First, lets identify the given information:

Since this is a collision problem, we can apply the law of conservation of momentum:

Because Car 2 is initially at rest, this equation can be simplified:

The equation can then be rearranged to solve for the mass of Car 2:

 By plugging in the known values, we can determine the mass of Car 2:

To calculate the pressure  on the floor, we need to know the force  acting on the floor, as well as the area  over which it acts.

The force acting is simply the weight of the cube, 

The area is the area of one side of the cube as it rests on the floor, 

Therefore, the pressure  is given as:

Plug in known values and solve.

Once the spacecraft had reached a constant speed, so had it's occupants. Thus, the astronauts were also moving at and they were experiencing no forces from their seats.

Thus, the astronauts were experiencing zero net force.

 and  cancel each other out in the horizontal direction due to the fact that they are equal and opposite about the vertical axis. Now that the resultant force in the x-direction is zero, we must find what  must be in order to zero out the other two forces' y-components, which are:

These forces are pointing in the positive y-direction (pulling the object up). Therefore, in order to have a resultant force of zero in the vertical direction, there must be a downward force of

Since we are asked for the magnitude, we are not particularly concerned with the sign of this value.

In these conceptual problems, it is always best to draw an accurate force diagram. In string problems, there is always a tension force, and here, it is causing the circular motion. The tension force causes the lasso to swing in a circle and pulls it toward the center of the circle. 

To answer this question, we'll need to be familiar with Isaac Newton's fundamental laws of physics, which forms the basis of classical mechanics.

Newton's first law states that an object in motion will remain in that state of motion indefinitely, unless an outside force acts on this object.

Newton's second law can be stated as follows:

This expression tells us that the acceleration experienced by an object is directly proportional to the applied force and inversely proportional to the object's mass.

Newton's third law states that for every action, there is always an equal and opposite reaction. Another way of saying this is that if one object were to exert a force on a second object, then the second object would exert the same force against the first object.

One of the answer choices states the following

"In order for an object to be in motion, a force needs to act on it."

While this may seem intuitive based on our everyday experience, and it may also show some resemblance to Newton's first law, this statement is actually incorrect. Force is not responsible for motion - force is responsible for changes in motion.

The force due to kinetic friction is calculated by the equation 

where  is the normal force on the box from the ground. The frictional force is in the opposite direction of the force applied by you and your friend. Therefore, the net force can be calculated:

This problem deals with the conservation of energy in the form of a spring. The formula for the conservation of energy is:

We can eliminate initial kinetic energy to get:

We have two forms of potential energy in this problem: gravitational and spring. Therefore, we can rewrite the expression to be:

There is no initial gravitational potential energy and no final spring potential energy. Subsituting our expressions for potential and kinetic energy, we get:

Rearranging for final velocity, we get:

 is the original displacement (the same as ).

We have all of the values, so we can solve:

Before the elevator begins to accelerate, the block has a weight of:

While the elevator is accelerating, the block has a weight of:

Now we can say that the weight of the block has effectively increased by 2N.

We can use this increase in force to find out how much the equilibrium position will shift:

Rearranging for x (displacement), we get:

We know that the maximum acceleration of a spring occurs when it is at its maximum displacement. At this point, we can write an expression for the force that the block is under:

Rearranging for the distance, we get:

This is also the point at which the spring is storing its maximum potential energy:

We can substitute our rearranged distance equation into the equation for potential energy:

We also know that the maximum velocity of a spring occurs when it is at the point of equilibrium. Since the spring is on a frictionless surface, we can say that its kinetic energy at this point is equal to the maximum potential energy:

Plugging in the expressions for these variables:

Rearranging for velocity:

We know all of the values, so we can plug and chug: