Can the sum of the magnitudes of two vectors ever be equal to the magnitude of the sum of the same two vectors? If no, why not? If yes when ?

Mark's work decreases when he climbs the same flight of stairs again in the same amount of time without the cello.

The correct answer is option D.

The amount of work Mark does depends on the weight of the cello, as well as the distance he climbs and the time it takes. Work is calculated using the formula :

Work = Force × Distance.
In the given scenario, Mark is carrying a full-sized cello while climbing the stairs. The weight of the cello adds to the force he exerts. So, the total force Mark exerts is the weight of the cello plus his own weight (375 N).

When Mark climbs the stairs with the cello, he is doing work against the force of gravity.

The work done is equal to the force exerted multiplied by the distance climbed (375 N + weight of cello) × 4 m.

Now, if Mark were to climb the same flight of stairs again in the same amount of time (3 seconds), but this time without the cello, the amount of work he does would decrease. This is because without the cello, the force exerted would only be Mark's weight (375 N), which is less than the total force exerted with the cello.

Therefore, mark's work decreases.

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Unless you have a diagram to include or any other additional info, I'll assume the block is being pulled by two opposing forces along the horizontal surface.

Horizontally, the block is under the influence of

• one rope pulling in one direction with magnitude 15 N,

• the other rope pulling in the opposite direction with mag. 5 N, and

• friction, opposing the direction of the block's motion, with mag. 3 N.

It stands to reason that the block is accelerating in the direction of the larger pulling force.

(A) By Newton's second law, we have

15 N + (-5 N) + (-3 N) = m (1 m/s²)

where m is the mass of the block. Solve for m :

7 N = m (1 m/s²)

m = (7 N) / (1 m/s²)

m = 7 kg

(B) The friction force is proportional to the normal force, so that if f is the mag. of friction and n is the mag. of the normal force, then f = µ n where µ is the coefficient of friction.

The block does not bounce up and down, so its vertical forces are balanced, which means the normal force and the block's weight (mag. w) cancel out:

n + (-w) = 0

n = w

n = m g

where g = 9.8 m/s² is the mag. of the acceleration due to gravity.

n = (7 kg) (9.8 m/s²)

n = 68.6 N

Then

3 N = µ (68.6 N)

µ = (3 N) / (68.6 N)

µ ≈ 0.044

Answer:

Yes

Explanation:

Beacause u have 25 kg,and falls off from a cliff hanger cause its too bit heavy

Mass over density is a mathematical expression that represents the ratio of mass to density. It is calculated by dividing the mass of an object or substance by its density. Mathematically, it can be represented as:

The equation relating mass (m) and density (ρ) is given by:

m = ρ * V

where:

m is the mass of the object or substance,

ρ is the density of the object or substance, and

V is the volume of the object or substance.

This equation states that the mass of an object is equal to the product of its density and volume. It shows that mass is directly proportional to density and volume.

Answer:

the commutator

Explanation:

took the quiz!

The part of the motor that causes the consistent motion of the electromagnet in the same direction is the commutator. The correct answer is C. The commutator.

The commutator is a critical component in a motor that enables the conversion of electrical energy into mechanical energy. It consists of a set of copper segments connected to the rotating coil or armature of the motor. As the armature spins, the commutator ensures that the electrical current flowing through the coil changes direction at the right time.

This change in current direction creates a rotating magnetic field that interacts with the permanent magnets, resulting in a continuous rotational motion of the motor. In essence, the commutator acts as a switch, controlling the flow of current and ensuring the electromagnet rotates in a consistent direction.

Therefore, the part of the motor that causes this motion is C. The commutator.

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The temperature when the mercury level is 6.5 cm above the lower mark is 26 °C.

To determine the temperature from the mercury level on a centigrade thermometer, you need to use the formula:

Temperature = (Mercury level / Distance between fixed points) * 100

In this case, the distance between the fixed points is 25cm, and the mercury level is 6.5 cm above the lower mark. Plugging these values into the formula gives:

Temperature = (6.5 cm / 25 cm) * 100 = 26 °C

So the temperature is 26 °C when the mercury level is 6.5 cm above the lower mark on a centigrade thermometer with fixed points 25 cm apart.

The speed of the wave that is propagated is 10 meters per second.

A wave is a disturbance or variation that gradually conducts electricity from point to point in a medium and can take the form of elastic deformation or a change in pressure, electric or magnetic intensity, electric potential, or temperature

The speed of a wave is determined by the frequency of the wave and its wavelength. In this case, the child is sending pulses down the rope at a rate of 2 pulses per second, so the frequency is f = 2 Hz.

The distance between the pulses is 5 meters, which is the wavelength of the wave, represented by lambda (λ).

The speed of the wave (v) is given by the formula:

v = f * λ

Substituting the values we have, we get:

v = 2 Hz * 5 m = 10 m/s

Therefore, the speed of the wave is 10 meters per second.

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Non-Malleable and Ductile: Non-metals are very brittle, and cannot be rolled into wires or pounded into sheets. Conduction: They are poor conductors of heat and electricity. Luster: These have no metallic luster and do not reflect light.

Group 15, the nitrogen family, contains two nonmetals: nitrogen and phosphorus. These non-metals usually gain or share three electrons when reacting with atoms of other elements. Group 16, the oxygen family, contains three nonmetals: oxygen, sulfur, and selenium.

Elements: Nitrogen; Oxygen; Phosphorus; Selenium...

a. The angle between a diagonal of a cube and one of its edges is approximately 54.7356°.

b. No, the line through (4,6,3) and (2,0, -1) is not parallel to the line through (6,22,12) and (1,7,2).

C. question is incomplete.

a. To show the working, consider the diagonal of a cube with edge length "a":

Diagonal = √(a^2 + a^2 + a^2) = √(3a^2) = a√3

The length of the edge is "a".

To find the angle between the two, use the dot product formula:

cos(θ) = (a * a) / (a * √(3a^2)) = a / √(3a^2) = a / (a√3) = 1 / √3

Therefore, θ = cos^-1 (1 / √3) = 54.7356°

b. The line through (4,6,3) and (2,0, -1) is not parallel to the line through (6,22,12) and (1,7,2).

Parallel lines have the same direction and therefore the same slope. To check for parallelism, we can find the direction ratios of the lines.

The direction ratio of the line through (4,6,3) and (2,0, -1) is: (2-4,0-6,-1-3) = (-2,-6,-4)

The direction ratio of the line through (6,22,12) and (1,7,2) is: (1-6,7-22,2-12) = (-5,-15,-10)

Since the direction ratios are different, the two lines are not parallel.

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Answer:

PE = MGH.  1375 x 9.8 x 2. = 26950 joules

Explanation:

First do 1375 x 9.8 which is MG then times it by 2 which is H

Mass x Gravity x Height

the gravity will always be 9.8

I would love a brainliest

The the potential energy of the weights lifted 2 meters above the surface is E[P] = 26950 joules.

The energy of a body by virtue of its position is called potential energy. Mathematically -

E[P] = mgh

Given is an Olympian who lifted a 1,375-kilogram set of weights a vertical distance of 2 meters in the weightlifting event.

We can write the given data as follows -

Mass of weights = [M] = 1375 Kg

Displacement = [h] = 2 meters

Therefore, using the formula for potential energy, we can write -

E[P] = mgh

E[P] = 1375 x 9.8 x 2

E[P] = 26950 joules

Therefore, the the potential energy of the weights lifted 2 meters above the surface is E[P] = 26950 joules.

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Answer:

An element

Explanation:

An element is a pure substance that cannot be broken down any smaller.  

Answer:

Element

Explanation:

Due to the fact that elements make up a compound and the compound and other elements allow is to be able to make a chemical reaction and organisms are made from elements

Answer:

11,000 kg

(a) 11.2 m/s

(b) 1.6 m/s

Explanation:

Momentum is conserved.

m₁u₁ + m₂u₂ = m₁v₁ + m₂v₂

(2200 kg) (60.0 km/h) + m (0 km/h) = (2200 kg) (10 km/h) + m (10 km/h)

132,000 kg km/h = 22,000 kg km/h + m (10 km/h)

110,000 kg km/h = m (10 km/h)

m = 11,000 kg

Momentum is conserved.

m₁u₁ + m₂u₂ = m₁v₁ + m₂v₂

(m) (-v) + (2m) (5v) = (m) (v₁) + (2m) (v₂)

-mv + 10mv = m v₁ + 2m v₂

9mv = m (v₁ + 2 v₂)

9v = v₁ + 2 v₂

Since the collision is elastic, kinetic energy is also conserved.

½ m₁u₁² + ½ m₂u₂² = ½ m₁v₁² + ½ m₂v₂²

m₁u₁² + m₂u₂² = m₁v₁² + m₂v₂²

(m) (-v)² + (2m) (5v)² = m v₁² + (2m) v₂²

mv² + 50mv² = m v₁² + 2m v₂²

51mv² = m (v₁² + 2 v₂²)

51v² = v₁² + 2 v₂²

We know v = 1.60 m/s.  So the two equations are:

14.4 = v₁ + 2 v₂

130.56 = v₁² + 2 v₂²

Solve the system of equations using substitution.

130.56 = (14.4 − 2 v₂)² + 2 v₂²

130.56 = 207.36 − 57.6 v₂ + 4 v₂² + 2 v₂²

0 = 6 v₂² − 57.6 v₂ + 76.8

0 = v₂² − 9.6 v₂ + 12.8

v₂ = [ 9.6 ± √(9.6² − 4(1)(12.8)) ] / 2(1)

v₂ = 1.6 or 8

If v₂ = 1.6 m/s, then v₁ = 14.4 − 2 v₂ = 11.2 m/s.

If v₂ = 8 m/s, then v₁ = 14.4 − 2 v₂ = -1.6 m/s.

We know v₁ can't be -1.6 m/s, since that would mean puck A didn't change speeds after the collision.  Therefore, v₁ = 11.2 m/s and v₂ = 1.6 m/s.

n unit vector notation, -22j is the torque about the origin on a particle located at coordinate (o, -4.0m, 3.0m)


Torque is defined as the force that can cause an object to rotate along an axis is measured as torque. Estimate the angle between the vector connecting the force's application point and the pivot point and the direction of the applied force. You may calculate the torque by multiplying r by F and sin.

T=R (distance) x F (Force)

R=-4j+3k

F=2J

Hence, t=  R x F vector product

=(-4j+3k)x2j

=-4x2x(y x J)

=+3x2y(k x r)

=-8x(-k)+6j

=(6j+8k) nm

b) F^2=2J+4K

Hence, t=r x f^2

=(-4j+3k)x(2j+4k)

=0-16( J x k)+6(K x J)+0

=-16j-6j

=-22j  

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The mass of Brachiosaurus moves with a momentum of 134,054 kgm/s  and the velocity is 3.9 m/s, which is 34.37 kg.

The momentum is the product of mass and velocity. The momentum is the vector quantity and the unit of momentum is Kgm/s.

Momentum = mass × velocity

 mass    = momentum/velocity

momentum =  134,052 kgm / s

velocity = 3.9 m/s

mass = 134052 / 3.9

         = 34.37 kg

Thus, the mass of Brachiosaurus is 34.37 kg.

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Answer:

\(3.24\times 10^{-7}\ \text{m}\)

Explanation:

m = Mass of bullet = 4.8 g

v = Velocity of bullet = 170 m/s

B = Magnetic field of Earth = \(5\times 10^{-5}\ \text{T}\)

q = Charge of bullet = \(1.06\times 10^{-8}\ \text{C}\)

a = Acceleration

Time the bullet will be in the air for is \(t=\dfrac{1000}{170}=5.88\ \text{s}\)

Force is given by

\(F=ma\)

Magnetic force is given by

\(F=qvB\)

So

\(ma=qvB\\\Rightarrow a=\dfrac{qvB}{m}\\\Rightarrow a=\dfrac{1.06\times 10^{-8}\times 170\times 5\times 10^{-5}}{4.8\times 10^{-3}}\ \text{m/s}^2\)

From the linear equations of motion we have

\(s=ut+\dfrac{1}{2}at^2\\\Rightarrow s=0+\dfrac{1}{2}\times \dfrac{1.06\times 10^{-8}\times 170\times 5\times 10^{-5}}{4.8\times 10^{-3}}\times 5.88^2\\\Rightarrow s=3.24\times 10^{-7}\ \text{m}\)

The defelection of the bullet is \(3.24\times 10^{-7}\ \text{m}\)

Answer:a car with 1,000kg

Explanation: A car with a mass of 1,000kg has more inertia than 150 kg

Out of the two objects a 1000-kilogram car and a 150-kilogram golf cart, the 1000-kilogram cart will have more inertia as the inertia of any object is directly proportional to its mass.

According to Newton's first law, until pushed to alter its condition by the intervention of an external force, every object will continue to be at rest or in uniform motion along a single direction.

The larger the mass of the object, the greater would be the inertia of the object.

Thus, a 1000-kilogram automobile will have higher inertia than a 150-kilogram golf cart since any object's inertia is directly proportionate to its mass.

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The spring constant of the spring is 178.4 N/m.

In this problem, we are given a mass of 0.25 kg that is attached to a spring and set into vibration with a period of 0.22 s.

We can use the equation for the period of a mass-spring system, which relates the period of oscillation to the mass and spring constant, to calculate the spring constant.

We can use the equation for the period of a mass-spring system:

T = 2π√(m/k)

where T is the period, m is the mass, and k is the spring constant.

Rearranging this equation to solve for k, we get:

k = \((4\pi^2m) / T^2\)

Substituting the given values, we get:

k = \((4\pi^2 \times 0.25 \:kg) / (0.22 s)^2\)

k = 178.4 N/m

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the area bounded by the line and the axes of a velocity-time graph is equal to the displacement of an object during that particular time period

Thank you

The area between the line and the x axis represent on a velocity vs time graph is the displacement.

The area under velocity-time graph is known as displacement.

In velocity-time graph, the y-axis represents the velocity axis while the x-axis represents the time axis.

Velocity is defined as the change in displacement per change in time.

\(v = \frac{dx}{dt}\)

where;

The integration of the velocity gives the area under the curve and that will be equal to the displacement.

\(\int\limits^a_b {v} \, dt = x\)

Thus, the area between the line and the x axis represent on a velocity vs time graph is the displacement.

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Answer:

Explanation:

a)

To pass the Coulomb barriers and undergo nuclear fusion, alpha particles must be burned at high temperatures. As a result, the ignition temperature needed for this reaction is 5.4168 × 10¹⁰ K. Helium must be burned at a high temperature and density. As a result, this must occur for hot stars with high densities.

b)

The amount of energy given up can be calculated as follows:

\(_2He^4 + _2He^4 \to _4Be^8 ---- (1) \\ \\ _4Be^8 + 2_He^4 \to _6C^{12} ---(2)\)

where;

\(M(_2He^4) = 4.002603 \ u \\ \\ M(_4Be^8) = 8.005305 10 \ u\)

Therefore, from the reaction (1);

\(Q = \Big ( M(_2He^4) + M(_2He^4) - M(_4Be^8) \Big ) ( 931.5 \ MeV) \\ \\ = \Big ( 2(4.002603 \ u) - (8.00530510 \ u) \Big) \Big ( 931.5 \ MeV/u \Big) \ \\ \mathbf{= -0.092 \ MeV}\)

From the second reaction:

\(Q = \Big ( M(_4Be^8) + M(_2He^4) - M(_6C^{12}) \Big ) ( 931.5 \ MeV) \\ \\ = \Big ( 8.00530510 \ u +4.002603 \ u -12 \ u \Big) \Big ( 931.5 \ MeV/u \Big) \ \\ \mathbf{= 7.37 \ MeV}\)

Answer:

Given,

Force = 441 N

mass = ?

Keep in mind that acceleration due to gravity is constant 10m/s.

Force = mass × acceleration due to gravity

mass = Force / acceleration due to gravity

m = 411 N /10m/s

m = 41.1 kg

Therefore her Jenny mass is 41.1 kg.

The object is on 81 cm high.

The energy that an item has or acquires when its location changes as a result of being in a gravitational field is known as gravitational potential energy. Gravitational potential energy can be defined as an energy that has a connection to gravitational force or gravity.

Given that: an 80kg object has 632 J of Potential energy.

Let the height is h: then,

mgh = PE

80 kg × 9.8× m/s^2 × h = 632 Joule

h = 0.81 m = 81 cm.

The object is on 81 cm high.

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Answer:

Explanation:

Find the diagram relating to the question for proper explanation of the question below.

Using the principle of moment

Sum of clockwise moments = Sum of anticlockwise moments

Moment = Force * perpendicular distance

For anti-clockwise moment:

Since the 30 kg moves in the anticlockwise direction according to the diagram

ACW moment = 30 * 1 = 30 kgm

For clockwise moment

If another child sits 0.75 m away from the pivot point on the opposite side, moment of the child in clockwise direction = M * 0.75 = 0.75M (M is the mass of the unknown child).

Equating both moments we have;

0.75M = 30

M = 30/0.75

M = 40 kg

The second child's mass is 40 kg

Answer:

the air is being stopped in the pocket of the parachutes theys why the parachute has a certain shape so that the air that gets caught inside of it as the skydiver goes down slows down the landing

In PBL teaching, an individual student will teach a particular topic to the group meaning the content of information taught will be dependent on the motivation of the individual students. Traditional courses tend to emphasise the foundations in biomedical knowledge required in medicine earlier on.

Answer:

Maximum height, h = 3062.5m

Total time of flight, T = 49.49secs or 50secs approx.

Range, R = 12250m

Explanation:

Given data:

U = 350m/s

Angle = 45°

Assume g = 10m/s

At the greatest height, v = 0

Therefore,

V^2 = U^2 sin^2 × angle - 2×g×h

Substituting values:

0^2 = 350^2 sin^2 (45) - 2 × 10 × h

Let h = maximum height reached

Rearranging gives:

350^2 sin^2(45) = 2 x 10 x h

h = 350^2 sin^2(45)/2×10

h = 122500 x 0.5/20

h = 61250/20

h = 3062.5m

2)Total time of flight, T

T = 2U sin(angle)/g

= 2x350 sin(45)/10

= 494.9747/10

= 49.49secs or 50sec approx.

3) Range of projectile, R

R = U^2 sin2(angle)

= 350^2 sin2 (45)

= 122500 x 1/10

= 12250m

Answer:

1.5 minutes

Explanation:

To find out how long it will take to heat 5 kg of water from 28 degrees Celsius to 88 degrees Celsius in an electric kettle, we can use the equation:

Q = mcΔT

Where Q is the heat energy added, m is the mass of the water, c is the specific heat capacity of water and ΔT is the change in temperature.

The heat energy added to the water can be calculated as:

Q = (5 kg) x (400 J/kg·K) x (88°C - 28°C) = (5 kg) x (400 J/kg·K) x (60°C) = 120000 J

The power of the electric kettle can be calculated using the formula:

P=VI

where P is the power, V is the voltage and I is the current,

P = (220 V) x (6 A)

= 1320 W

Now we can calculate the time it takes to heat the water by dividing the heat energy added by the power:

time = Q/P = 120000 J / 1320 W

= 90.909 seconds or 1.5 minutes

It will take 1.5 minutes to heat 5 kg of water from 28 degrees Celsius to 88 degrees Celsius in an electric kettle taking 6 amperes from a 220 volt supply.

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Answer:As the temperature increases, the helium in the ballon expands.

Explanation:

I took the quiz already

The answer is C) As the temperature increases, the helium in the balloons expands.

Have a blessed day!

The moment of inertia of the uniform cylindrical grinding wheel is 2,150 kgm².

What is the moment of inertia?

This refers to the angular mass or rotational inertia can be defined with respect to the rotation axis, as a property that shows the amount of torque needed for a desired angular acceleration or a property of a body due to which it resists angular acceleration. The unit is kgm².

From the question:

Mass,M =4.2kg

Radius, R=32Cm

The formula for calculating the moment of inertia for uniform cylindrical grinding wheel:

moment of inertia, I =1/2MR²

I =\(\frac{1}{2}\) * 4.2 * 32²

  =2,150.4 kgm²

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The torque would be 240 Nm

The ratio of the rise/run has to be the same in order to have a constant slope (option C).

Slope, in mathematics, is the ratio of the vertical and horizontal changes between two points on a surface or a line.

The slope is zero if the line is horizontal and undefined if it is vertical.

The vertical change between two points is called the rise while the horizontal change is called the run. This means that the slope equals the rise divided by the run.

Therefore, this suggests that the ratio of the rise/run has to be the same in order to have a constant slope.

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