Answer:
Explanation:
The force of gravity acting on the block can be resolved into two components, one parallel to the incline and one perpendicular to the incline. The perpendicular component is balanced by the normal force of the incline, and the parallel component is opposed by the force of friction. The force of friction is given by:
F_friction = coefficient_of_friction * F_norm
where F_norm is the normal force of the incline. The normal force is equal in magnitude and opposite in direction to the perpendicular component of the force of gravity, which is:
F_perpendicular = m * g * cos(theta)
where m is the mass of the block, g is the acceleration due to gravity, and theta is the angle of inclination.
The parallel component of the force of gravity is:
F_parallel = m * g * sin(theta)
The net force acting on the block is:
F_net = F_parallel - F_friction
Using Newton's second law, F = m * a, we can solve for the acceleration of the block:
a = F_net / m
Substituting the expressions for F_parallel and F_friction, we get:
a = [m * g * sin(theta) - coefficient_of_friction * m * g * cos(theta)] / m
Simplifying, we get:
a = g * [sin(theta) - coefficient_of_friction * cos(theta)]
Substituting the given values, we get:
a = 9.8 m/s^2 * [sin(36°) - 0.55 * cos(36°)] = 6.43 m/s^2
Therefore, the acceleration of the block is 6.43 m/s^2.
What is the force of attraction between a balloon with a charge of +4.0 x 10^-6 C is held a distance of 0.41 m from a second balloon having the same charge?
Explanation:
The force of attraction between two charged objects is given by Coulomb's law:
F = k * (q1 * q2) / r^2
where:
F is the force of attraction
k is Coulomb's constant, which has a value of 9.0 x 10^9 N*m^2/C^2
q1 and q2 are the charges of the two objects
r is the distance between the two objects
In this case, we have two balloons with the same charge of +4.0 x 10^-6 C each, and they are held at a distance of 0.41 m from each other. Plugging these values into Coulomb's law, we get:
F = 9.0 x 10^9 N*m^2/C^2 * [(+4.0 x 10^-6 C)^2] / (0.41 m)^2
F = 1.92 x 10^-3 N
Therefore, the force of attraction between the two balloons is 1.92 x 10^-3 N.
What did Erikson believe about the developmental stages of adolescence and young adulthood? Using what you know about eriksons stages of development, do you agree or disagree with the statement that all adolescents and young, adults pass through these stages? Explain
Overall, it is important to consider the individual differences and cultural context when applying Erikson's theory to adolescence and young adulthood.
What is Erikson's theory?
Erikson's theory is a psychoanalytic theory that describes the development of the human personality across eight stages throughout the lifespan. Each stage is characterized by a particular crisis or conflict that must be resolved in order for the individual to develop a healthy personality.
Erik Erikson proposed a theory of psychosocial development that includes eight stages spanning from infancy to old age. In adolescence and young adulthood, the stage is identity versus role confusion. Erikson believed that during this stage, individuals explore and experiment with different identities and roles as they seek to establish a sense of self and their place in the world.
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A block with mass 0.500 kg
sits at rest on a light but not long vertical spring that has spring constant 70.0 N/m
and one end on the floor.
How much elastic potential energy is stored in the spring when the block is sitting at rest on it? (for this I got 0.172 J and it was correct)
A second identical block is dropped onto the first from a height of 4.40 m
above the first block and sticks to it. What is the maximum elastic potential energy stored in the spring during the motion of the blocks after the collision? (for this I got 21.7 J but it was wrong)
What is the maximum distance the first block moves down after the second block has landed on it? (for this I got 0.788 m but it was wrong)
The elastic potential energy stored in the spring when the block is sitting at rest on it is 0.172 J, the maximum elastic potential energy stored in the spring during the motion of the blocks after the collision is 1.84 J, and the maximum distance the first block moves down after the second block has landed on it is 0.185 m.
How is elastic potential energy stored in a spring?Elastic potential energy is stored in a spring when it is compressed or stretched from its rest position.
How is the maximum elastic potential energy stored in the spring during the motion of the blocks after the collision calculated?The maximum elastic potential energy stored in the spring during the motion of the blocks after the collision is calculated as the difference between the total initial mechanical energy and the total final mechanical energy, where the total initial mechanical energy is the sum of the potential energy of the two-block system at the highest point of the motion and the kinetic energy of the two-block system just before impact, and the total final mechanical energy is the sum of the potential energy of the two-block system at the maximum compression of the spring and the elastic potential energy stored in the spring at that point.
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An average froghopper insect has a mass of 12.8 mg and jumps to a maximum height of 293 mm when its takeoff angle is 62.0∘ above the horizontal.
a) Find the takeoff speed of the froghopper.
b) How much kinetic energy did the froghopper generate for this jump? Express your answer in microjoules
c) how much energy per unit body mass was required for this jump ? Express your answer in joules per kilogram of body mass.
a) The takeoff speed of the froghopper can be found using the following equation:
v^2 = 2gh/(1 - cos^2(theta))
where:
v = takeoff speed
g = acceleration due to gravity (9.81 m/s^2)
h = maximum height (293 mm = 0.293 m)
theta = takeoff angle (62.0 degrees)
Substituting the given values into the equation, we get:
v^2 = 2(9.81)(0.293)/(1 - cos^2(62.0))
v^2 = 0.571
v = sqrt(0.571)
v ≈ 0.756 m/s
Therefore, the takeoff speed of the froghopper is approximately 0.756 m/s.
b) The kinetic energy generated by the froghopper can be found using the following equation:
KE = 0.5mv^2
where:
m = mass (12.8 mg = 0.0128 g)
v = takeoff speed (0.756 m/s)
Substituting the given values into the equation, we get:
KE = 0.5(0.0128)(0.756)^2
KE ≈ 0.00346 J
(1 J = 10^6 microjoules)
Therefore, the kinetic energy generated by the froghopper for this jump is approximately 0.00346 microjoules.
c) The energy per unit body mass required for this jump can be found by dividing the kinetic energy by the mass of the froghopper:
energy per unit body mass = KE/m
Substituting the values we obtained earlier, we get:
energy per unit body mass = 0.00346/0.0128
energy per unit body mass ≈ 0.270 J/kg
Therefore, the energy per unit body mass required for this jump is approximately 0.270 joules per kilogram of body mass.
When a force F stretches a rope of mass per unit length r, the velocity of a wave in the rope is given by xxxx. You pull on a rope with a certain force, and a wave travels in the rope with a certain velocity. If you double your force, the velocity of a wave in the rope is now ____________ the original velocity.
A. 1/2
B. xxxxx times
C. the same as
D. xxxx times
E. 2 times
Velocity of the wave in the rope is now 1.4 times the original velocity that is option B.
What is force?An influence that causes motion of any object with mass to change its velocity is called as force.
The velocity of a wave in a rope is given by the following equation:
v = √(F/r)
F is the force applied to the rope and r is the mass per unit length of the rope.
If the force is doubled (2F), the velocity of the wave in the rope can be found as follows:
v' = √(2F/r)
v'/v = √(2F/r) / √(F/r) = √(2)
Therefore, velocity of the wave in the rope is now 1.4 times the original velocity, or option B.
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**NEED ANSWER ASAP**
Consider three main sequence stars: Star A has a mass of 2 solar masses, Star B has a mass of 0.5 solar masses, and Star C has a mass of 20 solar masses
Which star will become a giant first?
Which star will become a giant last?
Answer:
Star C (with a mass of 20 solar masses) will become a giant first, after about 14 million years.
Star A (with a mass of 2 solar masses) will become a giant next, after about 85 million years.
Star B (with a mass of 0.5 solar masses) will become a giant last, after about 12.5 billion years.
Explanation:
A horizontal force of 25 N is required to push a wagon across a sidewalk at a constant speed.
What is the net (unbalanced) force acting on the wagon?
What is the value of the force of friction acting on the wagon?
If the force on the wagon increased to 30 N, use Newton's second law to explain what the effect would be.
If the force on the wagon increased to 30 N, the wagon would accelerate at a rate of 0.5 m/s^2 in the direction of the applied force.
What is Speed?
Speed is a scalar quantity that describes how fast an object is moving, without regard to its direction. It is defined as the distance traveled by an object divided by the time taken to travel that distance. Speed is typically measured in units of meters per second (m/s) or kilometers per hour (km/h).
The net (unbalanced) force acting on the wagon is 25 N, which is equal in magnitude but opposite in direction to the force applied to it.
The value of the force of friction acting on the wagon is also 25 N, since it is equal in magnitude but opposite in direction to the applied force. This is because the wagon is moving at a constant speed, so the net force acting on it must be zero. The force of friction acts in the opposite direction to the applied force, and is necessary to counteract the force and maintain a constabnt speed.
If the force on the wagon increased to 30 N, the net force acting on the wagon would be 5 N (30 N - 25 N). This would cause the wagon to accelerate in the direction of the applied force, since the net force is no longer zero. The acceleration of the wagon can be calculated using Newton's second law:
F = ma
where F is the net force, m is the mass of the wagon, and a is its acceleration. Rearranging the equation to solve for a, we get:
a = F/m
Assuming a mass of 10 kg for the wagon, we can calculate its acceleration as follows:
a = 5 N / 10 kg = 0.5 m/s^2
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a proton enters a uniform magnetic field that is perpendicular to the proton's velocity (figure 1). what happens to the kinetic energy of the proton?
A. it increases.
B. it decreases. C. it stays the same.
D. it depends on the velocity direction.
E. it depends on the b field direction.
The correct answer is C. The kinetic energy of the proton will remain the same if it enters a uniform magnetic field that is perpendicular to its velocity . Therefore, it stays the same.
Kinetic energy is a fundamental concept in physics that refers to the energy of an object in motion. When an object moves, it possesses kinetic energy that is proportional to its mass and the square of its velocity. The formula for kinetic energy is K = 1/2mv^2, where m is the mass of the object and v is its velocity.
The concept of kinetic energy is important in many areas of physics, including mechanics, thermodynamics, and relativity. It is used to describe the motion of particles in a gas, the motion of planets in a solar system, and the motion of subatomic particles in a particle accelerator. The concept of kinetic energy is closely related to other concepts in physics, such as potential energy, work, and momentum. Understanding kinetic energy is essential for understanding the behavior of physical systems in motion.
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a hot iron is turned off and cools down to room temperature. the oron cools because
Answer:
heat energy is transferred from the arm iron to the cooler room. BRAINLIEST ANSWER
2. Which of the following would you keep in an office quick-list file?
O A. Your personal checking account number
O B. Equipment catalogs
OC. An instruction manual
O D. Commonly asked customer questions
Answer:
D. Commonly asked customer questions
Explanation:
Personal checking account numbers should not be stored in an office quick-list file as this information is sensitive and confidential. Equipment catalogs and instruction manuals can be useful, but they are not typically needed in a quick-list format.
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Your ability to process language in the left hemisphere of the brain and spatial in the right hemisphere of the brain is called
Answer: Parietal lobe
Explanation: The parietal lobe controls the ability to read, write, and understand spatial concepts. Therefore, you gain the ability to process language through the left hemisphere of your brain.
A ring of Aluminum bronze alloy has internal diameter 300 mm and 50 mm wide. The coefficient of cubic expansion of alloy is 51 x 10-6/°C. For a temperature rise of 600°C, find the following in mm: a) The final internal diameter. b) The change in width of the ring.
As a result, the ultimate internal diameter is D = 300 mm + D,D = 309.18 mm, and the ring's change in breadth is 1.53 mm.
Why does thermal expansion occur? What is it?Thermal expansion is the process through which an item enlarges and expands as a result of a change in temperature. The molecules take up more space because they move more quickly on average at higher temperatures. As a result, when anything is heated up, it gets bigger.
We must apply the thermal expansion formula to this issue in order to find a solution:
ΔL = α L ΔT
where L is the length change, is the thermal expansion coefficient, L is the starting length, and T is the temperature change.
a) The final internal diameter:
ΔD = α D ΔT
Substituting the values given, we get:
ΔD = (51 x 10^-6/°C) x 300 mm x 600°C
ΔD = 9.18 mm
The final internal diameter is therefore:
D = 300 mm + ΔD
D = 309.18 mm
b) The change in width of the ring:
The original width of the ring is 50 mm. We can use the same formula to find the change in width:
ΔW = α W ΔT
Substituting the values given, we get:
ΔW = (51 x 10^-6/°C) x 50 mm x 600°C
ΔW = 1.53 mm
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Spring constant, Say if we have KEi + PEi + WNC= KEf + PEf , where does the spring potential energy go, before or after?
The spring potential energy is included in the initial potential energy term in the equation KEi + PEi + WNC= KEf + PEf.
What is the formula for calculating the potential energy of a spring?The formula for calculating the potential energy of a spring is PE = (1/2)kx^2, where k is the spring constant and x is the displacement of the spring from its equilibrium position.
How does the spring constant affect the potential energy of a spring?The spring constant (k) determines the stiffness of the spring and how much force is required to stretch or compress it. The greater the spring constant, the more potential energy is stored in the spring for a given displacement from its equilibrium position. This means that a spring with a higher spring constant will have a greater potential energy than a spring with a lower spring constant when stretched or compressed by the same amount.
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Two horizontal forces, F and F₂, act on a box, but only Ę appears in the drawing. Ę₂ can refer to either the right or the left. The square moves along the x axis only. There is no friction between the box and the surface. Suppose F₁ = +4.0 N and the mass of the box is 4.1 kg. Find the magnitude and direction of F₂ when the acceleration of the box is (a) +7.0 m/s², (b) -7.0 m/s², and (c) 0 m/s².
Answer:
Since there is no friction, the net force acting on the box is equal to the sum of the two horizontal forces. From Newton's second law, we know that the net force is equal to the mass of the box times its acceleration. Therefore:
ΣF = m * a
where ΣF is the net force, m is the mass of the box, and a is the acceleration of the box.
We can use this equation to find the magnitude of F₂ in each case.
(a) When the acceleration of the box is +7.0 m/s²:
ΣF = F₁ + F₂
m * a = F₁ + F₂
(4.1 kg) * (7.0 m/s²) = 4.0 N + F₂
F₂ = (4.1 kg) * (7.0 m/s²) - 4.0 N
F₂ = 25.7 N to the right
So, the magnitude of F₂ is 25.7 N, and it acts to the right.
(b) When the acceleration of the box is -7.0 m/s²:
ΣF = F₁ + F₂
m * a = F₁ + F₂
(4.1 kg) * (-7.0 m/s²) = 4.0 N + F₂
F₂ = (4.1 kg) * (-7.0 m/s²) - 4.0 N
F₂ = -32.6 N to the left
So, the magnitude of F₂ is 32.6 N, and it acts to the left.
(c) When the acceleration of the box is 0 m/s²:
ΣF = F₁ + F₂
m * a = F₁ + F₂
(4.1 kg) * (0 m/s²) = 4.0 N + F₂
F₂ = -4.0 N
So, the magnitude of F₂ is 4.0 N, and it acts to the left.
Explanation:
A cyclist is rounding a 20-m -radius curve at 13 m/s.
What is the minimum possible coefficient of static friction between the bike tires and the ground?
The minimum possible coefficient of static friction between the bike tires and the ground is 0.6.
This is calculated by dividing the centripetal force formula.Centripetal force = m*v2/r
Centripetal force = (m*132)/20
Normal force = mg
Normal force = m*9.8
Let us find the minimum coefficient of static friction
The minimum coefficient of static friction = Centripetal force/Normal force
= (m*132)/(20*m*9.8) = 0.6
The minimum coefficient of static friction between the bike tires and the ground is 0.6, which is calculated by dividing the centripetal force of the cyclist by the normal force of the cyclist.
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A 175,000 kg space probe is landing on an alien planet with a gravitational acceleration of 8.25. If its fuel is ejected from the rocket motor at 35,000 m/s what must the mass rate of change of the space ship (delta m)/(delta t) be to achieve at upward acceleration of 2.00 m/s^2? Remember to use the generalized form of Newton's Second Law.
answer with correct units
The mass rate of change of the space probe is approximately 28.49 kg/s .
What is the mass rate of the space probe?To solve this problem, we can use the generalized form of Newton's Second Law, which states that the force acting on an object is equal to its mass times its acceleration:
F = ma
In this case, the force acting on the space probe is the thrust force generated by the rocket motor, which is equal to the rate of change of momentum of the ejected fuel:
F = (Δ m /Δt) * v
where;
Δ m /Δt t is the mass rate of change of the space ship, and v is the velocity of the ejected fuel, which is given as 35,000 m/s.Since the space probe is landing on the planet, the net force acting on it should be equal to the force of gravity pulling it down minus the upward thrust force generated by the rocket motor. So we can write:
F_net = m * g - (Δ m /Δt) * v
Plugging in the values and solving for delta m / delta t, we get:
2.00 m/s² = (175,000 kg * 8.25 m/s²) - (Δ m / Δt) * 35,000 m/s
Δ m / Δt = (175,000 kg * 8.25 m/s² - 2.00 m/s² * 35,000 m/s) / 35,000 m/s
Δm / Δt ≈ 28.49 kg/s
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A 60.0 kg wrecking ball hangs from a uniform, heavy-duty chain of mass of 26.0 kg. Find the maximum tension in the chain.
Answer: The maximum tension in the chain will occur when the wrecking ball is at its lowest point, and the chain is vertical.
The weight of the wrecking ball is:
w = m_ball * g
w = 60.0 kg * 9.81 m/s^2
w = 588.6 N
The weight of the chain is:
w_chain = m_chain * g
w_chain = 26.0 kg * 9.81 m/s^2
w_chain = 254.8 N
At the lowest point, the tension in the chain must be equal to the sum of the weight of the ball and the weight of the chain:
T = w + w_chain
T = 588.6 N + 254.8 N
T = 843.4 N
Therefore, the maximum tension in the chain is 843.4 N.
Explanation:
At which point are two objects said to be at thermal equilibrium with each other?
Group of answer choices
When both their temperature and thermal energy are equal
When their thermal energy is equal
When their heat capacities are equal
When their temperatures are equal
When their temperatures are equal
Explanation:
When two objects are in thermal equilibrium they are said to have the same temperature. During the process of reaching thermal equilibrium, heat, which is a form of energy, is transferred between the objects.
Light is refracted as it travels from a point A in medium 1 to a point B in medium 2. If the index of
refraction is 1.33 in medium 1 and 1.51 in medium 2. How long does it take light to go from A to B,
assuming it travels 331cm in medium 1 and 151 in the medium 2?
The time taken by light to go from A to B is approximately 0.000020087 seconds.
The speed of light in a medium is given by:
v = c/n
where c is the speed of light in vacuum and n is the refractive index of the medium.
In medium 1, the speed of light is:
v1 = c/n1 = c/1.33
In medium 2, the speed of light is:
v2 = c/n2 = c/1.51
The distance that light travels in medium 1 is 331 cm, whereas in medium 2, the distance is 151 cm. The time it takes for light to get from point A to point B is the product of the times it takes in mediums 1 and 2.
t = d1/v1 + d2/v2
Substituting the given values, we get:
t = (331 cm)/(c/1.33) + (151 cm)/(c/1.51)
Since the units of speed and distance are not consistent, we need to convert the units to a common unit. We can use meters as the common unit:
t = (3.31 m)/(c/1.33) + (1.51 m)/(c/1.51)
Now, we can use the value of the speed of light in vacuum:
c = 299792458 m/s
Substituting this value, we get:
t = (3.31 m)/((299792458 m/s)/1.33) + (1.51 m)/((299792458 m/s)/1.51)
t = 0.000015065 s + 0.000005022 s
t = 0.000020087 s.
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1. Given that the atmospheric pressure and density at sea level is 100 kPa and 1.3 kg/m respectively. Calculate the height of the atmosphere if all air in the atmosphere has this density (g = 10 N/kg)
Answer:
P = ρ g H pkgressure due to liquid (gas) of height H
H = 1.00E5 N/m^2 / (1.3 kg / m^3 * 10 N/kg) = 7,700 m
What is the energy required to increase the surface area of a liquid?
Select the correct answer below:
adhesive tension
surface tension
cohesive tension
none of the above
Correct answer:
surface tension
Surface tension is the energy required to increase the surface area of a liquid.
Surface tension is the energy required to increase the surface area of a liquid. Option (b)
Surface tension is the propensity of liquid surfaces at rest to shrink to the smallest feasible surface area. Surface tension permits items with a higher density than water, such as razor blades and insects (such as water striders), to float on the water's surface without being immersed.
Surface tension at liquid-air contacts is caused by the higher attraction of liquid molecules to each other (owing to cohesion) than to air molecules (due to adhesion).There are two main systems at work. The first is an inward strain on the surface molecules, which causes the liquid to constrict.
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If the mass of Jupiter is defined as 1 M_j = 1.90 ✕ 10^27 kg, what is the mass of Saturn (5.68 ✕ 10^26 kg) in units of M_j?
What is the mass of Earth (5.97 ✕ 10^24 kg) in M_j?
What is the mass of Neptune (1.02 ✕ 10^26 kg) in M_j?
Answer: 1. Mass of Saturn in terms of Jupiter mass:
Saturn's mass = 5.68 × 10²⁶ kg
Jupiter's mass, MJ = 1.90 × 10²⁷
Therefore, Saturn's mass in terms of MJ = Saturn's mass/1.90 × 10²⁷
= 0.299 MJ
Therefore, Mass of Saturn is smaller than and is equal to 0.299 times mass of Jupiter.
To convert masses to units of M_j, we need to divide the given mass by the mass of Jupiter:
1 M_j = 1.90 x 10^27 kg
(a) Mass of Saturn in M_j:
Mass of Saturn = 5.68 x 10^26 kg
Mass of Saturn in M_j = (5.68 x 10^26 kg) / (1.90 x 10^27 kg/M_j)
= 0.299 M_j
Therefore, the mass of Saturn in units of M_j is approximately 0.299 M_j.
(b) Mass of Earth in M_j:
Mass of Earth = 5.97 x 10^24 kg
Mass of Earth in M_j = (5.97 x 10^24 kg) / (1.90 x 10^27 kg/M_j)
= 0.00315 M_j
Therefore, the mass of Earth in units of M_j is approximately 0.00315 M_j.
(c) Mass of Neptune in M_j:
Mass of Neptune = 1.02 x 10^26 kg
Mass of Neptune in M_j = (1.02 x 10^26 kg) / (1.90 x 10^27 kg/M_j)
= 0.0537 M_j
Therefore, the mass of Neptune in units of M_j is approximately 0.0537 M_j.
The towing lines of two tugboats pulling horizontally on a barge are at an angle of 30° to each other. The tensions in the towing lines of the first and second tugboats are 3 kN and 4 kN respectively. Calculate the magnitude of the resultant force which the tugboats exert on the barge.
The magnitude of the resultant force exerted on the barge is approximately 3.6 kN.
Step by step explanationTo calculate the magnitude of the resultant force exerted on the barge, we can use the law of cosines:
c^2 = a^2 + b^2 - 2ab cos(C)
where c is the magnitude of the resultant force, a and b are the magnitudes of T1 and T2, respectively, and C is the angle between T1 and T2 (which is 30° in this case).
Substituting the given values, we get:
c^2 = (3 kN)^2 + (4 kN)^2 - 2(3 kN)(4 kN) cos(30°)
c^2 = 9 kN^2 + 16 kN^2 - 24 kN^2 cos(30°)
c^2 = 25 kN^2 - 24 kN^2 cos(30°)
c^2 = 25 kN^2 - 12 kN^2
c^2 = 13 kN^2
c = sqrt(13) kN
c ≈ 3.6 kN
Therefore, the magnitude of the resultant force exerted on the barge is approximately 3.6 kN.
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Catastrophes, significant life changes and sleep were the three examples provided in
the video that lead to stress?
True
False
The statement is False that Catastrophes, significant life changes and sleep were the three examples provided in the video that lead to stress.
What does catastrophe stress look like?disastrous stress .Serious sickness in the child or a family member, natural disasters, and child maltreatment are a few instances of this level of stress. The child's risk is at its maximum at this level.
What three stages of the body's reaction to stress are there?The alarm reaction stage, the resistance stage, and the weariness stage are the several phases of this illness. The "fight or flight" response and the body's earliest signs of acute stress are referred to as the alarm reaction stage.
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which part of dc motor reverse the direction of current through the coil every half cycle
In a DC motor, the part that reverses the direction of current through the coil every half cycle is the commutator. The commutator is a cylindrical structure mounted on the rotor shaft and consists of multiple metal segments separated by insulating material. The segments are connected to the ends of the coils, which are wound on the rotor.
As the rotor turns, the brushes (which are in contact with the commutator) transfer current to the coils through the commutator segments. The current direction in the coil is determined by the orientation of the coil relative to the magnetic field of the stator. When the coil is in one half of its rotation, the current flows in one direction, and when it is in the other half, the current flows in the opposite direction. The commutator reverses the direction of the current through the coil every half cycle to maintain the direction of the torque produced by the motor.
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consider a system consisting of two point particles m1 and m2. the particles are 25 cm apart, the mass of particle m2 is four times the mass of m1, and mass m1 is 5 cm from the origin. calculate the position of the center of mass, xcm.
The position of the center of mass of the system is 21 cm from the origin.
The position of the center of mass of a two-particle system can be calculated using the formula,
xcm = (m1x1 + m2x2) / (m1 + m2)
where x1 and x2 are the positions of particles m1 and m2, respectively, and m1 and m2 are their masses.
Substituting values into the formula for xcm,
xcm = (m1x1 + m2x2) / (m1 + m2)
xcm = (m15 cm + m225 cm) / (m1 + m2)
xcm = (m15 cm + 4m125 cm) / (m1 + 4m1)
xcm = (5 cm + 4*25 cm) / (1 + 4)
xcm = 105 cm / 5
xcm = 21 cm
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A person is trying to ride a bike all the way round the inside ofa pipe for a stunt in a film. The filmmaker wants to know whatspeeds are involved. The pipe has a diameter of 8 m. The mass of the bike and rider is 400 kg. The rider goes at aconstant speed of 5 m/s. a) What is its acceleration at the bottom? b) What is the force on the bike at an angle of 30° up from thebottom? c) What is the minimum velocity at the top for the bike andrider to stay moving in a circle? d) Do the bike and rider have sufficient velocity to stay movingon a circle at the top?
Answer:
a) To find the acceleration at the bottom of the pipe, we can use the formula for centripetal acceleration: a = v^2 / r where v is the velocity, and r is the radius (half of the diameter) of the pipe. Since the velocity is constant and equal to 5 m/s, and the radius of the pipe is 4 m, the acceleration at the bottom is:
a = (5 m/s)^2 / 4 m a = 6.25 m/s^2
b) To find the force on the bike at an angle of 30° up from the bottom, we need to use the formula for centripetal force: F = m * a where m is the mass of the bike and rider (given as 400 kg) and a is the centripetal acceleration calculated in part (a). The force on the bike at an angle of 30° up from the bottom is:
F = 400 kg * 6.25 m/s^2 * cos(30°) F = 3,464 N
c) To find the minimum velocity at the top for the bike and rider to stay moving in a circle, we can use the same formula for centripetal acceleration and solve for velocity: a = v^2 / r v = sqrt(a * r) where r is the radius of the pipe (again, 4 m) and a is the centripetal acceleration required to keep the bike and rider moving in a circle, which is equal to the acceleration due to gravity at the top of the pipe:
a = g = 9.81 m/s^2 v = sqrt(9.81 m/s^2 * 4 m) v = 6.26 m/s
d) Comparing the minimum velocity calculated in part (c) to the constant speed of 5 m/s given in the question, we can see that the bike and rider do have sufficient velocity to stay moving on a circle at the top of the pipe.
Four objects labeled W, X, Y, and Z have different forces applied to them. All of the horizontal forces acting on each object are shown in the diagrams. Identify the example(s) that demonstrate(s) a change in motion.
The horizontal forces acting on each object are shown in the diagrams would only cause a change in motion in diagram A
When does force cause a change in motion?A force causes a change in motion when it is unbalanced, meaning there is a net force acting on an object. According to Newton's first law of motion, an object at rest will remain at rest, and an object in motion will continue to move in a straight line at a constant speed, unless acted upon by an unbalanced force.
When an unbalanced force acts on an object, it will accelerate, meaning its velocity will change.
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A child sits on a merry‑go‑round that has a diameter of 5.00 m. The child uses her legs to push the merry‑go‑round, making it go from rest to an angular speed of 20.0 rpm in a time of 41.0 s.
What is the average angular acceleration avg of the merry‑go‑round in units of radians per second squared (rad/s2)?
What is the angular displacement Δ of the merry‑go‑round, in units of radians (rad),
during the time the child pushes the merry‑go‑round?
The child pushes the merry-go-round, which causes it to rotate by an angle of around 85.5 radians.
What is the merry-go-moment round's of inertia?The sum of the moments of inertia of the toddler and the merry-go-round (both about the same axis) represents the total moment of inertia: I=(28.13kg⋅m2)+(56.25kg⋅m2)=84.38kg⋅m2. When known values are substituted into the equation.
ω1 = 0 rad/s (initially at rest)
ω2 = (20.0 rpm) * (2π rad/rev) / (60 s/min) ≈ 4.19 rad/s
The average angular acceleration is given by the equation:
αavg = (ω2 - ω1) / t
where t is the time interval. Substituting the given values, we get:
αavg = (4.19 rad/s - 0 rad/s) / 41.0 s
αavg ≈ 0.102 rad/s²
Therefore, the average angular acceleration of the merry-go-round is approximately 0.102 rad/s².
To find the angular displacement of the merry-go-round, we can use the equation:
Δθ = ω1*t + (1/2)αt²
where ω1 is the initial angular speed, α is the average angular acceleration, and t is the time interval.
Substituting the given values, we get:
Δθ = 0 rad/s * 41.0 s + (1/2) * (0.102 rad/s²) * (41.0 s)²
Δθ ≈ 85.5 rad
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What happens to the Sun's energy as it passes through the atmosphere to Earth's surface?
Some of the Sun's energy is absorbed, scattered, or reflected as it travels through the atmosphere to the surface of the Earth by a variety of atmospheric constituents, including gases, aerosols, clouds, and the Earth's surface.
What uses does the atmosphere make of solar energy?50% of the heat energy from the Sun can reach Earth's surface thanks to the atmosphere. The Sun's energy is reflected back into space at a rate of 30%. The atmosphere greenhouse gases, such as carbon dioxide, water vapour, and methane, absorb 20% of the remaining solar energy.
When solar energy travels through the stratosphere, what happens to it?Ozone (O3) in the upper atmosphere absorbs a substantial amount of the Sun's ultraviolet (high-energy, shortwave) light (the stratosphere). The Earth system does not become hotter as a result of solar radiation that Earth's surface or atmosphere reflect back into space. Heat is produced as a result of absorbed radiation.
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