Does potential energy increase,kinetic energy decrease when a book is placed on a shelf

A large rock of mass me materializes stationary at the orbit of Mercury and falls into the sun. Itf the Sun has a mass ms and ra

son4ous [18]

Answer:

The answer is $v = \sqrt{2G\frac{M_s}{R^2}(R-r_s)}$ .

Explanation:

From the law of gravity,

$F = G \frac{Mm}{r^2}$

considering F as a conservative force, $F = - \nabla U$ ,

the general expression for gravitational potential energy is

$U = -G \frac{Mm}{r}$ ,

where G is the gravitational constant, M and m are the mass of the attracting bodies, and r is the distance between their centers. The negative sign is because the force approaches zero for large distances, and we choose the zero of gravitational potential energy at an infinite distance away.

However, as the mass of the Sun is much greater than the mass of the rock, the gravitational acceleration is defined as

$g = -G \frac{M}{r^2}$ ,

(the negative sign indicates that the force is an attractive force), and the potential energy between the rock and the Sun is

$U = g M_e R$ ,

which is actually the total energy of the system, because the rock materializes stationary at this point (there is no radial kinetic energy).

When the rock hits the surface of the Sun, almost all potential energy is converted to kinetic energy, but not all because the Sun is not a puntual mass. So the potential energy converted to kinetic energy is

$U_p = g M_e(R- r_s)$ ,

then, the kinetik energy when the rock hits the surface is

$U_k =\frac{1}{2}M_e v^2 = g M_e(R- r_s)$ ,

so

$v = \sqrt{2g(R-r_s)}$

where g is the gravitational acceleration generated by the Sun at R,

$g = G \frac{M_s}{R^2}$ .

8 0

3 years ago

3. The soccer kicker kicks a 2 kg football with a force of 68 N. How fast will the ball accelerate down the field?

Katen [24]

Answer:

$\boxed {\boxed {\sf m= 2 \ kg , \\a= 34 \ m/s^2, \\\F= 68 \ N}}$

Explanation:

The formula for force is:

$F=m*a$

If we rearrange the formula to solve for a (acceleration), the formula becomes

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

The force is 68 Newtons. Let's convert the units to make the problem easier later on. 1 N is equal to 1 kg*m/s², so the force of 68 N is equal to 68 kg*m/s².

The mass is 2 kilograms.

$F=68 \ kg*m/s^2 \\m= 2\ kg$

Substitute the values into the formula.

$\frac{68 \ kg*m/s^2}{2 \ kg} =a$

Divide. Note that the kilograms will cancel each other out (hence why we changed the units).

$\frac{68 \ m/s^2}{2}=a$

$34 \ m/s^2=a$

The acceleration is 34 meters per second squared.

6 0

3 years ago

If time travel to the future existed, doesn't that mean that the future has already occurred and that we are living in the past?

kodGreya [7K]

Answer:

As of right now the techology has not been invented to time travel

if we were to time travel to the future from where that person travled from would be the past and to them the people from where they came from are living in the past

Explanation:

3 0

3 years ago

A woman of mass 50 kg is swimming with a velocity of 1.6 m/s. If she stops stroking and glides to a stop in the water, what is t

Snezhnost [94]

Answer:

Impulse of force = -80 Ns

Explanation:

Given the following data;

Mass = 50kg

Initial velocity = 1.6m/s

Since she glides to a stop, her final velocity equals to zero (0).

Now, we would find the change in velocity.

$Change \; in \; velocity = final \; velocity - initial \; velocity$

Substituting into the equation above;

Change in velocity = 0 - 1.6 = 1.6m/s

$Impulse \; of \; force = mass * change \; in \; velocity$

Substituting into the equation, we have;

$Impulse \; of \; force = 50 * -1.6$

Impulse of force = -80 Ns

Therefore, the impulse of the force that stops her is -80 Newton-seconds and it has a negative value because it is working in an opposite direction, thus, bringing her to a stop.

5 0

2 years ago

Write the formular of force experienced by charge in electric field

lesya [120]

The answer is b) force exponerse by charge in electric field

7 0

3 years ago

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