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AlladinOne [14]
3 years ago
15

An automobile with a mass of 961.000 kg has 3.27 m between the front and rear axles. Its center of gravity is located 0.615 m be

hind the front axle. With the automobile on level ground, determine the magnitude of the force from the ground on (a) each front wheel (assuming equal forces on the front wheels) and (b) each rear wheel (assuming equal forces on the rear wheels).
Physics
1 answer:
aleksandrvk [35]3 years ago
8 0

Answer:

a)  3830 N

b) 887 N

Explanation:

WOW, you know the mass to within ± ½gram and position of CG to ± 0.5 mm! that's some impressive measuring!!!

Let FR be the total rear wheels force

Let FF be the total front wheels force

Sum moments about the front wheels to zero

961(9.81)[0.615] - FR[3.27] = 0

FR = 1,773.045

so each rear tire supports

Fr = 1,773.045/2 = 886.5225 N

Fr ≈ 887 N when rounded to three significant digits

Sum moments about the rear wheels to zero

961(9.81)[3.27 - 0.615] - FF[3.27] = 0

FF = 7,654.365

so each front tire supports

Ff = 7,654.365/2 = 3,827.1825

Ff = 3830 N (to 3 s.d.)

verify by summing vertical forces to zero

7,654.365 + 1,773.045 - 961(9.81) ?=? 0

                                                      0 = 0   checks out

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andreyandreev [35.5K]

Before we solve this, we should know this fact:

According to Newton's Law of Gravitation, the force between two objects is directly proportional to the product of their masses and inversely proportional to the square of the distance between them. The force acts along the line joining the centres of the two objects. It can be shown by this:

F ∝ \frac{Mm}{ {d}^{2} }

Now, let us check all the options.

A. As we move to higher altitudes, the force of gravity on us decreases.

<em>This </em><em>statement </em><em>is </em><em>true.</em>

The force of gravity is inversely proportional to the square of distance from the centre of the earth. If, we go up the surface of the earth, the distance from the centre of the earth increases and hence the value of force of gravity decrease. So, force of gravity decreases with altitude.

B. As we move to higher altitudes, the force of gravity on us increases.

<em>This </em><em>statement</em><em> </em><em>is </em><em>false.</em>

We have already got the result in option A. that the force of gravity decreases with altitude. It never increases with altitude.

C. As we gain mass, the force of gravity on us decreases.

<em>This </em><em>statement</em><em> </em><em>is </em><em>false.</em>

The force of gravity is directly proportional to the product of the masses. So, if increase our mass, then the force of gravity will also increase and if we decrease our mass, then the force of gravity decreases.

D. As we gain mass, the force of gravity on us increases.

<em>This </em><em>statement</em><em> is</em><em> </em><em>true.</em>

As mentioned earlier in option C., the force of gravity is directly proportional to the product of the masses of the earth and another object. So, as we gain mass, the force of gravity on us increases.

E. As we move faster, the force of gravity on us increases.

<em>This </em><em>statement</em><em> is</em><em> </em><em>true</em><em>.</em>

Here, we have to consider a different formula. According to Newton's Second Law,

F = ma, where F is the force, m is the mass and a is the acceleration.

In other words,

F ∝ a, i.e., force is directly proportional to acceleration.

We know, acceleration is the rate of change of velocity of an body within a time period.

So, if speed is increased, then acceleration will also be greater, which results in the increase of force. So, as we move faster, the force of gravity on us increases.

<u>Answers:</u>

A: As we move to higher altitudes, the force of gravity on us decreases.

D: As we gain mass, the force of gravity on us increases.

E: As we move faster, the force of gravity on us increases.

Hope you could understand.

If you have any query, feel free to ask.

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2 years ago
Two red and two overlapping balls in the center are surrounded by a green, fuzzy, circular cloud with a white line running throu
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Answer:

  • A. The line leading a bracket around the balls, labeled A, represents the nucleus of the atom.

  • B. The white line, labeled B, is signaling the first main energy level, as per the quantum model of the atom.

Explanation:

You are describing the model of an atom with two protons, two neutrons, the electron density (orbital), and two electrons.

Then, you want to know what the <em>labels A</em> and <em>B</em> represent.

The nucleus of the atom is at the center, where protons and neutrons are placed. This is supported by three models: Rutherford's model, Bohr's model, and the (currently accepted) quantum model.

Hence, the red balls and the two overlapping balls in the center are representing the protons and neutrons.

The <em>line leading a bracket around the balls</em>, labeled A, represents the nucleus of the atom, since it is signaling both protons and neutrons in the nucleus.

The green fuzzy circular cloud depicts the region where the electrons are: it is fuzzy in correspondence to the quantum model, which states the electrons are not in a fixed position but in a region around the atom. That region is named orbitals. As per the model you cannot tell the exact position of the electron, and that is what the fuzzy cloud means.

In the the Bohr's model that white line,  which should be circular, where the electrons are, depicts the orbit of the electrons, and the shell, which were idenfified with letters L, M, N, K. The first shell was the L shell.

In the quantum  model, that line corresponds to the principal quantum number n, which is the main energy level. Hence, the line leading to a bracket overlapping the white line depicts the main energy level.

The atom is neutral because it contains the same number of electrons aroud the nucleus as protons inside the nucleus.

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<h2>Given that,</h2>

Mass of two bumper cars, m₁ = m₂ = 125 kg

Initial speed of car X is, u₁ = 10 m/s

Initial speed of car Z is, u₂ = -12 m/s

Final speed of car Z, v₂ = 10 m/s

We need to find the final speed of car X after the collision. Let v₁ is its final speed. Using the conservation of momentum to find it as follows :

m_1u_1+m_2u_2=m_1v_1+m_2v_2

v₁ is the final speed of car X.

m_1u_1+m_2u_2-m_1v_1=m_2v_2\\\\m_2v_2=m_1u_1+m_2u_2-m_2v_2\\\\m_1v_1=125\times 10+125\times (-12)-125\times 10\\\\v_1=\dfrac{-1500}{125}\\\\v_1=-12\ m/s

So, car X will move with a velocity of -12 m/s.

3 0
3 years ago
A .5kg bird is perched on its nest so that it has 50J of potential energy. how far is it off the of the ground?
pshichka [43]

It is 10.20 m from the ground.

<u>Explanation:</u>

<u>Given:</u>

m = 0.5 kg

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P. E = m \times g \times h

where m is the is mass in kg;  g  is acceleration due to gravity which is 9.8 m/s  and  h  is height in meters.

PE is the Potential Energy.

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Here, if we substitute the values in the formula, we get

P. E = m \times g \times h

50 = 0.5 × 9.8 × h

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h = \frac {50} {4.9}

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A car runs for about 10 years during its average useful life. If the odometer reads 120,000 miles at the end, what was the avera
Eva8 [605]

Answer:

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So, the average speed of the car is 12000 mph.

7 0
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