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3 years ago

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Newton's law of universal gravitation is represented by f = g mm r2 where f is the gravitational force, m and m are masses, and

r is a length. force has the si units kg · m/s2. what are the si units of the proportionality constant g?

1 answer:

Sedbober [7]3 years ago

6 0

Answer: ${kg^{-1}}{s^{-2}}m^3$

$F=G \frac {mM}{R^2}$

force has the SI units:

$kg . ms^{-2}$

SI unit of mass is kg and SI unit of distance is m.

we can bring gravitational constant on one side of the formula and rest all the other terms on right hand side

$G= \frac {F}{mM}\times R^2=\frac{kg . ms^{-2}}{kg^2} \times m^2\\ = {kg^{-1}}{s^{-2}}m^3$

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Two 90.0-kilogram people are separated by 3.00 meters. What is the magnitude of the gravitational force that one person exerts o

VARVARA [1.3K]

Answer:

the magnitude of gravitational force is 6 x 10⁻⁸ N.

Explanation:

Given;

mass of the two people, m₁ and m₂ = 90 kg

distance between them, r = 3.0 m

The magnitude of gravitational force exerted by one person on another is calculated as;

$F = \frac{Gm_1m_2}{r^2} \\\\$

where;

G is gravitational constant = 6.67 x 10⁻¹¹ Nm²/kg²

$F = \frac{Gm_1m_2}{r^2} \\\\F = \frac{6.67\times 10^{-11} \times \ 90 \ \times \ 90}{3^2} \\\\F = 6\times 10^{-8} \ N$

Therefore, the magnitude of gravitational force is 6 x 10⁻⁸ N.

4 0

3 years ago

A ball of mass 0.120 kg is dropped from rest from a height of 1.25 m. It rebounds from the floor to reach a height of 0.820 m. W

Vikentia [17]

Answer:

1.0752 kgm/s

Explanation:

Considering when the drop was dropped from rest from a height,

mass of the ball, m = 0.120 kg

height, h = - 1.25 m

the initial velocity, u = 0 m/s

the acceleration due to gravity, g = - 9.8 m/s²

From equation of motion

$V^{2} = U^{2} + 2gh$

Substituting the values,

$V^{2} = 0^{2} + 2(-9.8 m/s^{2})(-1.25 m)$

$V^{2} = 24.5 m/s$

$V = \sqrt{24.5} \ m/s$

$V = 4.95 \ m/s$

V = ± 4.95 m/s

V = - 4.95 m/s

Since the ball is moving downward, the final velocity of the ball when it hits the floor is V = - 4.95 m/s

Considering when the ball rebounds from the floor,

assume the mass of the ball still remain, m = 0.120 kg

height, h = 0.820 m

the final velocity, v = 0 m/s

the acceleration due to gravity, g = - 9.8 m/s²

From equation of motion

$V^{2} = U^{2} + 2gh$

Substituting the values,

$0^{2} = U^{2} + 2(-9.8 m/s^{2})(0.820 m)$

$0 = U^{2} - 16.072 m/s$

$U^{2} = 16.072 m/s$

$U = \sqrt{16.072} \ m/s$

U = ± 4.01 m/s

U = + 4.01 m/s

Since the ball is moving upward, the initial velocity of the ball from the bounce from the floor is U = + 4.01 m/s

From Newton's second law of motion, applied force is directly proportional to the rate of change in momentum.

$F = \frac{mv - mu}{t}$

$F.t = m(v - u)$

⇒ Impulse = Change in momentum

To calculate the impulse, the moment before the ball hits the ground will be the initial momentum while the moment the ball rebounces will be the final velocity,

∴ F.t = 0.120 kg(4.01 m/s - (-4.95 m/s) )

F.t = 0.120 kg(4.01 m/s + 4.95 m/s) )

F.t = 0.120 kg × 8.96 m/s

Impulse = 1.0752 kgm/s

The impulse given to the ball by the floor is 1.0752 kgm/s

6 0

3 years ago

A kangaroo can jump over an object 2.46 m high. (a) Calculate its vertical speed (in m/s) when it leaves the ground.

Elenna [48]

Answer:

a) 6.95 m/s

b) 1.42 seconds

Explanation:

t = Time taken

u = Initial velocity

v = Final velocity

s = Displacement

a = Acceleration due to gravity = 9.81 m/s²

$v^2-u^2=2as\\\Rightarrow -u^2=2as-v^2\\\Rightarrow -u^2=2\times -9.81\times 2.46-0^2\\\Rightarrow u=\sqrt{2\times 9.81\times 2.46}\\\Rightarrow u=6.95\ m/s$

a) The vertical speed when it leaves the ground. is 6.95 m/s

$v=u+at\\\Rightarrow t=\frac{v-u}{a}\\\Rightarrow t=\frac{0-6.95}{-9.81}\\\Rightarrow t=0.71\ s$

Time taken to reach the maximum height is 0.71 seconds

$s=ut+\frac{1}{2}at^2\\\Rightarrow 2.46=0t+\frac{1}{2}\times 9.81\times t^2\\\Rightarrow t=\sqrt{\frac{2.46\times 2}{9.81}}\\\Rightarrow t=0.71\ s$

Time taken to reach the ground from the maximum height is 0.71 seconds

b) Time it stayed in the air is 0.71+0.71 = 1.42 seconds

3 0

3 years ago

Which statements describe Earth? Select three options. It is an outer planet. It is a terrestrial planet. It was formed from gas

AVprozaik [17]

The formation of Earth is supported by the statements like, it is a terrestrial planet. it was formed from gas and dust. it was formed in a debris disk from colliding planetesimals.

The given problem is based on the correct statements entitling the description of Earth. Earth is amongst 8 planets in our solar system, that happen to orbit around the sun.

The statements given to describe the Earth are as follows:

Earth is not an Outer planet. It is an inner planet that lies closest to the sun after Mercury and Venus.
Earth is a terrestrial planet because it is having a compact and rocky surface. Also, it is known to be an as largest terrestrial planet in the solar system with extensive regions of liquids and water.
The abundant rocky surfaces have evolved from the cloud of dust and gas, during the post-Big Bang Era. So, it is somewhere true to say that Earth is formed from gas and dust.
The earlier atmosphere of Earth was known for having proportional layers of Hydrogen and Helium. Hence is quite true to say that the Earth is having an atmosphere of Hydrogen and helium gases, but it is not as thick as the like sun.
Majority of terrestrial planets are formed from the collision of planetesimals in a debris disk. With Earth being one of them, it is quite correct to consider the given statement.

Thus, we can conclude that the formation of Earth is supported by the statements like: it is a terrestrial planet, it was formed from gas and dust and it was formed in a debris disk from colliding planetesimals.

Learn more about the planet Earth here:

brainly.com/question/24878669

3 0

2 years ago

The composition of the protoplanetary disk varies with distance from the protostar due to temperature.

lesantik [10]

Answer:

b) 1. Iron, silicates, carbon

2. Water

3. Methane, Ammonia, Carbon Dioxide.

Explanation:

Protoplanetry disk is the disk of gases and clouds of dust that rotates around the newly made star. The temperature of the protoplanetry disk actually determines the type of the planet that is to be formed. Inner part of the protoplanetry disk is closer to the sun thats why it is the hottest and denser part and composed of the materials like Iron, silicates, carbon as they have high melting points. Then comes those materials that exist in the solid form at lower temperatures such as the volatile materials like water. Ater that the protoplanetry disk is made of highly volatile materials that exists in solid from only at low coldest temperatures. So the outer part of the protoplanetry disk is made up of the Methane, Ammonia and Carbon Dioxide.

7 0

3 years ago