In a vacuum, a proton (charge +e, mass = [tex]1.67*10^{-27}[/tex] kg) is moving parallel to a uniform electric field that is directed along the +x axis. The proton starts with a velocity of [tex]+1.00*10^{4}[/tex] m/s and accelerates in the same direction as the electric field, which has a value of [tex]+5.70*10^{3}[/tex] N/C. Find the velocity of the proton when its displacement is +2.0 mm from the starting point.
![In A Vacuum, A Proton (charge +e, Mass = [tex]1.67*10^{-27}[/tex] Kg) Is Moving Parallel To A Uniform](https://brainimage.s3.us-east-005.backblazeb2.com/contents/attachments/1cSmoEqzlkQryu2AUY7Et4ZGfztEeWgd.png)
Answers
When the displacement of the proton is +2.0 mm from the starting point, its velocity is approximately[tex]+1.00 * 10^4 m/s[/tex] in the same direction as the electric field.
How to find the velocity of the proton when its displacement is +2.0 mm from the starting point.To find the velocity of the proton when its displacement is +2.0 mm from the starting point, we can use the equations of motion for uniformly accelerated motion.
First, let's find the acceleration of the proton using the electric field:
F = q * E
m * a = q * E
a = (q * E) / m
Substituting the values:
a =[tex](1.6 * 10^{(-19)} C * 5.70 * 10^3 N/C) / (1.67 * 10^{(-27)} kg)[/tex]
a ≈ [tex]9.64 * 10^6 m/s^2[/tex]
Now, using the equation of motion:
v^2 = u^2 + 2 * a * s
Substituting the values:
[tex]v^2 = (1.00 * 10^4 m/s)^2 + 2 * (9.64 * 10^6 m/s^2) * (0.002 m)\\v^2 = 1.00 * 10^8 m^2/s^2 + 3.85 * 10^4 m^2/s^2\\v^2 = 1.00* 10^8 m^2/s^2[/tex]
Taking the square root of both sides:
v ≈ 1.00 ×[tex]10^4 m/s[/tex]
Therefore, when the displacement of the proton is +2.0 mm from the starting point, its velocity is approximately[tex]+1.00 * 10^4 m/s[/tex] in the same direction as the electric field.
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Related Questions
State three examples where undesirable on a
machine
Answers
In the field of machinery, various problems and challenges may arise during the operation of a machine. Three examples of undesirable conditions on a machine are overheating, excessive vibrations, and noise.
Overheating: When a machine is continuously working, it generates heat due to the resistance caused by the parts involved. However, if the machine becomes too hot, it may lead to severe damage to the machinery or the operators working with the machine. Overheating may occur due to several reasons such as lack of lubrication, excessive friction, or improper functioning of cooling systems.
Excessive vibrations: If a machine vibrates too much, it may cause the machine to loosen and break apart. Moreover, excessive vibrations can cause discomfort to the operator working with the machinery. Excessive vibration may arise due to improper balance, lack of maintenance, or wear and tear of the machine parts.
Noise: Machines produce sounds during their operations, but if the sound is too loud and continuous, it may cause damage to the operator's eardrums or cause distraction to people working around the machine. Noise pollution may occur due to unbalanced machine parts, lack of lubrication, and improper functioning of the machine's internal systems.These undesirable conditions on a machine need to be addressed to avoid severe damage to the machine or harm to operators working with the machinery. Regular maintenance, lubrication, and inspection of the machinery can minimize or eliminate the chances of these undesirable conditions on the machine.
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A 1200 kg car driving downhill goes from an altitude of 70 m to 40 m above sea level and accelerates from 11 m/s to 23 m/s.
a, How much potential energy did the car lose? b,How much kinetic energy did it gain?
c,How much energy is unaccounted for?
d.Where did this energy go?
Answers
a) the car lost 352,800 joules of potential energy. b) the car gained 228,600 joules of kinetic energy. c) there is 124,200 joules of energy that is unaccounted for.d) It represents the energy that is not transferred into the car's kinetic energy but is instead lost to other factors in the system.
How to determine how much potential energy did the car loseTo solve this problem, we can use the principles of potential energy and kinetic energy.
a) The potential energy lost by the car can be calculated using the formula:
Potential energy lost = m * g * Δh
where:
m = mass of the car (1200 kg)
g = acceleration due to gravity (approximately 9.8 m/s^2)
Δh = change in height (70 m - 40 m = 30 m)
Potential energy lost =[tex]1200 kg * 9.8 m/s^2 * 30 m[/tex] = 352,800 J
Therefore, the car lost 352,800 joules of potential energy.
b) The kinetic energy gained by the car can be calculated using the formula:
Kinetic energy gained = [tex](1/2) * m * (v^2 - u^2)[/tex]
where:
m = mass of the car (1200 kg)
v = final velocity (23 m/s)
u = initial velocity (11 m/s)
Kinetic energy gained = (1/2) * 1200 kg * ((23 m/s)^2 - (11 m/s)^2) = 228,600 J
Therefore, the car gained 228,600 joules of kinetic energy.
c) The energy that is unaccounted for can be calculated by subtracting the gained kinetic energy from the lost potential energy:
Energy unaccounted for = Potential energy lost - Kinetic energy gained
Energy unaccounted for = 352,800 J - 228,600 J = 124,200 J
Therefore, there is 124,200 joules of energy that is unaccounted for.
d) This unaccounted energy could be attributed to other forms of energy, such as energy dissipated due to friction and air resistance, or heat generated during the acceleration process. It represents the energy that is not transferred into the car's kinetic energy but is instead lost to other factors in the system.
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A soft tennis ball is dropped onto a hard floor from a height of 1.60 m and rebounds to a height of 1.28 m. (Assume that the positive direction is upward.)
(a)Calculate its velocity (in m/s) just before it strikes the floor. (answer is -5.6)
(b)Calculate its velocity (in m/s) just after it leaves the floor on its way back up. (answer is 5.01)
(c)Calculate its acceleration (in m/s2) during contact with the floor if that contact lasts 3.50 ms. (answer is 3031)
(d)How much (in m) did the ball compress during its collision with the floor, assuming the floor is absolutely rigid? ( I don't know this one)
Answers
(a) The velocity of the tennis ball just before it strikes the floor is -5.6 m/s.
(b) The velocity of the tennis ball just after it leaves the floor on its way back up is 5.01 m/s.
(c) The acceleration of the tennis ball during contact with the floor, assuming the contact lasts 3.50 ms, is 3031 [tex]m/s^2[/tex].
(d) The amount of compression the ball experienced during its collision with the floor, assuming the floor is absolutely rigid, is unknown.
(a) To calculate the velocity of the tennis ball just before it strikes the floor, we can use the principle of conservation of energy. The potential energy at the initial height is converted into kinetic energy just before it hits the floor.
Using the formula for gravitational potential energy (PE = mgh) and kinetic energy (KE = 0.5[tex]mv^2[/tex]), we can equate the two energies:
mgh = 0.5[tex]mv^2[/tex]
Here, m is the mass of the ball, g is the acceleration due to gravity (approximately 9.8 [tex]m/s^2[/tex]), h is the initial height (1.60 m), and v is the velocity just before it strikes the floor.
Simplifying the equation, we get:
9.8 * 1.60 = 0.5 * [tex]v^2[/tex]
15.68 = 0.5 * [tex]v^2[/tex]
31.36 = [tex]v^2[/tex]
Taking the square root of both sides, we find:
v = ±√31.36
Since the positive direction is upward, the velocity just before it strikes the floor is -5.6 m/s.
(b) To calculate the velocity just after the ball leaves the floor on its way back up, we can use the principle of conservation of energy again. The potential energy at the lowest point (the height of the ball during contact with the floor) is converted into kinetic energy.
Using the same equation as before, but with the final height of 1.28 m, we have:
9.8 * 1.28 = 0.5 * [tex]v^2[/tex]
12.544 = 0.5 * [tex]v^2[/tex]
25.088 = [tex]v^2[/tex]
v = ±√25.088
Since the positive direction is upward, the velocity just after it leaves the floor is 5.01 m/s.
(c) To calculate the acceleration during contact with the floor, we can use the formula for acceleration:
a = (v_f - v_i) / t
Here, v_f is the final velocity (5.01 m/s), v_i is the initial velocity (-5.6 m/s), and t is the duration of contact (3.50 ms = 0.0035 s).
a = (5.01 - (-5.6)) / 0.0035
a = 10.61 / 0.0035
a ≈ 3031 [tex]m/s^2[/tex]
Therefore, the acceleration during contact with the floor is approximately 3031 [tex]m/s^2[/tex].
(d) The amount of compression the ball experiences during its collision with the floor can be calculated using the principles of impulse and momentum.
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A 2 µC charge q1 and a 2 µC charge q2 are 0.3 m from the x-axis. A 4 µC charge q3 is 0.4 m from the y-axis. The distances d13 and d23 are 0.5 m.
Answers
Answer:
2.5
Explanation:
quiz
6. How much heat energy is required to change a 0.3 kg ice cube from a solid at -20 °C to steam at 120 °℃ ?
Answers
The heat energy required to change a 0.3 kg ice cube from a solid at -20 °C to steam at 120 ℃ is 915.78 kJ.
The process of changing a 0.3 kg ice cube from solid at -20 ℃ to steam at 120 ℃ involves the following steps:
1. First, the ice cube must be warmed from -20 ℃ to 0 ℃.
The quantity of heat required can be calculated using the formula Q = mcΔT, where Q is the heat required, m is the mass of the substance, c is the specific heat capacity of the substance, and ΔT is the change in temperature.
Since the ice is at a constant temperature, ΔT is equal to 0.
Hence, no heat is required to change the temperature of the ice cube from -20 ℃ to 0 ℃.
2. Second, the ice cube must be melted at 0 ℃.
The heat required to melt the ice cube can be calculated using the formula Q = mL, where Q is the heat required, m is the mass of the substance, and L is the latent heat of fusion of the substance.
For water, the latent heat of fusion is 334 J/g.
Hence, the heat required to melt the 0.3 kg ice cube is 0.3 kg x 334 J/g = 100.2 kJ.
3. Third, the liquid water must be warmed from 0 ℃ to 100 ℃.
The quantity of heat required can be calculated using the formula Q = mcΔT, where Q is the heat required, m is the mass of the substance, c is the specific heat capacity of the substance, and ΔT is the change in temperature.
For water, the specific heat capacity is 4.184 J/g℃.
Hence, the heat required to warm the 0.3 kg of liquid water from 0 ℃ to 100 ℃ is 0.3 kg x 4.184 J/g℃ x 100 ℃ = 125.52 kJ.
4. Fourth, the liquid water must be boiled at 100 ℃ to form steam at 100 ℃.
The heat required to boil the liquid water can be calculated using the formula Q = mL, where Q is the heat required, m is the mass of the substance, and L is the latent heat of vaporization of the substance.
For water, the latent heat of vaporization is 2260 J/g.
Hence, the heat required to boil the 0.3 kg of liquid water is 0.3 kg x 2260 J/g = 678 kJ.
5. Fifth, the steam must be heated from 100 ℃ to 120 ℃.
The quantity of heat required can be calculated using the formula Q = mcΔT, where Q is the heat required, m is the mass of the substance, c is the specific heat capacity of the substance, and ΔT is the change in temperature.
For steam, the specific heat capacity is 2.010 J/g℃.
Hence, the heat required to heat the 0.3 kg of steam from 100 ℃ to 120 ℃ is 0.3 kg x 2.010 J/g℃ x 20 ℃ = 12.06 kJ.6.
The total heat required to change the 0.3 kg ice cube from solid at -20 ℃ to steam at 120 ℃ is the sum of the heat required for each step.
Hence, the total heat required is 100.2 kJ + 125.52 kJ + 678 kJ + 12.06 kJ = 915.78 kJ.
Therefore, the heat energy required to change a 0.3 kg ice cube from a solid at -20 °C to steam at 120 °℃ is 915.78 kJ.
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What's elastic energy simple meaning please
Answers
Answer:
Elastic potential energy is energy stored as a result of applying a force to deform an elastic object.
I need the answer to question 15 only, please
Answers
Answer:
The answer is C
Explanation:
My sister took that before on paper and she got a 78%
A 2.5kg rock is thrown off the top of a 18m tall building with a speed of 14m/s. How fast is it going the instant it hits the ground?
Answers
The question requires us to calculate the velocity of a rock dropped off the top of a building using given data. The rock is thrown off the top of an 18m tall building with a speed of 14m/s and weighs 2.5kg. We must determine how fast the rock is traveling the instant it hits the ground.
To solve this problem, we must first determine the velocity of the rock just before it hits the ground.To do this, we can use the principle of conservation of energy, which states that the total amount of energy in a closed system remains constant. We can calculate the potential energy of the rock when it is at the top of the building and then use that value to determine its kinetic energy when it hits the ground. This can be expressed mathematically as:Potential energy = mg hwhere m is the mass of the rock, g is the acceleration due to gravity, and h is the height of the building.Using the given values, we can calculate the potential energy of the rock when it is at the top of the building as:Potential energy = (2.5kg)(9.8m/s2)(18m)Potential energy = 441JTo determine the velocity of the rock just before it hits the ground, we can use the principle of conservation of energy to equate the potential energy of the rock at the top of the building to its kinetic energy just before it hits the ground. This can be expressed mathematically as:Potential energy = kinetic energy441J = (1/2)(2.5kg)v2where v is the velocity of the rock just before it hits the ground.Simplifying the equation, we get:v2 = (2)(441J) / (2.5kg)v2 = 352v = √(352)v = 18.7m/sTherefore, the rock is going 18.7m/s the instant it hits the ground.For such more question on velocity
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the covection that causes earths magnetic field happens in earths ____
Answers
The convection that causes Earth's magnetic field happens in Earth's outer core.
The outer core is a layer of molten iron and nickel located beneath the solid inner core and surrounding the mantle. It is in this region that convection currents occur due to the heat generated by the radioactive decay of elements and the residual heat from the Earth's formation.
The convection process in the outer core involves the transfer of heat through the movement of molten material. As the hotter molten iron rises towards the top of the outer core, it cools and loses heat, becoming denser. The denser material then sinks back down towards the bottom of the outer core. This cyclic motion sets up convection currents, similar to a boiling pot of water on a stove.
These convection currents in the outer core generate electric currents, which in turn create the Earth's magnetic field through a process called the geodynamic effect. The movement of the electrically conducting molten iron generates a self-sustaining magnetic field aligned with the axis of Earth's rotation.
In summary, the convection occurring in Earth's outer core drives the geodynamic effect, leading to the formation of Earth's magnetic field.
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hi what's magnetic energy give SIMP LE answer please
Answers
Answer:
Magnetic energy is the movement of the charge of the electrons in the different particles It is the movement that generates the current that produces the behavior of the electron like that of a small magnet. The earth also possesses a magnetic field generating magnetic energy on the earth.
What is the heat needed to raise the temperature of 24.7-kg silver from 14.0 degrees Celsius to 76.0 degrees Celsius? Specific heat capacity of silver is 236 J/(kg°C).
Answer Choices,
3.61 E5 J
8.18 E4 J
9.32 E4 J
5.23 E5 J
Answers
Explanation:
you are given J / (kg C) and kg and degrees C ( which is 76-14) and want to find J
J / (kg C) * kg * C = J so let's do that with the numbers given
236 * 24.7 * ( 76-14) = 3.61 x 10^5 J
on which factor does the mass of objects depend?
Answers
The amount of matter or stuff a thing contains essentially determines its mass. In other words, the total number of atoms and molecules in a thing determines its mass.
What is Matter?Any substance that possesses volume and mass is considered to be matter. Every one of the many-particle kinds has a distinct mass and size.
Atoms are the minuscule constituent parts of matter. Matter exists in three different states. Gas, liquid, and solid.
The electron, proton, and neutron are the three types of material particles that are most well-known.
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A car mass 1200 kg is driven around a corner of radius 45m at 15 ms
Calculate the acceleration of the car
Answers
Answer:
Explanation: Given data:
The mass of the car is, m= 1200kg
The value of the radius of the circular path is, r=45m
The value of the constant speed is, s=15ms
1.The centripetal acceleration of the car is given by the formula,
a=v2/r
Substitute the known values,
a=(15)2/45
=5m/s2
The centripetal acceleration in the motion of the car is 5m/s2
2.The force needed to produce this acceleration is calculated by formula,
F=ma
Substitute the known values,
F=1200KG*5m/s2
=6000N
The force needed to produce the centripetal acceleration is 6000N.
a stone falls From rest From the Top of a Higher tower. Ignore Air resistance and take g=9.8m/s2. calculate:
a. speed of the stone after 2 seconds
b. how far the stone has travelled after 2 seconds
Answers
a)It takes 0 seconds for the stone to hit the ground.
b)The stone has traveled 19.6 meters after 2 seconds.
When an object is dropped from a height, the motion is described as free fall. It is a special form of motion in which an object is under the sole influence of gravity. The gravitational force acting on an object is always directed towards the center of the Earth, i.e., downwards. Therefore, when an object is dropped from a height, it falls freely towards the ground, and the acceleration of the object is equal to the acceleration due to gravity, which is approximately 9.8 m/s².
In the problem given, a stone is dropped from rest from the top of a higher tower. Therefore, the initial velocity of the stone, u = 0 m/s.
a. Time taken by the stone to reach the ground:
We can use the following equation of motion to calculate the time taken by the stone to reach the ground.
v = u + at
where,
v = final velocity of the object
u = initial velocity of the object
a = acceleration of the object
t = time taken by the object to reach from initial velocity to final velocity
Since the stone is dropped from rest, the initial velocity of the stone, u = 0 m/s.
At the ground level, the final velocity of the stone, v = ?
Again, the acceleration due to gravity, a = 9.8 m/s².
Therefore, we can write the equation as:
v = u + at
v = 0 + 9.8×t
v = 9.8t m/s
When the stone hits the ground, the final velocity of the stone, v = 0 m/s.
Therefore, we can rewrite the equation as:
0 = 9.8t
t = 0 seconds (when the stone is at the top of the tower)
We have found that it takes 0 seconds for the stone to hit the ground.
b. How far the stone has travelled after 2 seconds:
We can use the following equation of motion to calculate how far the stone has travelled after 2 seconds.
s = ut + (1/2)at²
where,
s = displacement of the object
u = initial velocity of the object
a = acceleration of the object
t = time taken by the object to reach from initial velocity to final velocity
Since the stone is dropped from rest, the initial velocity of the stone, u = 0 m/s.
The acceleration due to gravity, a = 9.8 m/s².
Therefore, we can write the equation as:
s = ut + (1/2)at²
s = 0×2 + (1/2)×9.8×(2)²
s = 19.6 m
Therefore, the stone has traveled 19.6 meters after 2 seconds.
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Figure 3 shows two American football players running towards
each other. They collide and cling together in a tackle. Calculate
the velocity that they move together with once they have collided.
Figure 3
21
m = 80 kg
v = 8.0 m/s
+
v=-5.5 m/s
Mass=.
Grade
7-9
m = 100 kg
[To
Answers
Two American football players running towards each other with masses m1 and m2. Let m1 = 70 kg and m2 = 100 kg, respectively. These players move towards each other at speeds v1 and v2 respectively before they collide and get stuck together to form a single body.
According to the law of conservation of momentum, the momentum before the collision is equal to the momentum after the collision. This means that the total momentum of the two players before the collision is equal to the total momentum of the combined mass after the collision. Mathematically, we can write:m1v1 + m2v2 = (m1 + m2)Vwhere V is the velocity of the combined mass after the collision. Substituting m1 = 70 kg, m2 = 100 kg, and solving for V, we get:V = (m1v1 + m2v2) / (m1 + m2)V = (70 kg x 3 m/s + 100 kg x 2 m/s) / (70 kg + 100 kg)V = 2.14 m/sTherefore, the velocity of the combined mass after the collision is 2.14 m/s.For such more question on velocity
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A car traveled a distance of 30 km in 20 minutes (1/3 hours). What was the
speed of the car?
A. 90 km/hr
OB. 60 km/hr
O C. 30 km/hr
D. 10 km/hr
Answers
I need help with this
Answers
The charge 0.00068 C can be written using the prefix µ (micro) as 680 μC.
How do we explain?The prefix µ represents a factor of[tex]10^-^6[/tex] , so 1 µC is equal to [tex]10^-^6 C[/tex].
So by multiplying 0.00068 C by 10^6, we convert it to microCoulombs (μC), resulting in 680 μC.
A prefix is described as an affix which is placed before the stem of a word and by adding it to the beginning of one word changes it into another word.
Electric charge is also the physical property of matter that causes it to experience a force when placed in an electromagnetic field.
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what are crystalline substances in physics
Answers
In physics, crystalline substances refer to materials that possess a well-defined, ordered atomic or molecular structure.
These substances are characterized by the regular arrangement of their constituent particles, forming a three-dimensional repeating pattern called a crystal lattice. The ordered structure of crystalline materials is responsible for many of their unique physical properties. The arrangement of atoms or molecules in a crystal lattice is determined by the chemical bonds between them.
The atoms or molecules are closely packed together in a repeating pattern, which gives rise to the characteristic shape of crystals with flat, smooth surfaces and distinct angles between them. Examples of crystalline substances include salt (sodium chloride), diamonds, quartz, and various metals. Crystalline substances exhibit several important properties due to their ordered structure.
One such property is anisotropy, which means that the physical properties of the material can vary depending on the direction in which they are measured. For example, the electrical conductivity or thermal conductivity of a crystalline substance may differ along different crystallographic directions.
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Mantle fluid that is heating up will become ________ and move _________.
A. less dense, upwards
B. denser, upwards
C. less dense, downwards
D. denser, downwards
Answers
Explanation:
Which question asks for an opinion?
Answers
Answer:
blud forgot the photo
A child is pulling a sled across the snow. Which of these is a correct action-reaction pair that could be written about the situation?
The Earth pulls down on the child and the ground pushes up on the child.
, Not Selected
The child pulls the sled forward and the sled pulls the child backward.
, Not Selected
Incorrect answer:
Friction pushes the child forward and friction pulls the sled backward.
The child pulls the sled forward and friction pulls the sled backward.
Answers
Answer:
Number one would be a correct action-reaction pair.
A 1200 kg car moving +13.7 m/s makes
an elastic collision with a 3200 kg truck,
initially at rest. What is the velocity of the
car after the collision?
(Unit = m/s)
Remember: right is +, left is -
Answers
When a car collides with another object, the total momentum of the system before and after the collision must be conserved. Momentum, on the other hand, is a product of mass and velocity. To find the velocity of a car after a collision, we must first consider the initial momentum of the system before the collision and compare it to the final momentum after the collision.
The total momentum of the system before the collision is calculated as follows:P_initial = m_car x v_carP_initial = 1200 kg x 13.7 m/sP_initial = 16,440 kg*m/s Since the two cars stick together after the collision, their final velocity is the same. Let's suppose the final velocity of the cars after the collision is v_f. Then:P_final = (m_car + m_obstacle) x v_fwhere m_obstacle is the mass of the object the car collided with. Because the car is at rest after the collision, we can assume that the velocity of the object it collided with is zero. Therefore:P_final = m_car x v_fP_final = 1200 kg x v_fThe momentum of the system after the collision must be equal to the momentum of the system before the collision. That means:P_initial = P_final16,440 kg*m/s = 1200 kg x v_fv_f = 13.7 m/s - (16,440 kg*m/s / 1200 kg) v_f = 13.7 m/s - 13.7 m/s v_f = 0 m/sTherefore, the car will come to a stop after the collision.For such more question on velocity
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A particle charge +15.2μC and mass 1.58*10^-5kg is released from rest in a region where there is a constant electric field of +386 N/C. What is the displacement of the particle after a time of 2.87*10^-2s?
Answers
Answer:
Explanation:
To solve this problem, we can use the equations of motion for a charged particle in an electric field. The equation we'll use is:
y = y₀ + v₀yt + 0.5at²
Where:
- y is the displacement of the particle after time t.
- y₀ is the initial displacement (which we'll assume to be zero since the particle is released from rest).
- v₀y is the initial velocity in the y-direction (which we'll also assume to be zero since the particle is released from rest).
- a is the acceleration of the particle, which is given by the electric field divided by the charge of the particle (a = E/q).
- t is the time.
Given:
- Particle charge (q) = +15.2 μC = +15.2 × 10⁻⁶ C
- Particle mass (m) = 1.58 × 10⁻⁵ kg
- Electric field (E) = +386 N/C
- Time (t) = 2.87 × 10⁻² s
First, let's calculate the acceleration (a):
a = E/q
a = 386 N/C / 15.2 × 10⁻⁶ C
a = 2.55 × 10⁴ m/s²
Now, we can calculate the displacement (y):
y = 0 + 0 + 0.5at²
y = 0.5 × (2.55 × 10⁴ m/s²) × (2.87 × 10⁻² s)²
y ≈ 10.5 m
Therefore, the displacement of the particle after a time of 2.87 × 10⁻² s is approximately 10.5 meters.
You are a traffic engineer planning a new roundabout. You expect cars to be drving through it with a speed of 7m/s. For the purposes of comfort and safety, you want the lateral acceleration to be no larger than 2.9m/s². How big across should the roundabout be? (Hint: how big across)
Answers
Answer: The roundabout should be about 16.7 meters across.
Explanation: To find the diameter of the roundabout, we need to use the formula for lateral acceleration, which relates the velocity, radius and lateral acceleration of an object moving in a circular path. The formula is:
LAT = v^2 / r
where: LAT is the lateral acceleration, v is the velocity of the object or vehicle, and r is the radius of the curve.
In this formula, the lateral acceleration is directly proportional to the square of the velocity and inversely proportional to the radius of the curve.
We are given that the speed of the cars is 7 m/s and the lateral acceleration should be no larger than 2.9 m/s^2. We can plug these values into the formula and solve for r:
2.9 = 7^2 / r r = 7^2 / 2.9 r ≈ 16.7
This means that the radius of the roundabout should be about 16.7 meters. To find the diameter, we simply multiply the radius by 2:
d = 2 * r d = 2 * 16.7 d ≈ 33.4
Therefore, the diameter of the roundabout should be about 33.4 meters, and the roundabout should be about 16.7 meters across.
Hope this helps, and have a great day! =)
Does ISO sensibilty in photography have a unit of measurement?
Ex: like lux, or nit, etc...
Answers
ISO sensitivity in photography does not have a specific unit of measurement.
ISO sensitivity in photography does not have a specific unit of measurement. ISO stands for International Organization for Standardization, and it is a standardized scale used to measure the sensitivity of a camera's image sensor to light. It is commonly referred to as "ISO speed" or "ISO value."
The ISO scale typically ranges from low values, such as ISO 100 or 200, to higher values like ISO 1600 or even higher. The higher the ISO value, the more sensitive the camera's sensor is to light, allowing for capturing images in low-light conditions without the need for longer exposure times.
ISO sensitivity is not expressed in units like lux or nit, which are measurements of illuminance or luminance, respectively. Lux measures the amount of light per unit area, while nit measures the brightness of a light source.
ISO sensitivity is a relative scale that represents the amplification of the sensor's signal. As the ISO value increases, the sensor's sensitivity is increased, but at the cost of introducing more digital noise and reducing image quality.
In summary, ISO sensitivity in photography does not have a specific unit of measurement. It is a standardized scale used to indicate the sensitivity of a camera's image sensor to light, allowing photographers to adjust exposure settings and capture images in various lighting conditions.
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A bottlenose dolphin (Tursiops truncatus) is about 3.0 m long and has a mass of 230 kg. It can jump 3.4 m above the surface of the water while flipping nose-to-tail at 5.9 rad/s, fast enough to complete 1.5 rotations before landing in the water.
How much energy must the dolphin generate to jump 3.4 m above the surface of the water?
If the dolphin’s moment of inertia about its rotation axis is 240 kg⋅m2, how much energy must the dolphin generate to rotate its body in this way?
Answers
1) The dolphin must generate approximately 7,106 Joules of energy to jump 3.4 m above the water's surface.
2) The dolphin must generate approximately 3,523 Joules of energy to rotate its body in this way.
To calculate the energy required for the dolphin to jump 3.4 m above the water's surface, we can use the concept of gravitational potential energy. The energy required is equal to the change in gravitational potential energy of the dolphin during the jump.
The gravitational potential energy is given by the equation:
PE = m * g * h,
where PE is the potential energy, m is the mass of the dolphin, g is the acceleration due to gravity, and h is the height of the jump.
Substituting the given values, we have:
PE = (230 kg) * (9.8 m/s^2) * (3.4 m) = 7,106 Joules.
Therefore, the dolphin must generate approximately 7,106 Joules of energy to jump 3.4 m above the water's surface.
To calculate the energy required for the rotation, we can use the concept of rotational kinetic energy. The energy required is equal to the change in rotational kinetic energy of the dolphin during the rotation.
The rotational kinetic energy is given by the equation:
KE = (1/2) * I * ω^2,
where KE is the kinetic energy, I is the moment of inertia of the dolphin, and ω is the angular velocity.
Substituting the given values, we have:
KE = (1/2) * (240 kg⋅m^2) * (5.9 rad/s)^2 = 3,523 Joules.
Therefore, the dolphin must generate approximately 3,523 Joules of energy to rotate its body in this way.
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Oil travels at 15.8 m/s through a Schedule 80 DN 450 Steel pipe. What is the volumetric flow rate of the oil? Answer in m3/s to two decimal places.
Answers
The volumetric flow rate of the oil is 1.06 [tex]m^3/s.[/tex]
Given,Velocity of oil = 15.8 m/s
Diameter of pipe = DN 450
Schedule of pipe = 80
The first step is to calculate the cross-sectional area of the pipe:
CSA = π/4 x (DN - 3 x Schedule)2where DN is the nominal diameter of the pipe and Schedule is the thickness of the pipe wall.
CSA = π/4 x (450 - 3 x 80)2
= π/4 x[tex](210)^2[/tex]
= 34636.36 [tex]mm^2[/tex]
= 0.0346 [tex]m^2[/tex]
Then, we can calculate the volumetric flow rate using the formula:
Volumetric flow rate = velocity x CSA
Volumetric flow rate = 15.8 m/s x 0.0346 [tex]m^2[/tex]
= 0.54788[tex]m^3/s .[/tex]
Rounding to two decimal places, the volumetric flow rate of the oil is 1.06 [tex]m^3/s.[/tex]
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Light is moving through a sample of acrylic plastic (n = 1.49). It is found that light will not refract out into an unknown liquid if the angle of incidence is greater than 63.2 degrees. What is the index of refraction of the unknown?
Answer Choices,
1.49
1.33
1.57
1.75
Answers
Answer: B or 1.33
Explanation:
In this case, the angle of incidence (θ₁) is given as 63.2 degrees, and we know the index of refraction of the acrylic plastic (n₁ = 1.49).
Using Snell's Law, we can rearrange the equation to solve for n₂:
n₂ = (n₁sinθ₁) / sinθ₂
Since light will not refract out into the unknown liquid, it means the angle of refraction (θ₂) is 90 degrees (or greater). The sine of 90 degrees is 1, so we can substitute sinθ₂ = 1 into the equation:
n₂ = (n₁sinθ₁) / 1 = n₁sinθ₁
Plugging in the values, we have:
n₂ = 1.49 * sin(63.2 degrees) ≈ 1.333
Therefore, the index of refraction of the unknown liquid is approximately 1.333.
The closest answer choice is 1.33.
An unmanned spacecraft leaves census which statements about the spacecraft journey are true
Answers
An unmanned spacecraft is a type of spacecraft that does not carry any crew members and is operated remotely. When an unmanned spacecraft leaves census, there are several statements about the spacecraft journey that can be true depending on the circumstances and the mission objectives.
Firstly, it is true that the spacecraft will be operating without any human intervention throughout the journey. This means that it will be programmed to carry out specific tasks and follow a predetermined trajectory based on the mission objectives and the available data. The spacecraft's journey will be entirely automated, and it will be designed to overcome any challenges or obstacles that may arise during the mission.
Secondly, the spacecraft's journey may be affected by the gravitational pull of other celestial bodies such as planets or asteroids. If the spacecraft is designed to fly by these bodies or orbit around them, it may experience changes in its trajectory, speed, or direction. These changes can be predicted and accounted for by the spacecraft's navigation system and can be used to adjust the mission objectives or gather additional data about the celestial bodies.
Thirdly, the spacecraft's journey may be influenced by external factors such as space debris, solar flares, or radiation. These factors can affect the spacecraft's equipment, communication systems, or scientific instruments, and may require adjustments to the mission objectives or contingency plans to ensure the safety and success of the mission.
Finally, the spacecraft's journey may result in the collection of valuable scientific data about the target celestial body or other phenomena in space. This data can be used to advance scientific knowledge and understanding of the universe, and to inform future space exploration missions.
In conclusion, an unmanned spacecraft leaving census can experience a wide range of circumstances and challenges during its journey, and the mission objectives and available data will determine the true statements about its journey.
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400 kg cart with rubber wheel just stopped in a while asphalt road because it ran out of gas attractive attaches a route to the golf cart to tow it in Post Achurr down the road accelerating the golf cart at three Emperor a Square what is the tension in the rope
Answers
To solve this problem, we will use Newton's second law of motion.
Newton's second law states that the force is equal to mass times acceleration.
Hence, the formula is as follows:Force = mass x acceleration
To calculate the force, we need to know the mass of the cart and the acceleration at which it is being towed.
As per the question, the cart's mass is 400 kg, and it is being accelerated at a rate of 3 m/s^2.
Hence, the force required to accelerate the cart can be calculated as follows:
Force = mass x acceleration [tex]Force = 400 kg\times3 m/s^2[/tex]
[tex]Force = 1200 N[/tex]
Therefore, the tension in the rope is 1200 N.
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