momentum = 0
final momentum of the combined mass = (5000 + 1000 kg) v
then, 15000 kg m/s + 0 = (5000 + 1000 kg) v
v = 2.4 m/s
Therefore, the common final velocity is 2. 4 m/s
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If the initial velocity of a ball is sent straight upward at 10.5m/s from the ground what will its final velocity be when it hits the ground at the end of its flight?
Answer: -10.08 m/s
Explanation:
Here we only need to analyze the vertical problem.
When the ball is in the air, the only force acting on it will be the gravitational force, this means that the acceleration of the ball, is equal to the gravitational acceleration, then:
a(t) = -9.8m/s^2
Where the negative sign is because gravity pulls the ball down.
To get the velocity equation we need to integrate over time, we get:
v(t) = (-9.8m/s^2)*t + v0
Where v0 is the initial vertical velocity, here it is v0 = 10.5 m/s
Then the velocity equation is:
v(t) = (-9.8m/s^2)*t + 10.5 m/s
To get the position equation, we need to integrate again over time, we get:
p(t) = (1/2)*(-9.8m/s^2)*t^2 + (10.5 m/s)*t + p0
Where p0 is the initial position, we know that the ball is sent upward from the ground, so p0 = 0m
Then the position equation is:
p(t) = (1/2)*(-9.8m/s^2)*t^2 + (10.5 m/s)*t
Now we need to find the value of t such that the position is equal to zero (this means that the ball hits the ground again).
Then we need to solve:
p(t) = 0 = (1/2)*(-9.8m/s^2)*t^2 + (10.5 m/s)*t
If we divide both sides by t, we get:
0 = (1/2)*(-9.8m/s^2)*t + (10.5 m/s)
Now we can solve it:
(1/2)*(9.8m/s^2)*t = 10.5 m/s
t = (10.5 m/s)/((1/2)*(9.8m/s^2)) = 2.14 s
This means that after 2.14 seconds, the ball will hit the ground again.
The velocity of the ball when it hits the ground is equal to:
v(2.14s) = (-9.8m/s^2)*2.14s + 10.5 m/s = -10.08 m/s
Skills Practice
4. Starting from one shore, you swim east across a narrow river to the other shore.
The river is 19.0 m wide. As you swim, the river current moves you north up the
river a distance of 12.0 m. Draw a diagram representing this situation What is you
resultant displacement? Express your answer in components, and then determin
the magnitude.
Answer:you think i know jesus im in y8 i barley know any g anyway someone asked me something that only albert eientsien knew .
Explanation:
I'm also cluless but i feel good for helpig other people out
The question involves calculating the resultant displacement of swimming across a river while also being carried north by the current. In this scenario, the eastward displacement is 19.0 m, and the northward displacement due to the current is 12.0 m. Using these vectors, the total displacement can be calculated as approximately 22.36 m.
Explanation:The subject of this question is Physics, specifically the concept of calculating displacement, which is a vector quantity. To solve this, we start by setting up a vector diagram. One vector represents your direction of swimming (east), which is 19.0 m long. The other vector represents the direction of the river current (north), which is 12.0 m long. The resultant displacement is the hypotenuse of the right-angled triangle they form. To calculate this magnitude, express your displacement in components: The eastward displacement is (19.0 m, 0) and the northward displacement is (0, 12.0 m). Finally, we can determine the resultant displacement using the Pythagorean theorem (sqrt[(19.0m)^2 + (12.0m)^2]), which gives a magnitude of approximately 22.36 m.
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Which of the filling is a fossil fuel?
A beam of 7.96-MeV protons is incident on a target of _13^27 text(Al). Those that collide produce the reaction shown below.
p + 27 13 Al → 27 14 Si + n 27 14
Si has a mass of 26.986721 u. Neglecting any recoil of the product nucleus, determine the kinetic energy of the emerging neutrons. MeV
Answer:
The kinetic energy = 2.35Mev
Explanation:
The standard value of the given mass of the elements are:
Mo= 1.007276U
Mn= 1.008665
M(Al)= 26.9815392u
We can now calculate Q
CHECK THE ATTACHMENT FOR DETAILED EXPLANATION
Select all the correct answers.
When people use plastic combs on their hair, the combs become negatively charged. Which statements about this situation are true?
The comb loses electrons.
The comb gains electrons.
The hair loses electrons.
The hair gains protons.
The hair loses protons.
Answer:
so therefore, the comb gains electron and the hair losses electrons
Explanation:
It is known that electron contain a negative charge.
So, when an atom gain electrons then number of electrons within the atom increases. As a result, the atom acquires a negative charge.
But when an atom loses electrons, there will be deficiency of electrons within the atom. As a result, the atom becomes positively charged.
Hence,, when people use plastic combs on their hair, the combs become negatively charged. The situation which is true about this is the comb gains electrons and the hair loses electrons.
A block of mass 0.1 kg is attached to a spring of spring constant 15 N/m on a frictionless track. The block moves in simple harmonic motion with amplitude 0.22 m. While passing through the equilibrium point from left to right, the block is struck by a bullet, which stops inside the block. The velocity of the bullet immediately before it strikes the block is 42 m/s and the mass of the bullet is 3 g. If the simple harmonic motion after the collision is described by x = B sin(ω t + φ), what is the new amplitude B? Answer in units of m.
The new amplitude B is 0.22 m.
Mass of block = M =0.1 kg
Spring constant = k = 15 N/m
Amplitude = A = 0.22 m
Mass of bullet = m = 3 g = 0.003 kg
Velocity of bullet = vᵇ = 42 m/s
Angular frequency of S.H.M is given by = ω₀ = \(\sqrt{\frac{k}{M}}\)
= \(\sqrt{\frac{15}{0.1} }\)
= 12.24 rad/sec
Speed of the block immediately before the collision:
Displacement of Simple Harmonic Motion is given as:
x= A Sin(ωt+Ф)
After differentiating:
v = A ω₀cos(ω₀t+Ф)
As bullet strikes at equilibrium position,
φ = 0
t= 2nπ
⇒ cos (ω₀t + φ) = 1
⇒ v= A ω₀
⇒ v= (0.22)(12.24)
⇒ \(v=2.692 ms^{-1}\)
If the simple harmonic motion after the collision is described by x = B sin(ωt + φ), new amplitude B:
S.H.M after collision is given as :
x= B Sin(ωt+Ф)
To find B, consider law of conservation of energy,
\(KE = PE\\KE =\frac{1}{2}(m+M)v^{2} \\PE= \frac{1}{2}kB^{2}\\\frac{(m+M)v^{2}}{k}=B^{2} \\B=\sqrt{\frac{(m+M)}{k}} v\\B= \sqrt{\frac{0.003+0.1}{15} } (2.69)\)
\(B= 0.22 m\)
Therefore, the new amplitude B is 0.22 m.
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define refractive index with reference to the law of reflection
The ratio of the velocity of light in a vacuum to its velocity in a specified medium.
Law of reflection:-also known as Snell's law defines the refractive index of a medium with respect to the other medium. First law of refraction states that, the ratio of the sine of the angle of incidence to the sine of the angle of refraction is constant.
A 2.0 cm tall object is placed 25 cm in front of a converging lens. The image is found 64 cm on the other side of the lens.
The focal length of the lens is ________.
0.011 cm
0.024 cm
41 cm
0.056 cm
18 cm
15 cm
Since focal length cannot be negative for a converging lens, we take the positive value: f ≈ 41 cm Option C
To determine the focal length of the lens, we can use the lens formula, which relates the object distance (u), image distance (v), and focal length (f) of a lens. The lens formula is given by:
1/f = 1/v - 1/u
In this case, the object distance (u) is 25 cm and the image distance (v) is 64 cm. We can substitute these values into the lens formula to solve for the focal length:
1/f = 1/v - 1/u
1/f = 1/64 cm - 1/25 cm
To simplify the equation, we can find a common denominator:
1/f = (25 - 64) / (64 * 25)
1/f = -39 / (64 * 25)
Now, we can invert both sides of the equation to solve for the focal length:
f = (64 * 25) / -39
f ≈ -41.03 cm
Since focal length cannot be negative for a converging lens, we take the positive value:
f ≈ 41 cm
Therefore, the correct answer is option C) 41 cm.
It's important to note that in the lens formula, distances are measured with respect to the lens, with positive values indicating distances on the opposite side of the incident light. The negative value obtained for the focal length indicates that the lens is a converging lens, as expected. Option C
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A 5kg mass is pushed with a force of 10N for a distance of 2.5 meters. The work done is
W = 25 J
Explanation:
Work done on an object is defined as
\(W = Fd = (10\:\text{N})(2.5\:\text{m}) = 25\:\text{J}\)