Would the field representation of a positive or negative charge be a better
representation for the gravitational field around one mass? Why?

a) 4225m or 4.225km b) 11.1s

For part a; convert 65km/h to km/min, to do so all you do is divide 65/60 as there are 60 minutes per hour. Afterwards, multiply by 3.90 to find the distance travelled in 3.90mins.

For part b; convert km/h to km/s, in this one we divide 65/3600 as there are 3600 seconds in one hour. Then, using the S = D/T, where S = speed, D = distance and T= time, we isolate for T and get T = D/S. So then we sub for T=0.20/0.018 (0.018 is the product of 65/3600) and we get T=11.1s.

According to the question This gives us a percent yield of 150%.

Percent yield is a measure used in chemistry to calculate the efficiency of a chemical reaction. It is expressed as a percentage and is calculated by comparing the actual yield of a product obtained in a reaction to the theoretical yield, which is the maximum amount of product that could have been produced.

The percent yield of a reaction is the ratio of the actual yield of the reaction to the theoretical yield of the reaction multiplied by 100.
Therefore, to calculate the percent yield, we need to first calculate the theoretical yield of the reaction. We can do this by multiplying the given mass of reactants, in this case 80 g, by the stoichiometric coefficient of the desired product, which is 1.
This gives us a theoretical yield of 80 g.
Now, to calculate the percent yield, we divide the actual yield, which is 120 g, by the theoretical yield, which is 80 g, and multiply by 100.
This gives us a percent yield of 150%.

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Two charged objects are separated a distance d,  the position vector of the object 1 with respect to the object 2 is P21 = d/2(√3i -j).

It is assumed in the problem that the origin is taken into account when determining the position of object 2. As a result, we may decompose the position vector of object 1 into its x and y components.

So, we can see from the diagram that the position vector's horizontal component is dcos30. This component is known as the x component because it lines up with the positive x axis. Hence, x=dcos30. Once more, dsin30 is the vertical component of the position vector. This component is known as the y component because it is congruent with the negative y axis. Hence, y=dsin30.

As a result, the position vector can be expressed as,

⇒P21=xi^+y(−j^)

The values P21=dcos30i+dsin30(j) are substituted

Now, the values of cos30 are 3-1/2 and sin30 are 12.

In order to substitute the values, we obtain P21=3-2di12dj.

Now, if we take the common, we get P21 = d/2(√3i -j).

This is the position vector of the object 1 with respect to the object 2.

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Answer:The concept of momemtum will be used to solve this question.A moving body's momemtum, which is generally equal to the product of the body's mass and velocity, is a quality that the body has as a result of its mass and motion.

Explanation:

Car B's velocity as observed by the person on the side of the road is -6.0 m/s, which means that it is moving in the negative x-direction.

explain about velocity ?

Velocity is a physical quantity that describes the rate of change of an object's position with respect to time. In other words, it is the speed and direction of an object's motion. Velocity is a vector quantity, which means that it has both a magnitude (or size) and a direction.

the relative velocity formula, which gives the velocity of one object as observed by another object or observer:

velocity of B with respect to observer = velocity of B with respect to A + velocity of A with respect to observer

In this problem, we have:

velocity of A with respect to observer = +21.4 m/s (positive because it is in the positive x-direction)

velocity of B with respect to A = -27.4 m/s (negative because it is in the opposite direction to A's velocity)

(Note that we use a negative sign for the velocity of B with respect to A because they are moving in opposite directions.)

Using the formula, we get:

velocity of B with respect to observer = -27.4 m/s + 21.4 m/s = -6.0 m/s

Therefore, Car B's velocity as observed by the person on the side of the road is -6.0 m/s, which means that it is moving in the negative x-direction.

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(a) The acceleration of each block is zero. (b) The tension in the rope is 97.7 N.

(a) The forces acting on each block are,

For m1,

F_net = T - mg*sin(35)

For m2,

F_net = mg*sin(35) - T

Since the two blocks are connected by a rope, they will have the same acceleration.

T - mgsin(35) = mgsin(35) - T

T = mg*sin(35)

Substituting this value of T,

F_net = T - mg*sin(35)

F_net = mgsin(35) - mgsin(35)

F_net = 0

Therefore, the net force acting on each block in the direction of motion is zero.

(b) To find the tension in the rope,

T = mg*sin(35)

T = (2.1 kg + 11 kg)9.81 m/s^2sin(35)

T = 97.7 N

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The magnitude of the GPE depends on the position of the object.

Some parts of the question appears to be missing but I will try to answer generally.

As an object falls, its gravitational potential energy (GPE) decreases.

Gravitational potential energy is the energy an object possesses due to its position in a gravitational field. The GPE of an object is directly proportional to its mass, the acceleration due to gravity, and its height above a reference level. The formula for gravitational potential energy is:

GPE = mgh

where m is the mass of the object, g is the acceleration due to gravity, and h is the height of the object above the reference level.

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The coefficient of kinetic friction is approximately 0.533.

To find the coefficient of kinetic friction, we can use the equation of the force of friction, which is given by:

f_friction = friction_coefficient  x f_norm

where;

Since the piano is being pulled at a constant speed, the net force on the piano must be zero, which means that the sum of the forces must be equal to zero:

f_net = f_horizontal - f_friction = 0

friction_coefficient = f_friction / f_norm

= (f_horizontal) / (f_norm)

= (1600 N) / (3000 N) = 0.533

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Given,

Initial velocity, u = 0

Distance covered, s = 600m

Time is taken, t = 12s

We know,

[tex]s = ut +[/tex] [tex]1/2 at^{2}[/tex]

[tex]600 = 0*12 + 1/2 (a) (12)^{2}[/tex]

[tex]a = 600 * 2 / (12)^{2} \\a = 100/12\\ = 8.3m/s^{2} \\[/tex]

Uniform acceleration = [tex]8.s m/s^{2}[/tex]

now using,

[tex]v = u + at\\ = 0 + (8.3) (12)\\ = 99.6 m/s[/tex]

Hence, the speed at the end of the 12 sec is 99.6 m/s

The speed at the end of 11 sec = at = (8.3)(11) = 91.3 m/s

Distance covered by the plane in 11 sec =

[tex]2as = v^{2} - u^{2} \\s = v^{2} - u^{2} /\f2a\\= (91.3)^{2} - (0)^{2} / 2(8.3)\\= 425.29m[/tex]

Thus, distance covered during 12th sec = distance covered in 12s - distance covered in 11s = 600 - 425.29 m = 174.71 m

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Answer:

Explanation:The object slows down as it moves upward until it reaches a maximum height, at which time the velocity is zero. Then the velocity increases as the object falls toward the ground.

The moment of inertia of the wheel about an axis through its center and perpendicular to the plane of the wheel is 2.09 kg·m^2.

The moment of inertia of the wheel about an axis through its center and perpendicular to the plane of the wheel can be calculated by using the parallel axis theorem, which states that the moment of inertia of a rigid body about any axis is equal to the moment of inertia about a parallel axis through the center of mass plus the product of the mass and the square of the distance between the two axes.

Here in the Question,

First, we need to find the moment of inertia of the hoop about an axis through its center and perpendicular to the plane of the hoop. This is a well-known result from basic mechanics and is given by:

I_hoop = 1/2 * m_hoop * r^2

where m_hoop is the mass of the hoop and r is its radius. Substituting the given values, we get:

I_hoop = 1/2 * 2.6 kg * (0.73 m)^2 = 1.26 kg·m^2

Next, we need to find the moment of inertia of a single spoke about an axis through its center and perpendicular to its length. This is also a well-known result from basic mechanics and is given by:

I_spoke = 1/12 * m_spoke * L^2

where m_spoke is the mass of the spoke and L is its length. Since the spokes are equally spaced around the hoop, we can consider a single spoke and multiply its moment of inertia by 7 to account for all the spokes. Substituting the given values, we get:

I_spoke = 1/12 * 0.11 kg * (0.73 m)^2 = 0.005 kg·m^2

Therefore, the moment of inertia of all the spokes combined is:

I_spokes = 7 * I_spoke = 0.035 kg·m^2

Finally, we can use the parallel axis theorem to find the moment of inertia of the entire wheel about an axis through its center and perpendicular to the plane of the wheel:

I_wheel = I_hoop + I_spokes + 7 * m_spoke * r^2

Substituting the given values, we get:

I_wheel = 1.26 kg·m^2 + 0.035 kg·m^2 + 7 * 0.11 kg * (0.73 m)^2 = 2.09 kg·m^2

Therefore, The wheel's moment of inertia about an axis passing through its center and perpendicular to its plane is 2.09 kg·m^2.

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The force of approximately 16.9 N is needed to hold the load stationary on the ramp.

Friction is the force that prevents two solid objects from rolling or sliding over one another.

Although frictional forces, such the traction required to walk without slipping, may be advantageous, they can provide a significant amount of resistance to motion.

Since the ramp is frictionless, the only forces acting on the load are its weight (mg) and the normal force (N) exerted by the ramp perpendicular to the surface.

We can break the weight into two components: one parallel to the ramp (mg sin θ) and one perpendicular to the ramp (mg cos θ).

To keep the load stationary on the ramp, the force applied parallel to the ramp (call it F) must balance the component of the weight parallel to the ramp:

F = mg sin θ

Substituting the given values, we get:

F = (5.00 kg) * (9.81 [tex]m/s^2[/tex]) * sin 20.0° ≈ 16.9 N

Therefore, a force of approximately 16.9 N is needed to hold the load stationary on the ramp.

The ideal mechanical advantage (IMA) of the ramp is the ratio of the length of the ramp (L) to its height (h):

IMA = L/h

Let's say the ramp has a height of h and a base of b. Then:

h = b sin θ

L = b cos θ

Substituting the given angle, we get:

h = b sin 20.0°

L = b cos 20.0°

Dividing L by h, we get:

IMA = L/h = (b cos 20.0°) / (b sin 20.0°) = cos 20.0° / sin 20.0° ≈ 1.16

Thus, the ideal mechanical advantage of the ramp is approximately 1.16.

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If m1 > m2, then the sign of the velocity of m2, v2, will be positive after the collision.

Why is the velocity positive?

This is because in a one-dimensional collision, the momentum of the system is conserved. Before the collision, only m1 has momentum, so the total momentum is mv0. After the collision, the two masses stick together, so the total momentum is (m1 + m2) * v, where v is the velocity of the combined masses.

Conservation of momentum gives:

mv0 = (m1 + m2) * v

Solving for v gives:

v = mv0 / (m1 + m2)

Since m1 > m2, the denominator is larger than the numerator, so v is smaller than v0. Therefore, after the collision, both masses will be moving in the positive x direction, and m2 will have a positive velocity, v2, while m1 will have a smaller positive velocity, v1. The actual values of v1 and v2 depend on the specific details of the collision (e.g., whether it is elastic or inelastic).

So the velocity of m2, v2, will be positive after the collision.

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Answer:

1.3 and 2.5

Explanation:

I did mental math

Answer:

(a) The change in magnetic flux is equal to the product of the magnetic field strength, the area of the coil, and the cosine of the angle between the magnetic field and the surface of the loop. Therefore, the change in magnetic flux is equal to 0.200T x (π x (25.0cm)^2) x cos(45°) = 7.85 x 10^-3 Tesla-square meters.

(b) The induced emf is equal to the change in magnetic flux divided by the time taken for the change to occur. Therefore, the induced emf is equal to 7.85 x 10^-3 Tesla-square meters / 0.250s = 3.14 Volts.

The rotational acceleration and speed are shared by all of the points of a rigid body. As a result, the angular acceleration is positive and the rotation is anticlockwise.

A- 2*[(m1 - m2)/(m1 + m2)] *g/L The angular acceleration is positive and the rotation is anticlockwise. (m1 - m2)/(m1+ m2 + mbar/3) B- 2* *g/L The angular acceleration is positive and the rotation is anticlockwise.

(A) The magnitude of angular acceleration of the seesaw in this case is .

2(m₁-m₂)g÷(m₁+m₂)L

(B) The magnitude of angular acceleration of the seesaw in this case is

(m₁ g-m₂ g)÷(m₁+m₂)L

For a massless sea saw bar, with attached masses at each end, the torque produced due to the masses is,

ω=(m₁+m₂)+1/2

And, moment of inertia of the system of two masses is,

I=(m₁+m₂)L/4

The using the expression of torque as,

Angular acceleration is the term used to describe the temporal pace at which angular velocity varies. Radians per second is the accepted unit of measurement. Therefore, = d d t. Angular acceleration is also known as rotational acceleration.

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At the neutral point, the distance between the Earth's center and the Moon's center is about 399,000 kilometers, or 3.989 x 10⁸ meters.

Planets, stars, and galaxies all move because it is one of the fundamental forces of the universe. According to Newton's law of gravitation, the distance between two objects and their masses determine the magnitude of the gravitational force

We can make use of the fact that the gravitational force between two objects is inversely proportional to the square of the distance between their centers and proportional to the product of their masses to calculate this distance. As a result, we can solve for the distance by setting the force of gravity that the Earth exerts on the object to be equal to the force of gravity that the Moon exerts on the object.

The masses of the Earth and the Moon, M_E and M_M, respectively, and the distance between their centers, d. The following factors determine the Earth's gravitational pull on the object:

F_E is equal to G × M_E × m / (d₂), where m is the mass of the object and G is the gravitational constant. The following factors determine the Moon's gravitational pull on the object:

F_M = G × M_M × m / ((R-d)²)

where R is the distance between the centers of the Earth and Moon

Setting F_E equal to F_M, we get:

G × M_E × m / (d²) = G × M_M × m / ((R-d)²)

Simplifying and solving for d, we get:

d = R × (M_E / (3 × M_M))¹/³

Values for the masses and the radius of the Earth-Moon system (R = 3.844 x 10⁸ meters), we get:

d = 3.989 x 10⁸ meters

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The water gauge pressure at location P is;

P p = 104525 Pa

We have been provided;

L = 4 cm = 0.04 m needle length

Water's viscosity; = 1 10(-3) Pa

r = 1 mm = 0.001 m Radius

v = 10 m/s is the speed.

The flow rate via a cylindrical pipe may be calculated using Poiseuille's equation for viscous liquid flow.

Q = (ΔP•πr⁴)/(8ηL)

Flow rate is now also written as;

Q = πr²v

Thus;

πr²v = (ΔP•πr⁴)/(8ηL)

This boils down to;

v = (ΔP•r²)/(8ηL)

Inserting the necessary values;

10 = (ΔP × 0.001²)/(8 × 10^(-3) × 0.04)

ΔP = (10 × 8 × 10^(-3) × 0.04)/(0.001²)

ΔP = 3200 Pa

This implies that;

P atm - P p = P

Where;

P p is the water gauge pressure at point P.

P atm is atmospheric pressure, which equals 101325 Pa.

Thus;

P p - 101325 = 3200

P p = 101325 + 3200

P p = 104525 Pa

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During the Vietnam War, journalists often referred to the military's press briefings as "five o'clock follies" because they felt that the information provided was often incomplete or misleading.

The two choices that are correct are:

•Called the military's press briefings "five o'clock follies"

•Did not witness any combat on a firsthand basis.

. Additionally, due to the dangers of the conflict, many journalists did not have the opportunity to witness combat on a firsthand basis.

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(a) Equilibrium is a state in which sum of all the forces acting on an object in a particular direction is zero.

(b) The triangle vector is in the image uploaded.

(c) The value of tension 1 and tension 2 are 191.4 N and 160.58 N.

Equilibrium is the condition of a system when neither its state of motion nor its internal energy state tends to change with time.

The value of the tensions, T1 and T2 is calculated as follows;

The sum of the vertical forces is calculated as follows;

T1 sin(50) + T2 sin(40) - 250 sin(90) = 0

0.766T1 + 0.643T2 - 250 = 0

0.643T2 = 250 - 0.766T1

The sum of the horizontal forces is calculated as follows;

-T1 cos(50) + T2 cos(40) + 250 cos(90) = 0

-0.643T1 + 0.766T2 + 0 = 0

0.766T2 = 0.643T1

T2 = (0.643T1) / (0.766)

T2 = 0.839T1

0.643 (0.839T1) = 250 - 0.766T1

0.54T1 + 0.766T1 = 250

1.306T1 = 250

T1 = 250 / 1.306

T1 = 191.4 N

T2 = 0.839T1

T2 = 0.839 x (191.4 N)

T2 = 160.58 N

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The reading on the spring scale will depend on the acceleration of the elevator and the direction of that acceleration.

If the elevator is traveling downward but slowing down (i.e., accelerating in the upward direction), the scale will read less than the woman's normal weight of 125 lb. This is because the upward acceleration of the elevator reduces the effective weight of the woman, making her appear lighter on the scale. To determine the reading on the scale, you would need to know the acceleration of the elevator at that particular moment. If the elevator is slowing down at a rate of, say,[tex]2 m/s^2,[/tex]then the scale would read:

Weight = mass x acceleration due to gravity

Weight =[tex]56.7 kg x (9.81 m/s^2 - 2 m/s^2)[/tex]

Weight =[tex]56.7 kg x 7.81 m/s^2[/tex]

Weight = [tex]442.5 N[/tex]

Converting this to pounds, the reading on the scale would be approximately:

Weight = [tex]442.5 N x (1 lb / 4.448 N)[/tex]

Weight[tex]≈ 99.4 lb[/tex]

So, the scale would read approximately 99.4 lb, which is less than the woman's normal weight of 125 lb.

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the ratio between the rate of heat flow through a cheap window with a single pane of glass that is only 4 mm thick to a nicer double pane window with an air gap of 6 mm is 76.6667.

K[tex]_{glass}[/tex]=0.80 W/m°C

K[tex]_{air}[/tex]=0.025 W/m°C

Q=[tex]\frac{\triangle T}{R_{Th} }[/tex]

(R[tex]_{Th}[/tex])[tex]_{double pane}[/tex]×Q[tex]_{double pane}[/tex]=(R[tex]_{Th}[/tex])[tex]_{single pane}[/tex]×Q[tex]_{single pane}[/tex]

(R[tex]_{Th}[/tex])[tex]_{double pane}[/tex]=∑[tex]\frac{l}{KA}[/tex]

                      =  [tex]\frac{3}{0.8A} +\frac{7}{0.025 A}+\frac{3}{0.8 A}\\[/tex]

                      =[tex]\frac{287.5}{A}[/tex]

(R[tex]_{Th}[/tex])[tex]_{single pane}[/tex]=[tex]\frac{3}{0.8A}[/tex]=[tex]\frac{3.75}{A}[/tex]

[tex]\frac{Q_{single pane} }{Q_{double pane}} =\frac{R_{Th}_{double pane} }{R_{Th}_{single pane}}[/tex]

               = 76.6667

Heat flow, also known as heat transfer, is the movement of thermal energy from a region of higher temperature to a region of lower temperature. This occurs due to the random motion of atoms and molecules within a material. There are three main mechanisms of heat flow: conduction, convection, and radiation. Conduction is the transfer of heat through a material by direct contact, while convection involves the movement of a fluid (such as air or water) due to temperature differences. Radiation is the transfer of heat through electromagnetic waves, such as from the sun or a fire. Heat flow is a fundamental concept in thermodynamics and plays a critical role in many fields, including engineering, physics, chemistry, and biology.

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Answer:

The momentum of a 0.0231 kg bullet fired at 621 m/s is calculated by multiplying the mass of the bullet by its velocity:0.0231 kg * 621 m/s = 14.3 kg·m/sSo the answer is D. 14.3 kg·m/s.

Explanation:

Formula for momentum:

[tex]p=mv[/tex]

momentum(measured in kg*m/s) = mass(measured in kg) * velocity(measured in m/s)

__________________________________________________________

Given:

[tex]m=0.0231kg[/tex]

[tex]v=621m/s[/tex]

[tex]p=?[/tex]

__________________________________________________________

Finding momentum:

[tex]p=mv[/tex]

[tex]p=0.0231\times621[/tex]

[tex]p=14.3kg*m/s[/tex]

__________________________________________________________

Answer:

[tex]\fbox{Option D}[/tex]

Heat will naturally flow from an object at 40°C to an object at 20°C.

Heat is described as the energy that is transferred from one body to another as the result of a difference in temperature.

Heat will naturally flow from an object at a higher temperature to an object at a lower temperature. So in the above scenario,  heat will naturally flow from an object at 40°C to an object at 20°C.

In conclusion, the basic concept of thermodynamics states that heat will flow spontaneously from a higher-temperature body to a lower-temperature body in order to equalize the temperatures of the two bodies.

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The magnitude of the acceleration of the elevator is approximately 1.40 m/s², and it is directed downwards.

Every procedure where the velocity varies is referred to as acceleration. There are only two methods to accelerate because velocity is a function of both speed and direction: changing your speed, changing your direction, or changing both.

Since the scale reads the magnitude of the normal force, we can equate the normal force with the weight of the person:

N = mg

N = (140 lb) * (4.448 N/lb) = 622.72 N

The scale reads 120 lb, which is equivalent to:

N' = (120 lb) * (4.448 N/lb) = 533.28 N

The magnitude of the acceleration can be calculated as:

ma = mg - N'

a = (g * m) - (N' / m) = [(9.81 [tex]m/s^2[/tex]) * (63.5 kg)] - (533.28 N / 63.5 kg) ≈ 1.40 [tex]m/s^2[/tex]

The elevator could be moving downwards at a constant velocity or accelerating downwards at a rate that is less than the acceleration due to gravity.

Thus, 1.40 [tex]m/s^2[/tex]  is the magnitude and direction of the acceleration and

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The frequency of the wave, given that 120 waves were produced per minutes is 2 Hertz

Frequency is defined as the number of complete oscillations made in 1 second.

From the question given above, the following were obtained:

Thus, to obtain the frequency (in per second), we shall convert 120 waves per minute to per second. Details below:

1 wave per minute = 1/60 wave per second

Therefore,

120 wave per minute = 120 × 1/60

120 wave per minute = 2 waves per second

120 wave per minute = 2 Hertz

Thus, we can conclude from the above calculation that the frequency is 2 Hertz

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Correct order in formation of coal as heat and pressure are increased and moisture content is decreased is (B) peat, lignite, bituminous, anthracite.

Peat is the first stage in the formation of coal, and is made up of partially decomposed plant material with a high moisture content. As heat and pressure are increased, the moisture content decreases and the plant material becomes more compressed, leading to the formation of lignite. Lignite is a low-grade coal with a relatively low carbon content, and is often referred to as brown coal.

With further increases in heat and pressure, lignite is transformed into bituminous coal, which has a higher carbon content and is often used for electricity generation. Finally, with even greater heat and pressure, bituminous coal is transformed into anthracite, which is the highest grade of coal and has the highest carbon content.

The stages of coal formation are important to understand because different types of coal have different uses and properties. For example, anthracite is often used for heating because it burns very cleanly and efficiently, while bituminous coal is often used for electricity generation because it has a higher energy content.

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A) 130m for distance, 100m for displacement

B)260m for distance, 0m for displacement

Distance is the sum of all movement taken from start to finish, regardless of position or direction. Since we are going from point A, which is halfway through the 30m side, to point B, which is also halfway through another 30m side, we divide both by 2 and add them together to get 30m once more. Then we take into account the long side of the track, measuring 100m, and can decide that the total distance is 130m.

The displacement, however, doesnt take into account the extra 15m travelled on either of the short sides of the track. When talking about displacement, we are only looking at the distance BETWEEN point A and point B, not the real distance travelled to get to them. Think of it as if youve drawn a line between both points and are mesuring that line and that line only. Because that line would have the exact length as the long side of the track, we can decide that the displacement is 100m.

For part B, the distance is easy to find as we just add up all sides of the track. The tricky part is understanding why displacement is zero. Like I said earlier, it's easiest to imagine a line drawn between both points of mesurment when talking about displacement. In this case, we are talking about the jogger leaving from point A and returning to point A. As I'm sure youve guessed, we cannot possibly draw a line between point A to point A, therefore making the displacement 0.

I'm sorry this is a lot of writing, but I, myself, had a lot of difficulty wrapping my head around the concept of displacement and wanted to make sure it was easy to understand. Hope this helps

3.27 g's of force will be applied to the driver during the turn.

In science, the term "force" has a particular definition. At this time, it is appropriate to refer to a force as a push or a pull. There is no such thing as a power that something "contains" or "has in it." A force is exerted on one item by another.

We must employ the centripetal acceleration formula to resolve this issue:

a = v² / r

In this case, the velocity is 80 m/s and the radius is 200 meters, so:

a = (80 m/s)² / 200 m = 32 m/s²

To convert this to g's, we divide by the acceleration due to gravity:

32 m/s² / 9.8 m/s²/g = 3.27 g's (rounded to two decimal places)

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The weight added to the piston is 175 N.

The weight that is added to the piston can be calculated using the Ideal Gas Law, which states that PV = nRT

where;

Since the initial pressure, volume, and temperature are known, we can use the Ideal Gas Law to find the number of moles of gas, n.

Then, we can use the equation for pressure force, to find the weight added to the piston.

F = PA

where;

First, we'll find the initial number of moles of gas:

P1V1 = nRT

n = P1V1 / RT

T = 298 K is the temperature (room temperature)

n = (105000 Pa x 860 cm^3) / (8.31 J/mol.K  x 298 K)

Next, we'll find the final number of moles of gas:

P2V2 = nRT

n = P2V2 / RT

n = (140000 Pa x 645 cm^3) / (8.31 J/mol.K  x  298 K)

Now, we have the number of moles of gas for both the initial and final conditions, and we can calculate the change in number of moles of gas, ∆n:

∆n = n2 - n1

Finally, we can use the equation for pressure force to find the weight added to the piston:

F = PA

∆F = P2A - P1A

∆F = (140000 Pa - 105000 Pa) x 5.0 x 10^-3 m^2

∆F = 35000 Pa x 5.0 x 10^-3 m^2

∆F = 175 N

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