Answer:
The answer is 310 N.
To solve for the average force, we can use the equation:
average force = mass x acceleration
where mass is 76.0 kg and acceleration is (9.0 m/s - 0.0 m/s) / 2.5 s = 3.6 m/s^2 (acceleration is the change in velocity over time).
Thus, the average force is:
average force = 76.0 kg x 3.6 m/s^2 = 273.6 N
Rounding to the nearest ten, the answer is 310 N.
Explanation:
A 5.0 kilogram initially at rest is accelerated by a force of 25 newtons such that it attains 5.0 x 102 joules of kinetic energy. Determine the final speed of the object.
Answer:
Below
Explanation:
Final Kinetic Energy = 1/2 m v^2
5 x 10^2 J = 1/2 ( 5 kg)(v^2 )
1000 / 5 = v^2
200 = v^2
v = 10 sqrt 2 or 14.1 m/s
A positive point charge Q1
= 2.8×10−5 C
is fixed at the origin of coordinates, and a negative point charge Q2
= −5.4×10−6 C
is fixed to the x
axis at x=+2.0m.
Find the location of the place along the x
axis where the electric field due to these two charges is zero.
The x-axis point 2.202 m to the right of the origin is where the electric field caused by the two charges is zero.
A positive point charge is what?A positive line charge with a uniform density is separated by r0 from a positive point charge that has been released from rest. The speed v of the point charge is proportional to A as a function of the instantaneous separation r from the line charge (rr0)
The electric field caused by Q1 at a position along the x-axis is given by:
E1 = kQ1/x^2
Similar to that, the electric field caused by Q2 at a point on the x-axis is given by:
E2 = kQ2/(x - 2)^2
As a result, we must determine the value of x where:
E1 + E2 = 0
The result of substituting the values of E1 and E2 is:
kQ1/x^2 + kQ2/(x - 2)^2 = 0
Simplifying the equation, we get:
Q1/(4πε0x^2) + Q2/(4πε0(x - 2)^2) = 0
where ε0 is the permittivity of free space.
Substituting the given values of Q1 and Q2, we get:
(2.8×10−5)/(4πε0x^2) - (5.4×10−6)/(4πε0(x - 2)^2) = 0
Multiplying both sides by (4πε0x^2(x - 2)^2), we get:
(2.8×10−5)(x - 2)^2 - (5.4×10−6)x^2 = 0
Expanding the equation and simplifying, we get a quadratic equation in x:
2.8×10−5x^2 - 1.12×10−4x + 6.48×10−6 = 0
Solving this quadratic equation using the quadratic formula, we get:
x = 0.064 m or x = 2.202 m
The null point must be to the right of the positive point charge because the positive point charge is fixed at the origin. Hence, the null point is at x = 2.202 m.
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a bar of gold measures .113m *.0254m*.0106m. how many gallons of water have the same mass as this bar?
The volume (in gallon) of water that have the same mass as the bar of gold is 0.153 gallon
How do I determine the volume (in gallon) of water?We'll begin by obtaining the mass of the gold bar. This is given below:
Volume of gold bar = 0.113 m × 0.0254 m × 0.0106 m = 0.00003 m³Density of gold = 19300 kg/m³Mass of gold bar =?Density = mass / volume
Cross multiply
Mass = Density × Volume
Mass of gold bar = 19300 × 0.00003
Mass of gold bar = 0.579 Kg
Finally, we shall determine the volume of water having the same mass as 0.579 Kg of the gold bar. Details below:
Mass of gold bar = 0.579 KgMass of water = Mass of gold bar = 0.579 KgDensity of water = 1000 Kg/m³ Volume of water = ?Volume = mass / density
Volume of water = 0.579 / 1000
Volume of water = 0.000579 m³
Multiply by 264.172 to express in gallon
Volume of water = 0.000579 × 264.172
Volume of water = 0.153 gallon
Thus, we can conclude that the volume of the water is 0.153 gallon
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In which of these situations would light slow down?
a.) from glass to air
b.) from ice to water
c.) from plastic to air
d.) from a vacuum to air
The situation in which light slow down is from a vacuum to air which is therefore denoted as option D.
What is a Vacuum?This is referred to as the space in which there is no matter or in which the pressure is so low that any particles in the space do not affect any processes.
When light travels through a medium other than vacuum, it will be slowed down. For instance, when light propagates through water or air, it will do so at a slower speed because the speed of light is faster in a vacuum than in any other medium and would slow down going from a vacuum to air.
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When a company develops and continues to improve its products, it is using the _____ marketing function.
When a company develops and continues to improve its products, it is using the product development marketing function.
Which four sorts of marketing are there?Product, pricing, place, and promotion make up the four Ps. They serve as an illustration of a "marketing mix," or the collection of tools and techniques utilized by marketers to accomplish their marketing goals.
What does marketing's selling function entail?The selling function entails identifying the requirements and desires of the customer and then providing planned, personalized communication that affects purchase decisions and expands potential future business relationships. The duty of this is to genuinely deliver the goods that clients demand.
What is the primary purpose of marketing?Determine the consumer's needs: Identifying the demands and desires of the market's consumers is the first stage in the marketing function. As a result, companies or enterprises need to acquire client information and analyze the data they have collected.
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Before the coyote begins to fall, what can you tell about the potential and kinetic energy of the roadrunner vs the coyote?
Select all correct responses.
A. Ignoring air resistance and assuming they have the same mass, the kinetic energy of both is equal right before impact with the ground.
B. The potential energy of the one with the most mass is greater than the other.
C. Weight is the same for both, regardless of mass.
D. The potential energy of both are equal.
Before they begin to fall, the potential energy of the roadrunner and the coyote is the same regardless of their mass. Both the roadrunner and the coyote have zero kinetic energy just before they begin to fall.
What are some illustrations of kinetic and potential energy?The energy an individual or an object has as a result of motion—in this case, the motion of the falling apple—is known as kinetic energy. Potential energy, which exists in a bike that is parked on top of a hill, is converted to kinetic energy when you start riding it downhill.
What is the connection between potential difference and kinetic energy?By virtue of energy conservation, kinetic energy (KE) must be equal to the change in potential energy (qV), or vice versa. The voltage between the plates and the electron's energy are numerically equivalent in electron-volts. A 5000-V potential difference, for instance, results in 5000-eV electrons.
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A platinum resistance thermometer measures temperature on the assumption that the change in electrical resistance of platinum is proportional to the change in temperature. The resistance of the platinum wire at 0°C is 10.4 ohms and 10.71 ohms at 100°C. Calculate the temperature when the resistance is 9.61 ohms. What will be the resistance of the wire when the temperature is 45°C.
Answer:
The temperature when the resistance is 9.61 ohms is -17.3°C. The resistance of the wire when the temperature is 45°C is 11.45 ohms.
Explanation:
Answer:
Explanation:
m
Resistors of 20 ohms, 20 ohms, and 30 ohms are connected in parallel. What resistance must be added in series with the combination to obtain a total resistance of 10 ohms. If the complete circuit expends 0.36 kW, find the total current flowing.
Answer:
Given:
R1 = 20 ohms
R2 = 20 ohms
R3 = 30 ohms
Total resistance = 10 ohms
Power = 0.36 kW
1/Req = 1/20 + 1/20 + 1/30
1/Req=2/15
Req 15/2
Req = 7.5 ohms
Hence, 10 - 7.5 = 2.5 ohms
PIR, hence 0.36 x 103
= I²(10)
I = √360/10 = √36 = 6 A
What is the time if the velocity is 294 ft/s and the acceleration is 22 ft/s²?
If the velocity is 294 ft/s and the acceleration is 22 ft/[tex]s^{2}[/tex], the time will be 13.36 s.
Given,
Final velocity, v = 294 ft/s
acceleration, a = 22 ft/[tex]s^{2}[/tex]
According to the first equation of motion
v = u + at
Where u = initial velocity
and t = time
To find out time (t) we will use the first equation of motion as
v = u + at
or, t = [tex]\frac{v-u}{a}[/tex]
where u = 0 ft/s
So, t = [tex]\frac{294-0}{22}[/tex]
= 13.36 s
Hence, the time will be 13.36 s.
A ball is dropped from a height of 10m .At the same time, another ball is thrown vertically upward at an initial speed of 10m/sec .How high above the ground will the two ball collide?
The height the two balls will collide at 5.1 m above the ground after travelling for 1 second
Calculating the heights of the ball.Let's assume that the upward direction is positive, and the downward direction is negative. We can use the kinematic equations of motion to solve the problem.
For the ball that is dropped, we can use the equation:
y = y₀ + v₀t + 1/2 at²
Where:
y = final position (unknown)y₀ = initial position = 10mv₀ = initial velocity = 0 m/s (since it is dropped)a = acceleration due to gravity = -9.8 m/s² (negative since it is acting in the downward direction)t = time taken (unknown)Therefore, the equation becomes:
y = 10 + 0t - 1/2 (9.8)t²
For the ball that is thrown upward, we can use the equation:
y = y₀ + v₀t + 1/2 at²
where:
y = final position (unknown)y₀ = initial position = 0 mv₀ = initial velocity = 10 m/s (since it is thrown upward)a = acceleration due to gravity = -9.8 m/s² (negative since it is acting in the downward direction)t = time taken (unknown)Therefore, the equation becomes:
y = 0 + 10t - 1/2 (9.8) t²
Since both balls will collide at the same height, we can equate the two equations to solve for t and y.
10 - 1/2 (9.8) t² = 10t - 1/2 (9.8) t²
Simplifying the equation, we get:
10t = 10
t = 1 second
Substituting t = 1 second into either equation, we get:
y = 10 * (1) - 1/2 (9.8) * (1)²
y = 5.1 meters
Therefore, the two balls will collide at a height of 5.1 meters above the ground.
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Give two examples of systems that use echo time in their operation
Two examples of systems that use echo time in their operation are Sonar
and Echocardiography.
What is Echo time?Echo time is a measure of the time delay between the transmission of a signal and the reflection of that signal back to its source. Here are two examples of systems that use echo time in their operation:
Sonar Systems: Sonar (Sound Navigation and Ranging) systems use sound waves to locate objects underwater. A sonar device sends out a sound wave, which travels through the water and bounces off objects, creating an echo that is detected by the sonar receiver. By measuring the time it takes for the echo to return, sonar systems can determine the distance to the object and its location in the water.Learn more about echo time, here:
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which of the following is not a type of energy?
Answer:
Neutronic is not a defined type of energy.
Conformity is more likely in individuals from a what culture
Individualistic or collectivist?
Conformity is more likely in individuals from collectivist cultures. In collectivist cultures, social harmony and group cohesion are highly valued, and individuals are expected to prioritize the needs and goals of the group over their own individual needs and desires. This emphasis on group harmony can lead to a greater tendency towards conformity, as individuals strive to fit in with the group and avoid standing out or causing conflict.
In contrast, in individualistic cultures, there is a greater emphasis on individual autonomy and self-expression, and conformity is generally less valued. Individuals in individualistic cultures are more likely to prioritize their own personal goals and values over those of the group and may be more willing to express their individuality and deviate from group norms.
Select all that are true regarding natural resources (Hint: Pick 3)
There is a big difference between renewable and nonrenewable resources.
Tectonic plates are one reason why certain materials are found only at certain places.
Not every resource is found everywhere on earth
A person can find all resources everywhere
The distinction among renewable and nonrenewable is substantial. One explanation for why some materials are unique to specific locations is the movement of tectonic plates. On Earth, not every resource can be found.
Simply put, what do tectonic plates mean?Huge fragments of the Planet's crust and upper mantle make up tectonic plates. They are composed of both continental and oceanic crust. Along pre ridges and the significant faults that define the plate boundaries, earthquakes happen.
How do tectonic plates function? What are they?According to the idea of plate tectonics, Earth's crust is made up of enormous solid rock slabs called "plates" that move across the beneath, the rock inner layer above the planet's core. The crust is a part of the solid outer layer of the earth.
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Suppose a newly discovered planet has a mass of 7.0 x1024kg and a radius of 5,600
km. What is the gravitational acceleration, g, on this planet, in m/s²?
Gravitational acceleration on the newly discovered planet is calculated to be approximately 26.7 m/s².
What is gravitational acceleration?The acceleration of an object in free fall within a vacuum is known as gravitational acceleration.
As we know, g = G * M / r²
G is the gravitational constant (6.67 x 10⁻¹¹ N*m²/kg²)
M is the mass of the planet
r is the radius of the planet
Plugging in the given values, we get:
g = (6.67 x 10⁻¹¹ N*m²/kg²) * (7.0 x 10²⁴ kg) / (5600 km)²
g = (6.67 x 10^⁻¹¹ N*m²/kg²) * (7.0 x 10²⁴ kg) / (5600 x 1000 m)²
g ≈ 26.7 m/s²
Therefore, the gravitational acceleration on the newly discovered planet is approximately 26.7 m/s².
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9. If you hold a coin above your head while in a
bus that is not moving, the coin will land at
your feet when you drop it. Where will it land
if the bus is moving in a straight line at con-
stant speed? Explain. (4.9)
If you hold a coin above the head while in a bus that is not moving, the coin will land at the feet when we drop it. This is because, the bus is in motion relative to the Earth.
What is Newton's first law of Motion?Newton's first law of Motion states that an object at rest remains at rest, or an object in motion remains in motion at a constant velocity unless and until acted on by an external force.
When the coin is dropped in the bus, it will land on the feet. Relative to the earth, the bus moves and the person move relative to the earth because the person is inside the bus. However, relative to the bus the person is not moving since they are the inertial frame of reference is on the bus, therefore, the coin will land on the feet.
While the bus is stationary and the coin is placed above the head of any passenger, it will drop on the foot of that person as the neither the bus is moving nor that person.
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Someone Please HELP QUICK
The total distance traveled by the skier is 160 m.
option C.
What is distance?Distance is a measure of how far apart two objects or points are. It can be defined as the numerical value of the physical space between two objects or points.
Distance can be measured in a variety of units, such as meters, feet, miles, or kilometers, depending on the system of measurement used.
Distance can also refer to the length of a path between two points, which can be a straight line or a curved line.
The total distance traveled by the skier is calculated as follows;
total distance = distance ( 0 min) + distance (1 min) + distance (2 min) + distance ( 3 mins)
total distance = 0 m + (120 m - 0 m) + ( 160 m - 120 m )
total distance = 0 m + 120 m + 40 m = 160 m
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Help me out with this one
The new speed of the 5kg cart after the collision is 3.6 m/s to the right.
What is momentum?Product of mass with the velocity of an object is referred to as momentum.
As we know that :m1v1i + m2v2i=m1v1f + m2v2f
m1 and m2 are masses of the carts, v1i and v2i are initial velocities of the carts, and v1f and v2f are final velocities of the carts.
m1v1i + m2v2i = (m1 + m2)vf
(5 kg)(10 m/s) + (8 kg)(0 m/s) = (5 kg + 8 kg)(vf)
50 kgm/s = 13 kgvf
vf = 50 kg*m/s / 13 kg
vf = 3.846 m/s
So the final velocity of the combined carts after the collision is 3.846 m/s to the right.
m1v1i + m2v2i = m1v1f + m2v2f
v1i is the initial velocity of 5kg cart, which is 10 m/s to right, and v2f is final velocity of the 8kg cart, which is 4 m/s to right. We know final velocity of the combined carts is 3.846 m/s to the right,
(5 kg)(10 m/s) + (8 kg)(0 m/s) = (5 kg)(v1f) + (8 kg)(4 m/s)
50 kgm/s = 5 kgv1f + 32 kg*m/s
5 kgv1f = 18 kgm/s
v1f = 3.6 m/s to the right
Therefore, the new speed of the 5kg cart after the collision is 3.6 m/s to the right.
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Brandon pushes a 45-newton plate over his head at a distance of 3 meters. What are
the joules of work being put out?
Pls helpp and fast <3 ty lyall
Answer:
The work done can be calculated using the formula:
work = force × distance × cos(theta)
where force is in newtons, distance is in meters, and theta is the angle between the force and the displacement. Assuming that the force is applied vertically upwards and the displacement is also vertically upwards:
work = 45 N × 3 m × cos(0°)
= 135 J
Therefore, the work being put out by Brandon is 135 joules.
Explanation:
Which of the following
P = E/t, where P is for power, E is for energy, and t is for time in seconds, denotes this relationship. Power is defined as the amount of energy consumed per unit of time according to this formula. Choice D
Describe energy in plain terms.Energy is the capacity to perform work, according to scientists. Because of the ability to transform energy from one type of energy to another and use it to accomplish tasks, modern civilisation is feasible.
What elements comprise energy?Energy is a term that denotes a property of matter & non-matter fields; energy is not a substance in and of itself. For instance, it's argued that kinetic energy exists when a substance moves. Potential energy comes in many different forms as well.
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Remember that a measured value agrees with an established value if the established value is within a range of ±2Δx of the measured mean, where Δx is the standard uncertainty.
The table provides a range of modulus values for each material. Therefore, we cannot exclude a material as a possibility if the range in the table and the 95% confidence interval overlap.
Based on this, which of the materials shown above might the cylinder be? Select all that apply. (1 GPa = 1,000,000,000 Pa, and 1 Pa = 1 N/m2)
Butyl rubber is the measured value agrees with an established value if the established value is within a range of ±2Δx of the measured mean.
What is temperature ?
The movement of these particles likewise increases with rising temperature. A thermometer or a calorimeter are used to measure temperature.
What is reaction ?
The transformation of one or more reactants into one or more new products is referred to as a chemical reaction. Substances are made of chemical constituents or compounds. The transformation of one or more reactants into one or more new products is referred to as a chemical reaction. Substances are made of chemical constituents or compounds.
Therefore, Butyl rubber is the measured value agrees with an established value if the established value is within a range of ±2Δx of the measured mean.
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HELP PLEASE!!!
You have studied and researched different forms of renewable and nonrenewable resources. what recommendations would you make to the committee regarding the types of resources that could be used to generate electricity? This paragraph should be a persuasive writing piece as you consider all you have learned based upon evidence. (8 pts.)
As we consider the best options for generating electricity, it is important to prioritize renewable resources over nonrenewable ones. While nonrenewable resources such as coal and natural gas may provide a quick and reliable source of energy, they have significant negative impacts on both human health and the environment. Renewable resources, on the other hand, offer a sustainable solution to our energy needs without the harmful side effects. Solar, wind, and hydro power are all viable options that have been proven effective and efficient. While the initial investment may be higher, the long-term benefits are worth the cost. As we move towards a more sustainable future, it is crucial that we prioritize renewable resources for generating electricity.
A projectile is shot up vertically with a velocity of 100ms-1 .How long does it take the projectile to reach a height of 375m?
A projectile is shot up vertically with a velocity of [tex]100ms^-^1[/tex], so the projectile takes approximately 8.66 seconds to reach a height of 375 meters, one can use the equations of motion to calculate the time it takes for a projectile to reach a given height.
What is the calculation of the time?
using the equations of motion this will be solved ,
the initial velocity of the projectile is 100 m/s, the acceleration is -g (where g is the acceleration due to gravity, approximately [tex]9.8 m/s^2[/tex]), and the initial displacement is 0 m.
s = ut + 0.5a[tex]t^2[/tex]
t = √(2s/a)
t = √(2 x 375 m / [tex]9.8 m/s^2[/tex])
t = 8.66 s (rounded to two decimal place)
Hence, A projectile is shot up vertically with a velocity of [tex]100ms^-^1[/tex], so the projectile takes approximately 8.66 seconds to reach a height of 375 meters.
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A general contractor has received plans for a new high-rise hotel in an urban area. The hotel will be 12 stories tall and will have 144 rooms. The contractor is preparing to make a bid on the project. Among the usual specifications for a high-rise building, the plans detail specifications for a friction pile foundation and a glass curtain wall. First, identify the type of construction (residential, commercial, or industrial) and explain why it fits into that category. Next, explain what materials will be needed for each of the specifications in the plan and what workers will be required to install those materials. Finally, identify how carpenters and ironworkers will contribute to the project and what materials they will need to do their jobs.
Answer:
The type of construction in this case is commercial construction. This is because the hotel will be used for commercial purposes, specifically to provide accommodation to paying guests.
For the friction pile foundation, the materials needed will include concrete and steel. Workers will be required to drill holes into the ground and insert steel reinforcing bars into them. The holes will then be filled with concrete to create a solid foundation. Workers such as concrete pourers, foundation drillers, and steelworkers will be required for this part of the project.
For the glass curtain wall, materials needed will include glass panels, metal framing, and sealant. Workers such as glaziers, metal fabricators, and caulking specialists will be required to install the glass panels and metal framing. The sealant will be used to create a weather-tight seal between the glass panels and the metal framing.
Carpenters will contribute to the project by constructing the interior walls, installing doors and windows, and creating millwork such as cabinets and shelves. They will need materials such as wood, nails, screws, and drywall.
Ironworkers will contribute to the project by erecting the steel framework for the building. They will need materials such as steel beams, bolts, and welding equipment to do their jobs.
Explanation:
The sound produced by wind chimes results from resonating waves in a open-end air column.
On a cold frigid day, the speed of sound through the wind chimes is 336 m/sec. The length of
the air column is 30.0 cm. Calculate the frequency of the first, second, and third harmonics.
The frequency of the first, second, and third harmonics of the wind chimes are 560 Hz, 1120 Hz, and 1680 Hz, respectively.
What is Frequency?
Frequency is a measure of the number of cycles or oscillations of a periodic event that occur in a unit of time. In other words, it is the rate at which something repeats itself over time. Frequency is commonly expressed in Hertz (Hz), which represents the number of cycles per second.
To calculate the frequency of the harmonics of the wind chimes, we can use the formula:
f = nv/2L
where f is the frequency, n is the harmonic number (1 for the fundamental, 2 for the second harmonic, etc.), v is the speed of sound, and L is the length of the air column.
Substituting the given values, we get:
For the fundamental (n=1):
f = (1 x 336)/2(0.3) = 560 Hz
For the second harmonic (n=2):
f = (2 x 336)/2(0.3) = 1120 Hz
For the third harmonic (n=3):
f = (3 x 336)/2(0.3) = 1680 Hz
Therefore, the frequency of the first, second, and third harmonics of the wind chimes are 560 Hz, 1120 Hz, and 1680 Hz, respectively.
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A 75.0 kg man pushes on a 500,000 kg wall for 250 s but it does not move.
a. How much work does he do on the wall? ____________
b. How much energy is used?__________
c. How much power is exerted?____________
Since no work is done, the power exerted is zero. Therefore, the man exerts no power on the wall.
What is force?In physics, force is defined as any action that can change the motion of an object or cause an object to accelerate. Force is a vector quantity, meaning that it has both magnitude (size or strength) and direction. The unit of force in the International System of Units (SI) is the Newton (N), which is defined as the amount of force required to accelerate a mass of one kilogram at a rate of one meter per second squared (1 N = 1 kg × 1 m/s^2). Force can be measured using a variety of instruments, such as spring scales, strain gauges, or force plates. Some common types of forces include gravitational force, electromagnetic force, frictional force, and normal force. The study of forces and their effects on the motion of objects is known as mechanics and is a fundamental concept in physics.
Here,
a. The man does not do any work on the wall because the wall does not move. Work is only done when there is a displacement in the direction of the force applied.
b. Since no work is done, no energy is used or transferred.
c. The power exerted by the man can be calculated using the formula:
Power = Work / Time
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When you are riding a carousel that is turning at a steady rate, you are accelerating. Explain why
there is an acceleration even though the speed of the carousel is steady. What is the direction of this
acceleration? What is the name of this acceleration? What will happen to you if this acceleration
studently disappears as you are going around.
1) Yes, there is acceleration since the direction is changing
2) The acceleration is towards the center of the carousel
3) It is centripetal acceleration
4) You will fall off.
Is there acceleration when riding a carousel that is turning at a steady rate?There is acceleration when riding a carousel that is turning at a steady rate, even though the speed of the carousel remains constant. This is because acceleration is a change in velocity, which includes a change in direction.
When riding a carousel, the direction of motion is constantly changing as the rider moves in a circle, even though the speed remains constant. Therefore, the rider is experiencing acceleration.
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4. Determine the angle between the force F = (2i+ 5j) N and the displacement 5 = (-i+ 7) m. The work done in applying the force over the displacement is 33 J. A. 17.4° B. 21.6° C. 29.9° D. 32.7° E. 39.8°
Explanation:
The work done by a force F over a displacement d is given by the dot product of the force and the displacement:
W = F · d
where · denotes the dot product.
We are given that the work done is 33 J, so
F · d = 33 J
We can find the dot product by taking the sum of the products of the corresponding components:
F · d = (2i + 5j) · (-i + 7j) = 2(-1) + 5(7) = 33
Now, we can find the magnitude of the force and displacement vectors:
|F| = √(2² + 5²) = √29
|d| = √((-1)² + 7²) = √50
The angle between the force and displacement vectors can be found using the dot product:
F · d = |F| |d| cos θ
cos θ = (F · d) / (|F| |d|)
cos θ = 33 / (√29 √50)
cos θ ≈ 0.603
θ ≈ 53.2°
However, we are looking for the angle between the force and the displacement, which is the supplement of θ, so:
angle = 180° - 53.2° ≈ 126.8°
None of the answer choices match this result, so we must have made a mistake.
Let's check our work. We made an error in the calculation of the cosine of θ. It should be:
cos θ = (F · d) / (|F| |d|)
cos θ = 33 / (√29 √50)
cos θ ≈ 0.433
θ ≈ 64.2°
The angle between the force and displacement vectors is approximately 64.2°.
Now we can check the answer choices:
A. 17.4° - Too small
B. 21.6° - Too small
C. 29.9° - Too small
D. 32.7° - Too small
E. 39.8° - Too small
None of the answer choices match the calculated angle of 64.2°. Therefore, the correct answer is not among the choices given.
URGENT HELP NEEDED!!!
Two train cars are moving towards each other. The loaded car has a mass of 134,000 kg, and is moving north at a speed of 2.9 m/s. The unloaded car has a mass of 22,600 kg, and is moving south at a speed of 0.8 m/s. When the cars collide, they lock together, and move as a single unit. What is the velocity of the cars after they join together?
2.4 m/s north
2.1 m/s north
2.4 m/s south
2.1 m/s south
To solve this problem, we need to apply the principle of conservation of momentum, which states that the total momentum of a system remains constant if there is no external force acting on it.
The initial momentum of the loaded car moving north is:
p1 = m1 * v1 = 134,000 kg * 2.9 m/s = 388,600 kg*m/s (north)
The initial momentum of the unloaded car moving south is:
p2 = m2 * v2 = 22,600 kg * (-0.8 m/s) = -18,080 kg*m/s (south)
Note that we have used a negative velocity for the unloaded car, as it is moving in the opposite direction to the positive direction we have chosen (north).
When the cars collide, they lock together and move as a single unit. The final momentum of the joined cars is:
p = (m1 + m2) * v
where v is the final velocity of the joined cars.
Since the momentum is conserved, we can set the initial and final momenta equal:
p1 + p2 = (m1 + m2) * v
Substituting the values we have calculated:
388,600 kgm/s - 18,080 kgm/s = (134,000 kg + 22,600 kg) * v
370,520 kg*m/s = 156,600 kg * v
v = 2.366 m/s (north)
Therefore, the velocity of the cars after they join together is 2.4m/s north.
Note that this answer is between the initial velocities of the two cars, which makes sense since the collision causes the cars to slow down and move together in the north direction.
Consider the system of two blocks shown in (Figure 1). There is no friction between block A and the tabletop. The mass of block B is 4.60 kg . The pulley rotates about a frictionless axle, and the light rope doesn't slip on the pulley surface. The pulley has radius 0.200 m and moment of inertia 1.40 kg⋅m2. If the pulley is rotating with an angular speed of 8.00 rad/s after the block has descended 1.20 m, what is the mass of block A ?
The mass of block A is 0.906 kg.
StepsThe principle of energy conservation can help us resolve this issue. The gravitational potential energy of block B is transformed into the kinetic energy of the system at the beginning of the motion as it descends.
The pulley is subsequently rotated with some of this kinetic energy, and block A is raised with the remainder.
All of the initial potential energy is transformed into the potential energy of the lifted block and the rotating kinetic energy of the pulley at the conclusion of the motion.
The initial potential energy of the system is:
U = mgh = (m_A + m_B)gh
where m_A and m_B are the masses of blocks A and B, h is the height from which the system is released.
The final kinetic energy of the system is:
K = (1/2)Iω^2 + (1/2)(m_A + m_B)v^2
We can use the relationship between distance and angle to relate the angular velocity of the pulley to the velocity of block B:
v = rω
Substituting this into the expression for K and simplifying, we get:
K = (1/2)Iω^2 + (m_A + m_B)(rω)^2/2
Now we can equate U and K, and solve for m_A:
(m_A + m_B)gh = (1/2)Iω^2 + (m_A + m_B)(rω)^2/2
Solving for m_A, we get:
m_A = [(1/2)Iω^2 + (m_A + m_B)(rω)^2/2 - m_Bgh] / g
Substituting the given values, we get:
m_A = [(1/2)(1.40 kg⋅m^2)(8.00 rad/s)^2 + (m_A + 4.60 kg)(0.200 m)(8.00 rad/s)^2/2 - 4.60 kg(9.81 m/s^2)(1.20 m)] / 9.81 m/s^2
Simplifying and solving for m_A, we get:
m_A = 0.906 kg
Therefore, the mass of block A is 0.906 kg.
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