A heavy object and a light object are dropped from the same height. If we neglect air resistance, which will hit the ground first?

Answer:

The linear velocity is represented by the following expression:

Explanation:

From Rotation Physics we know that linear velocity of a point moving with uniform circular motion is:

(Eq. 1)

Where:

- Radius of rotation of the particle, measured in meters.

- Angular velocity, measured in radians per second.

- Linear velocity of the point, measured in meters per second.

But we know that angular velocity is also equal to:

(Eq. 2)

Where:

- Angular displacement, measured in radians.

- Time, measured in seconds.

By applying (Eq. 2) in (Eq. 1) we get that:

(Eq. 3)

From Geometry we must remember that circular arc (), measured in meters, is represented by:

The linear velocity is represented by the following expression:

Final answer:

Internal energy is the sum of potential and kinetic energies in the particles of a substance.

Explanation:

The type of energy that refers to the sum of potential and kinetic energies in the particles of a substance is internal energy.

Internal energy is the total energy of all the particles in a substance, including the energy associated with their motion and stored energy due to their positions or arrangements. It consists of both potential energy (energy stored in the particles' positions) and kinetic energy (energy of the particles' motion).

For example, consider a gas in a container. The internal energy of the gas would be the sum of the potential energy of the gas particles due to their positions and the kinetic energy of the particles due to their motion.

Learn more about Internal Energy here:

brainly.com/question/36602494

Answer:

it A

Explanation:

Its a negative ion that hss one less valence electron than a netural bromine atom

Answer:

The Jupiter´s mass is approximately 1.89*10²⁷ kg.

Explanation:

The only force acting on Calisto while is rotating around Jupiter, is the gravitational force, as defined by the Newton´s Universal Law of Gravitation:

Fg = G*mc*mj / rcj²

where G = 6.67*10⁻¹¹ N*m²/kg², mc= Callisto´s mass, mj= Jupiter´s mass, and rcj = distance from Jupiter for Callisto= 1.88*10⁹ m.

At the same time, there exists a force that keeps Callisto in orbit, which is the centripetal force, that actually is the same gravitational force we have already mentioned.

This centripetal force is related with the period of the orbit, as follows:

Fc = mc*(2*π/T)²*rcj.

In order to be consistent in terms of units, we need to convert the orbital period, from days to seconds, as follows:

T = 16.69 days* 86,400 (sec/day) = 1.44*10⁶ sec.

We have already said that Fg= Fc, so we can write the following equality:

G*mc*mj / rcj² = mc*(2*π/T)²*rcj

Simplifying common terms, and solving for mj, we get:

mj = 4*π²*(1.88*10⁹)³m³ / ((1.44*10⁶)² m²*6.67*10⁻11 N*m²/kg²)

mj = 1.89*10²⁷ kg.

Answer: Mass of Jupiter ~= 1.89 × 10^23 kg

Explanation:

Given:

Period P= 16.69days × 86400s/day= 1442016s

Radius of orbit a = 1.88×10^6km × 1000m/km

r = 1.88 × 10^9 m

Gravitational constant G= 6.67×10^-11 m^3 kg^-1 s^-2

Applying Kepler's third law, which is stated mathematically as;

P^2 = (4π^2a^3)/G(M1+M2) .....1

Where M1 and M2 are the radius of Jupiter and callisto respectively.

Since M1 >> M1

M1+M2 ~= M1

Equation 1 becomes;

P^2 = (4π^2a^3)/G(M1)

M1 = (4π^2a^3)/GP^2 .....3

Substituting the values into equation 3 above

M1 = (4 × π^2 × (1.88 × 10^9)^3)/(6.67×10^-11 × 1442016^2)

M1 = 1.89 × 10^27 kg

Answer:

0.123 m.

Explanation:

From Hook's law,

The potential energy of the book = the energy stored in the spring.

mgh = 1/2ke².................. Equation 1

Where m= mass of the book, g = acceleration due to gravity, h = height, k = spring constant of the spring, e = distance of compression.

make e the subject of the equation

e = √(2mgh/k).................. Equation 2

Given: m = 1.3 kg, h = 0.8 m, k = 1350 N/m

Constant: g = 9.8 m/s²

Substitute into equation 2

e = √(2×1.3×0.8×9.8/1350)

e = √(20.384/1350)

e = √(0.0151)

e = 0.123 m.

Answer:

0.015m (downwards)

Explanation:

When the book is dropped on the top of the spring at that height, the potential energy () of the book is converted to elastic energy () on the spring thereby causing a compression on the spring. i.e

=

But;

The potential energy of the mass (book), is the product of the mass(m) of the book, the height(h) from which it was dropped and the acceleration due to gravity (g). i.e

= - m x g x h         [the -ve sign shows a decrease in height as the mass (book) drops]

Also;

The elastic energy () of compression of the spring is given by

= x k x c

Where;

c = compression length of the spring

k = the spring's constant

Substitute these values of and E into equation (i) as follows;

- m x g x h = x k x c             ----------------(ii)

From the question;

m =  1.3kg

h =  0.8m

Take g = 10m/s²

k =  1350N/m

Substitute these values into equation (ii) as follows;

- 1.3 x 10 x 0.8 = x 1350 x c

- 10.4 = 675c

Solve for c;

c = - 0.015 m          [The negative sign shows that the spring actually compresses]

Therefore, the maximum distance the spring will be compressed is 0.015m (downwards of course).