The weight of the object on Earth's surface is:

The force on the new planet is five times that on Earth, so we can simply multiply:

We know that the weight of an object is given by:

 is the mass of the object and  is the gravitational acceleration of whatever planet the object happens to be on.

We know the gravity on the unkown planet, so the weight of the woman is given by:

We need only to find the mass of the woman to solve the problem. Since the mass of the woman is constant, we can use the information about her weight on Earth to figure out her mass.

Use this mass to solve for her weight on the new planet.

Escape velocity is the velocity at which the kinetic energy of an object in motion is equal in magnitude to the gravitational potential energy. This allows us to set two equations equal to each other: the equation for kinetic energy of an object in motion and the equation for gravitational potential energy. Therefore:

In this case,  . Substitute.

Since the radius of the new planet is  or  the radius of the original planet, and they have the same masses, we can equate:

Where  is the escape velocity of the larger planet and  is the escape velocity of the smaller planet.

Since the direction of the gravitational force is directly towards the center of the Sun, it lies in the plane of the comet's orbit. Since torque is , the torque is always zero. That is why the comet's angular momentum is conserved in orbit.

Since the gravitational force cannot exert torque on the satellite about the Earth's center, angular momentum is conserved in this orbit:

Since the speed of the satellite at apogee is too low for a circular orbit at that orbital radius, the satellite needs to speed up to circularize the orbit.

Relevant equations:

Determine the clockwise torque caused by the bucket.

Write an expression for the counterclockwise torque caused by the rope.

Combine the torque of the rope and the torque of the bucket into the net torque equation.

Since the system has no angular acceleration, net torque must be zero, allowing us to solve for the force of the rope.

The correct answer is external force. External forces applied to an object will result in non-zero acceleration, causing the object to move. In contrast, internal forces contribute to the properties of the object and do not result in acceleration of the object.

Either positive or negative forces can result in the acceleration of an object. The sign on the force simply conveys information about its relative direction.

When the rocket launches it produces a downward force of 30000N. Due to the third law of motion, the rocket experiences a 30000N reaction force that pushes it upwards. 

In addition, the rocket experiences the downward force of its own weight. This is given by:

We know that .

We know the mass of the rocket is 1000kg, so we need only to find the net force to solve for acceleration.

We know that  (since  is directed upwards and  is directed downwards).

Finally we solve for acceleration:

Since the boxes are all connected by ropes, we know that the acceleration of each box is exactly the same. They all move simultaneously, in tandem, with the same velocity and acceleration.

A quick analysis of each box will produce a very simple system of equations. Each rope experiences some tension, so we will label the tension experienced by the rope between  and  as . Similarly, we will label the tension experienced by the rope between  and  as .

For the box on the right (of mass ) we know that the force  pulls to the right and the rope pulls it to the left with a tension of .

We get the equation: .  is the mass of the box and  is its acceleration (which is the same for the other boxes).

For the middle box (of mass ) we have a rope pulling on it on the right with tension  and a rope pulling on the left with tension .

So we get the equation: .  is the mass of the box and  is its acceleration (which is the same for the other boxes).

Finally, for the box on the left (of mass ) we have only one rope pulling it to the right with a tension .

So we get the equation: .  is the mass of the box and  is its acceleration (which is the same for the other boxes).

Now it is just a matter of simple substitution. We have three equations:

From them we can get an expression for the force. Isolate  in the second equation.

Substitute the expression of  from the first equation and simplify.

Use this value of  in the third equation to get an expression for the force.

So we have:

Solve for acceleration.