Ask question

Ask question

All categories

3 years ago

15

A 5.0-kg rock and a 3.0 × 10−4-kg pebble are held near the surface of the earth.(a)Determine the magnitude of the gravitational

force exerted on each by the earth.(b)Calculate the magnitude of the acceleration of each object when released.

2 answers:

liraira [26]3 years ago

4 0

Answer:

A) Gravitational Force of Rock = 48.995N

Gravitational Force of Pebble = 2.94 x 10^(-3) N

B) Magnitude of acceleration of rock = 9.8 m/s²

Magnitude of acceleration of pebble = 9.8 m/s²

Explanation:

A) First of all, let's solve for the rock;

From Newton's law of universal gravitation, gravitational force is;

Fg = (Gm1m2)/r²

Where G is a constant = 6.67 × 10^(-11) Nm² /kg2²

Mass of earth (m1) = 5.97 × 10^24 kg

Radius of earth (r) = 6.38 × 10^6 m²

Mass of rock (m2) = 5kg.

Thus, Fg = [6.67 × 10^(-11) x 5.97 × 10^24 x 5] / (6.38 × 10^6)² = 48.995N

Doing the same for the pebble of mass 3 x 10^(-4) kg;

Thus, Fg = [6.67 × 10^(-11) x 5.97 × 10^(24) x 3 x 10^(-4)] / (6.38 × 10^6)² = 2.94 x 10^(-3) N

B) Let's calculate for the acceleration of the rock;

We know that Fg = ma

Thus, Let's make a the subject of the formula,

So, Fg/m = a

Substituting rock value of Fg and m to get;

48.995/5 = 9.8 m/s²

Now let's do the same for the pebble;

Fg/m = a

Substituting pebble value of Fg and m to get;

[2.94 x 10^(-3) N] / (3 x 10^(-4)) = 9.8 m/s²

a_sh-v [17]3 years ago

3 0

Answer:

a). Determine the magnitude of the gravitational force exerted on each by the earth.

Rock: $F = 49.06N$

Pebble: $F = 29.44N$

(b)Calculate the magnitude of the acceleration of each object when released.

Rock: $a =9.8m/s^{2}$

Pebble: $a =9.8m/s^{2}$

Explanation:

The universal law of gravitation is defined as:

$F = G\frac{m1m2}{r^{2}}$ (1)

Where G is the gravitational constant, m1 and m2 are the masses of the two objects and r is the distance between them.

<em>Case for the rock </em> $m = 5.0 Kg$ <em>:</em>

m1 will be equal to the mass of the Earth $m1 = 5.972×10^{24} Kg$ and since the rock and the pebble are held near the surface of the Earth, then, r will be equal to the radius of the Earth $r = 6371000m$ .

$F = (6.67x10^{-11}kg.m/s^{2}.m^{2}/kg^{2})\frac{(5.972x10^{24} Kg)(5.0 Kg)}{(6371000 m)^{2}}$

$F = 49.06N$

Newton's second law can be used to know the acceleration.

$F = ma$

$a =\frac{F}{m}$ (2)

$a =\frac{(49.06 Kg.m/s^{2})}{(5.0 Kg)}$

$a =9.8m/s^{2}$

<em>Case for the pebble </em> $m = 3.0 Kg$ <em>:</em>

$F = (6.67x10^{-11}kg.m/s^{2}.m^{2}/kg^{2})\frac{(5.972x10^{24} Kg)(3.0 Kg)}{(6371000 m)^{2}}$

$F = 29.44N$

$a =\frac{F}{m}$

$a =\frac{(29.44 Kg.m/s^{2})}{(3.0 Kg)}$

$a =9.8m/s^{2}$

You might be interested in

When a fixed amount of ideal gas goes through an isobaric expansion A) its internal (thermal) energy does not change.B) the gas

Bingel [31]

<h2>Answer: its temperature must increase.</h2>

Explanation:

In an isobaric process the pressure remains constant, which means the initial pressure and the final pressure will be the same.

In addition, during this thermodynamic process, the volume of the ideal gas expands or contracts in such a way that the variation of pressure $\Delta P$ is neutralized.

Now, according to the First law of Thermodynamics that establishes the conservation of energy:

$\Delta U=\Delta Q-\Delta W$ (1)

Where:

$\Delta U$ is the internal energy

$\Delta Q$ is the heat transferred

$\Delta W$ is the work

Now, for an isobaric process:

$\Delta W=P\Delta V$ (2)

Where:

$P$ is the pressure (<u>always positive</u>)

$\Delta V$ is the volume variation of the gas

<u />

<u>Here we have two possible results:</u>

-If the gas expands (positive $\Delta V$ ), the work is positive.

-If the gas compresses (negative $\Delta V$ ), the work is negative.

In this case we are talking about the first result (work is positive).

Then, according to the above, equation (1) can be written as follows:

$\Delta U=\Delta Q - P\Delta V$ (3)

Clearing $\Delta Q$ :

$\Delta Q=\Delta U+P \Delta V$ (4)

Then, for an ideal gas in an isobaric process, part of the heat ( $Q$ ) added to the system will be used to do work (positive in this case) and the other part <u>will increase the internal energy</u>, hence <u>the temperature will increase as well.</u>

7 0

3 years ago

A private aviation helicopter's main rotor blades rotate at approximately

Arisa [49]

Answer: 7.5 rev/s

Explanation:

We are given the angular velocity $\omega$ a helicopter's main rotor blades:

$\omega=450 rpm=450 \frac{rev}{min}$

However, we are asked to express this $\omega$ in the International Systrm (SI) units. In this sense, the SI unit for time is second ( $s$ ):

$\omega=450 \frac{rev}{min} \frac{1 min}{60 s}$

$\omega=7.5 \frac{rev}{s}$

4 0

3 years ago

1. The mass defect of iron-56 is 0.52875 amu. What is the energy equivalent of this mass?

Delvig [45]

Answer:

Hello! Your answer is BELOW

Explanation:

1.About 91.754% of all iron is iron-56. Of all nuclides, iron-56 has the lowest mass per nucleon. With 8.8 MeV binding energy per nucleon, iron-56 is one of the most tightly bound nuclei.

2.The atomic weight of lead is quite variable in nature because the three heaviest isotopes are the stable end-products of the radioactive decay of uranium (238U to 206Pb and 235U to 207Pb) and thorium (232Th to 208Pb).

3.Mass defect for uranium-238 is 3.983 × 10-25 kg.

4.Energy and Mass Are Relative

The equation E = mc^2 states that the amount of energy possessed by an object is equal to its mass multiplied by the square of the speed of light.

Hope I helped! Ask me anything if you have any questions. Brainiest plz!♥ Hope you make a 100%. Have a nice morning! -Amelia♥

7 0

3 years ago

In the woman's mouth if

Tpy6a [65]

Answer:

hi mate,

interesting question, first of all the pressure is determined by using the following formula:

Pg = p * G * h

where p is the density of the liquid, G is the gravity and h is the height difference, in you case you have:

p = 1015 kg/m3

G = 9.8m/s2

h = 0.085 m

insert these values into the equation above:

Pg = 1015 kg/m3 * 9.8m/s2 * 0.085 m = 849.81 kg·m-1·s-2 or 849.81 pascal

hope it helps, :-)

please mark me as brainliest

7 0

2 years ago

If the object represented by the FBD below has a mass of 2.5 kg, what is the acceleration of the object?

Debora [2.8K]

Answer:

4 m/s² down

Explanation:

We'll begin by calculating the net force acting on the object.

The net force acting on the object from the left and right side is zero because the same force is applied on both sides.

Next, we shall determine the net force acting on the object from the up and down side. This can be obtained as follow:

Force up (Fᵤ) = 15 N

Force down (Fₔ) = 25 N

Net force (Fₙ) =?

Fₙ = Fₔ – Fᵤ

Fₙ = 25 – 15

Fₙ = 10 N down

Finally, we shall determine the acceleration of the object. This can be obtained as follow:

Mass (ml= 2.5 Kg

Net force (Fₙ) = 10 N down

Acceleration (a) =?

Fₙ = ma

10 = 2.5 × a

Divide both side by 2.5

a = 10 / 2.5

a = 4 m/s² down

Therefore, the acceleration of the object is 4 m/s² down

6 0

3 years ago