A roller coaster car is released from rest as shown in the image below.
Ignoring friction, what will be the approximate velocity of the car when it
reaches the bottom of the roller coaster in the image? (Recall that g = 9.8
m/s².)
49 m
OA. 16 m/s
OB. 48 m/s
OC. 55 m/s
OD. 31 m/s

Recall the definition of average velocity:

average v = ∆x / ∆t

The driver moves a distance of ∆x = 4.25 km = 4250 m in 2 min = 120 s, so the average velocity is

average v = (4250 m) / (120 s) ≈ 35.4 m/s

Under constant acceleration, the average velocity can also be computed by taking the average of the initial and final velocities:

average v = (initial v + final v) / 2

Solve for (final v) :

35.4 m/s = (20 m/s + final v)/2

final v ≈ 50.83 m/s

Recall the definition of average acceleration:

average a = ∆v / ∆t

Solve for a :

a = (50.83 m/s - 20 m/s) / (120 s)

a ≈ 0.257 m/s²

The magnetic force per unit length of the wire is (C) (0.49i - 0.51j - 1.37k) N/m.

To calculate the magnetic force per unit length of the wire, we can use the formula:

F = I * (L x B),

where F is the force, I is the current, L is the length vector of the wire, and B is the magnetic field.

Given:

Current, I = 3A

Length vector, L = √√3 * (i + j + k)

Magnetic field, B = 0.75i + 0.4k

Let's calculate the cross product of L and B:

L x B = | i j k |

|√√3 √√3 √√3|

|0.75 0 0.4|

To evaluate this cross product, we calculate the determinants:

(i) component: (√√3 * 0 - √√3 * 0.4) = -0.4√√3

(j) component: (-√√3 * 0.75 - √√3 * 0) = -0.75√√3

(k) component: (√√3 * 0.75 - √√3 * 0) = 0.75√√3

Now, multiply the cross product by the current:

F = 3A * (-0.4√√3i - 0.75√√3j + 0.75√√3k)

Simplifying this expression gives:

F = (-1.2√√3i - 2.25√√3j + 2.25√√3k) N

Therefore, the magnetic force per unit length of the wire is approximately (-1.2√√3i - 2.25√√3j + 2.25√√3k) N/m.

Comparing the given answer options, the closest match is C. (0.49i - 0.51j - 1.37k) N/m.

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The speed does the block move after it is hit by the bullet that remains stuck inside the block will be 23.7 m/sec and it takes 12.07 seconds to stop.

According to the law of conservation of momentum, the momentum of the body before the collision is always equal to the momentum of the body after the collision.

Apply the law of conservation of momentum principle;

m₁v₁+m₂v₂cosΘ =(m₁+m₂)V

3 kg ×  12 m/s +  0,1 kg × 400 m/s cos 20° = (3+0.1)V

36 + 40 cos 20° = 3.1 V

V=23.7 m/sec

The time it takes to stop when the friction coefficient between the block and the surface is 0.2 is found as;

V = u +at

V = 0+ μgt

23..7=0.2× 9.81 ×t

t=12.07 sec

Hence, it takes 12.07 seconds to stop.

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B=0I2R(at centre of loop), B = 0 I 2 R(at centre of loop), where R is the loop's radius, gives the magnetic field strength at the loop's centre.

The magnetic field strength diminishes with increasing radius. Radius of the loop has an inverse relationship with magnetic field intensity.

With its plane normal to an external field of magnitude 5.0102T, a circular coil with a radius of 10 cm and 16 turns that is carrying a current of 0.75 A is at rest. The coil is unrestricted in its ability to rotate around an axis in a plane perpendicular to the field direction.

Hence, the integral around any circle's diameter that is centred on a wire.

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Movement of an object with negative (-) slope in the negative (-) quadrant of a velocity/time graph is that the object constantly speeds up.

The slope of velocity-time graph of an object represents the magnitude of acceleration of the object,

Velocity-Time graph can be possible only in two quadrants, either first or fourth, Velocity-time graph is not possible in the third and second quadrant because in these two quadrants, time becomes negative and no such thing as negative time has been discovered till now.

Negative slope means the lines making an angle in clock-wise direction with respect to co-ordinate axes.

Negative Quadrant can only mean the fourth quadrant here, because in first quadrant both velocity and time are positive.

Negative (-) slope in the negative fourth quadrant of a velocity/time graph means, that the velocity of the object is increasing with time but in negative direction.

Because the Velocity is constantly increasing in negative direction, the movement of the object can be said to be speeding up is negative direction.

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Answer:

\(a=0.08\ m/s^2\)

Explanation:

Given that,

Mass of a box, m = 18 kg

It is pushed with a force of 250 N

The coefficient of friction is 0.8

We need to find the acceleration of the box.

Normal force acting on the box,

N = mg

M = 18 × 10

N = 180 N

The force acting on the force in terms of coefficient of friction is given by :

\(F=\mu mg\\\\\text{or}\\\\ ma=\mu mg\\\\a=\dfrac{\mu }{g}\\\\a=\dfrac{0.8}{10}\\\\a=0.08\ m/s^2\)

So, the acceleration of the box is \(0.08\ m/s^2\)

Answer:

false

Explanation:

Answer:

please tell me what does w.r mean ? then I will try to give answer

Answer:

192.6N

Explanation:

Let's consider the forces acting on the beam:

Weight of the beam (W): It acts vertically downward and has a magnitude of W = mass * gravitational acceleration = 39.4 kg * 9.8 m/s^2.

Force exerted by the link on the beam (F_link): It acts at an angle of 90 degrees with respect to the beam and has two components: the vertical component and the horizontal component.

Tension in the cable (T): It supports the far end of the beam and acts at an angle of 90 degrees with respect to the beam. Since the angle between the beam and the cable is 90 degrees, the tension in the cable only has a vertical component.

Let's break down the forces acting on the beam:

Vertical forces:

W (weight of the beam) - T (vertical component of tension) = 0

T = W

Horizontal forces:

F_link (horizontal component of the force exerted by the link) = ?

To find the magnitude of the horizontal component of the force exerted by the link on the beam (F_link), we need to consider the equilibrium of forces in the horizontal direction.

Since the beam is inclined at an angle of θ = 33.1 degrees with respect to the horizontal, the horizontal equilibrium equation can be written as:

F_link = W * sin(θ)

Let's substitute the given values:

W = 39.4 kg * 9.8 m/s^2

θ = 33.1 degrees

F_link ≈ (39.4 kg * 9.8 m/s^2) * sin(33.1 degrees)

Using a calculator, we find that the magnitude of the horizontal component of the force exerted by the link on the beam (F_link) is approximately 192.6 N.

(a) The work done by the donkey on the cart is 59,721.9 J.

(b) The work done by the force of gravity on the cart is -48,434.87 J.

(c) The work done on the cart by friction during this time is 11,315.12 J.

(a) The work done by the donkey on the cart is calculated as follows;

Wd = Fd cosθ

where;

Wd = 375 N x 163 m x cos(12.3)

Wd = 59,721.9 J

(b) The work done by the force of gravity on the cart is calculated as;

Wg =  Fg x d x cosθ

Where;

θ = 90⁰ + 4.03⁰ = 94.03⁰

Wg = (431 kg x 9.81 m/s²) x 163 m x cos (94.03)

Wg = -48,434.87 J

(c) The work done on the cart by friction during this time is calculated as;

Wf = Ff x d x cosθ

where;

Ff = μmg cosθ

Ff = 0.0165 x 431 kg x 9.81 x cos (4.03)

Ff = 69.59 N

Wf = 69.59 x 163 x cos (4.03)

Wf = 11,315.12 J

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Answer:

Fossil fuels are energy sources that come directly from nature. First, the sun's radiant energy is stored as chemical energy in plants by photosynthesis. When the plants die, they start decaying. After many years, the plants are turned into fossil fuels.

Explanation:

Fossil fuels rely on the Sun's energy because the energy in fossil fuels came from plants and algae as they performed photosynthesis, which requires sunlight.

When sunlight strikes a plant, some of the energy is trapped through photosynthesis and is stored in chemical bonds as the plant grows.

(u should paraphrase it)

The total energy of all the particles makes up thermal energy. This implies that larger objects with slower-moving particles at low temperatures can have more energy than smaller ones with higher temperatures.

Thermal energy is the sum of the energies of all the particles. This implies that larger objects at low temperatures can have more energy than smaller ones at higher temperatures due to slower-moving particles.

These molecules and atoms move more quickly when something is heated, providing it with more thermal energy. Compared to cold water, hot water has more thermal energy.

Therefore, molecules and atoms in colder objects move more slowly and have less thermal energy than those in warmer ones. The ability of particles to transfer energy increases with speed.

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Answer:

o.o7m bb

Explanation:

Answer:

True.

Explanation:

A synthesis reaction is a type of chemical reaction in which two or more substances combine to form a new compound. Methane (CH4) and oxygen (O2) can combine in a synthesis reaction to form carbon dioxide (CO2) and water (H2O). This reaction is exothermic and is the basis of combustion reactions.

The balanced equation for this reaction is:

CH4 + 2O2 -> CO2 + 2H2O

In this reaction, one methane molecule and two oxygen molecules combine to form one carbon dioxide molecule and two water molecules.

It's worth mentioning that methane is considered a greenhouse gas, and the combustion of methane releases carbon dioxide and water vapor into the air, which contribute to global warming and climate change.

Answer: Constant Speed

Explanation:

Object's speed does no(sic) change over its entire distance.

No change in speed means that the object is either at constant speed, or is stationary.

Answer:

Approximately \(0.10\), assuming that \(g = 9.81\; {\rm N\cdot kg^{-1}}\) and a level surface.

Explanation:

Under the assumption, the normal force between the ice and the hockey puck is equal to the weight of the puck:

\(\begin{aligned}m\, g &= (0.16\; {\rm kg})\, (9.81\; {\rm N\cdot kg^{-1}}) \\ &\approx 1.57\; {\rm N}\end{aligned}\).

The friction on the puck is considered "static" when as long as the puck is not moving relative to that surface. In this question, the maximum value of this static friction is \(0.157\; {\rm N}\). When the external horizontal force exceeds \(0.157\; {\rm N}\!\), the puck would start moving relative to the ice.

Divide maximum static friction by the normal force to find the coefficient of static friction:

\(\begin{aligned}\mu_{s} &= \frac{(\text{maximum static friction})}{(\text{normal force})} \\ &\approx \frac{0.157\; {\rm N}}{1.57\; {\rm N}} \\ &\approx 0.10\end{aligned}\).

The electron number cannot be used instead because electrons can be removed from or added to an atom (option C)

The element of an atom is determined by its proton count, while the electron count can exhibit variability. Take, for instance, a sodium atom, which encompasses 11 protons and 11 electrons. However, it has the capacity to relinquish one electron, transforming into a sodium ion housing only 10 electrons.

This occurs due to the relatively loose binding of electrons to the nucleus, enabling their removal through the influence of an electric field or alternative mechanisms.

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(a) The fraction of neutron's kinetic energy transferred to the atomic nucleus is 0.0787.

(b) The final kinetic energy of the neutron is 7.63 x 10⁻¹³  J.

The final velocity of the atomic nucleus is calculated by applying the principle of conservation of linear momentum as follows;

initial momentum of the neutron = final momentum of the atomic nucleus

m₁u₁  = m₂u₂

where;

The mass of the atomic nucleus = 12.7 m₁

u₂  = m₁u₁ / m₂

u₂  = m₁u₁ / (12.7 m₁)

u₂  = 0.0787u₁

The initial kinetic energy of the neutron is calculated as;

K.Ei = ¹/₂m₁u₁²

The final kinetic energy of the atomic nucleus is calculated as;

K.Ef =  ¹/₂m₂u₂²

K.Ef =  ¹/₂(12.7 m₁)(0.0787u₁)²

K.Ef = 0.0787 (¹/₂m₁u₁²)

K.Ef = 0.0787 (K.Ei)

The fraction of neutron's kinetic energy transferred to the atomic nucleus is calculated as;

= 0.0787 (K.Ei) / K.Ei

= 0.0787

= 7.87 %

The final kinetic energy of the neutron is calculated as follows;

K.E.f (neutron) = (1 - 0.0787) x (8.28 x 10⁻¹³ J)

K.E.f (neutron) = 7.63 x 10⁻¹³ J

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Of the options listed, the only effect that can be caused by exposure to infrared light is overheating (option a).

Infrared light is a form of electromagnetic radiation that is invisible to the human eye but can be detected as heat. When exposed to high levels of infrared light, such as in close proximity to a powerful infrared source, it can lead to overheating of the body or objects. Skin cancer (option b) is not directly caused by infrared light. It is primarily associated with overexposure to ultraviolet (UV) radiation from the sun or artificial sources like tanning beds. UV radiation falls in the higher energy range of the electromagnetic spectrum, while infrared radiation has lower energy. Radiation sickness (option c) is caused by exposure to high-energy ionizing radiation, such as gamma rays or X-rays. Infrared light does not possess enough energy to cause ionization and is therefore not capable of inducing radiation sickness. Memory loss (option d) is not a known effect of exposure to infrared light. Memory loss can be attributed to various factors, such as neurological conditions, head injuries, or aging, but not specifically to infrared light exposure. In summary, while exposure to high levels of infrared light can lead to overheating, it does not cause skin cancer, radiation sickness, or memory loss.

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Complete question: Conditions are:

(A) The plane and the yz plane are parallel. You could be presuming that the electric field and rectangular plane are not in the same relative direction.

(b) The plane is perpendicular to the x-y plane. \(N·m^2/C \s\)

(C) The y-axis is contained within the plane, and its normal intersects the x-axis at a 39.0° angle. \(Nm2/C\)

Values of electric flux for different conditions in electric field are (a) 0.861 \(Nm^2/C\), (b) no electric flux and (c) 0.697 \(Nm^2/C\)

The electric flux is the flow of electric field through a surface and is calculated by multiplying the surface area with the component of the electric field that is perpendicular to the surface.

In electric flux of electric field:

(a) If the rectangular plane is parallel to the yz plane, the electric field is perpendicular to the plane and the electric flux will be equal to the surface area multiplied by the electric field. The surface area of the plane is 0.350 m * 0.700 m = 0.245 \(m^2\). Thus, the electric flux = 0.245 \(m^2\)* 3.54 kN/C = 0.861 \(Nm^2/C.\)

(b) If the plane is parallel to the xy plane, the electric field will be parallel to the plane and there will be no electric flux through the plane.

(c) If the plane contains the y axis and its normal makes an angle of 39.0° with the x axis, the component of the electric field perpendicular to the plane will be 3.54 kN/C * cos(39.0°). The electric flux = 0.245 \(m^2\) * 3.54 kN/C * cos(39.0°) = 0.697 \(Nm^2/C\).

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Answer:

No

Explanation:

Answer:

answer 1 is A, Answer 2 is A, Answer 3 is c

When an asteroid moves away from our planet the gravitational attraction between it and the earth as it zooms away increases.

The term gravitational force is a force that is attractive and acts between any two masses on the earth surface.

If you took your weight first at sea level and then on top of a very tall mountain, you would find that your weight increases.

It is false that Smaller masses experience more gravitational force than bigger masses.

When an asteroid moves away from our planet the gravitational attraction between it and the earth as it zooms away increases.

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The acceleration of Thomas is 0.233 m/s^2.

Acceleration is the rate of change of velocity. Thomas the Train chugs along at a velocity of 2 m/s.

Thomas needs to go faster so more coal is shoveled into his engine and he accelerates for 10 seconds until he is going 4.33 m/s.

We are to find the acceleration of Thomas.

The formula for acceleration is given as :

acceleration = (final velocity - initial velocity) / time

In the given problem, the initial velocity of Thomas, u = 2 m/s.

The final velocity of Thomas, v = 4.33 m/s The time for which Thomas accelerates, t = 10 s.

Therefore, the acceleration of Thomas will be given as:

a = (v - u) / ta = (4.33 - 2) / 10s => 2.33 / 10s => 0.233 m/s^2

Thus, the acceleration of Thomas is 0.233 m/s^2.

To summarize, the acceleration of Thomas is 0.233 m/s^2.

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The bus resultant displacement is approximately 4.14 km at an angle of 59.5 degrees north of east.

The first movement is 2 km due east, which means it has an x-component of 2 km and a y-component of 0 km.

The second movement is 5 km at 45 degrees north of east. This can be broken down into x and y components using trigonometry: x = 5 km * cos(45) = 3.54 km y = 5 km * sin(45) = 3.54 km

The third movement is 4 km at 30 degrees north of west. This can also be broken down into x and y components using trigonometry: x = -4 km * cos(30) = -3.46 km (negative because it’s towards the west) y = 4 km * sin(30) = 2 km

The fourth movement is 2 km due south, which means it has an x-component of 0 km and a y-component of -2 km.

Adding up all the x and y components, we get: x_total = 2 + 3.54 + (-3.46) + 0 = 2.08 km y_total = 0 + 3.54 + 2 + (-2) = 3.54 km

The magnitude of the resultant displacement can be calculated using the Pythagorean theorem: resultant_displacement = sqrt(x_total^2 + y_total^2) = sqrt(2.08^2 + 3.54^2) ≈ 4.14 km

The direction of the resultant displacement can be calculated using the arctan function: direction = arctan(y_total / x_total) ≈ 59.5 degrees north of east

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Answer:

what are the choices

Explanation:

Answer:

Landforms are a result of a combination of constructive and destructive forces. Collection and analysis of data indicates that constructive forces include crustal deformation, faulting, volcanic eruption and deposition of sediment, while destructive forces include weathering and erosion.

Explanation: