This question tests your understanding of the concept of centripetal force. Centripetal force is a force that maintains a body's circular travel along a curved surface and points inward towards the center of the curve from each point that the body travels along. Centripetal force is calculated as follows:

Therefore the centripetal force on the car is .

Let's use the midpoint as our point of reference. With that said,  is  from the center, and  is  from the center. However, each of these are on different sides of the midpoint. When we set up our center of gravity equation, we must determine a (+) and (-) side in order to denote under which side our mobile string will fall. It may be helpful to look at the mobile as a number line, with the left being negative, and the right side positive, but you can really use which ever is more comfortable.

Our main equation is this:

Where  is our weight in newtons and  is our distance in meters. Typically, we would want to convert everything to SI units, so let's go ahead and do that (ex: )

Now let's plug in our numbers, remember about our negative/positive sides!

This should give us 

Now, because this number is negative, we know it's to the left of our midpoint (if you chose to set up your -/+ sides opposite of how we did it, your answer will be positive). Regardless of the outcome, this measurement is meant to be taken from object A to the midpoint. Well, do any of our answers have either (+) or (-) ? No. But if we read them carefully, we can determine that the answer is  from the left of the dowel by using simple subtraction.

One side is 

Think about it logically too (use your pencil). The heavier end of a pencil usually has a bulky eraser on it (just like the bulkier object on the left). Try holding the pencil at the tip's end, and then gradually try balancing it in the same manner as you move closer to the eraser. 

ALSO NOTE: the question states the weight of the dowel as well. But look we didn't even need it. Sometimes the AP exam will give you some aspects in the question to distract you.

Newton's first law states that an object in motion tends to stay in motion unless if acted upon by a net force. This means that if friction is not being accounted for, there is no net force required to keep an object moving if it's in motion. A net force is only required to change an object's motion. The 500 kg object is moving at a constant velocity; therefore, there is no net force (0 Newtons) acting on the object.

Newton's first law of motion refers to objects with no external forces acting on them. Objects with no external forces will maintain the same velocity, meaning that

(1) if they are not moving, they will continue not moving

(2) if they are moving, they will keep moving with the same speed and direction

The answer "Dropping a box causes it to accelerate downwards" refers to a box with a force acting upon it—the force of gravity. Also, the box is accelerating, unlike objects referred to by Newton's first law of motion, which have constant velocities.

In a vacuum, there is no friction due to air resistance. Newton's first law states that an object in motion stays in motion unless acted upon by a net force. Thus the spaceship will travel at the constant speed (zero acceleration) of  indefinitely and the net force on the spaceship must be zero. This can also be shown mathematically:

Since both you and your friend are traveling at a constant speed, the acceleration of you and your friend is zero. Thus, neither you nor your friend experiences any acceleration. This can be shown mathematically using the equation for acceleration:

Since there is no change in velocity over time acceleration is zero. Also note that when acceleration is zero, so is the net force.

Because an object at rest tends to stay at rest, when your car is hit your body/neck will 'want' to stay where it was. This will cause your body and neck to 'whip' as it will take time for it to speed up from being hit. 

The acceleration of the person in the elevator is determined by the net forces and his/her mass. The net force is calculated to be 20N upwards. To find the mass of the passenger, use the following formula:

Then, to find the net acceleration, use Newton's second law.

Recall Newton's first law of motion: an object will remain in its state of uniform motion unless acted upon by an external force. The car's motion is described as having a constant velocity which is a uniform state so there are no external forces.

If the box is moving at a constant velocity, we know that the sum of the forces acting up and down the inclined plane must add to zero. If the only forces acting are gravity and friction, we can show:

We can gain information about the normal force  by looking at the forces acting perpendicular to the plane, shown by: 

Putting all of this together lets us write the following expression for the forces in acting along the plane, and finally, our answer: