Chapter 4: Newton's Second Law of Motion

State Newton's second law of motion.

"The acceleration of an object is directly proportional to the net force acting on the object, is in the direction of the net force, and is inversely proportional to the mass of an object." Acceleration ~ Net Force / Mass

What is the condition for an object experiencing free fall?

An object only experiences free fall when the only force acting on it is the force of gravity, and nothing else not even friction.

When you push horizontally on a crate on a level floor that doesn't slide, how great is the force of friction on the crate?

Basically, if the crate doesn't slide it is because the amount of force, I apply is equal to the amount of friction force opposing me.

Sketch the path of a ball tossed vertically into the air. (Ignore air resistance.) Draw the ball halfway to the top, at the top, and halfway down to its starting point. Draw a force vector on the ball in all three positions. Are the vectors the same or different in the three locations? Are the accelerations the same or different in the three locations?

Basically, the vectors are representing different forces thus they will be facing different directions.

When your car moves along the highway at constant velocity, the net force on it is zero. Why, then, do you have to keep running your engine?

Because it is the engine that is keeping the car at a constant velocity. If I were to shut it off the friction between the tire and the ground would change thus ending the constant velocity.

Why does a cat that accidentally falls from the top of a 50-story building hit a safety net below no faster than if it fell from the 20th story?

Because the cat most likely hit his terminal velocity, thus the cat can no longer accelerate any more than it already has. (Not unless the cat spreads itself out)

Aristotle claimed that the speed of a falling object depends on its weight. We now know that objects in free fall, whatever the gravitational forces on them, undergo the same gain in speed. Why don't differences in their gravitational forces affect their accelerations?

Because the force and mass end up equalizing the acceleration. Even if both objects have different masses, they will require different force that would result in them having the same free fall acceleration.

Once the crate is sliding, how hard do you push to keep it moving at constant velocity?

In order to keep the crate sliding at a constant velocity, you must push it with the same force that is equal to the opposing friction force.

In the string-pull illustration in Figure 4.8, a sharp jerk on the bottom string results in the bottom string breaking. Does this occur because of the ball's weight or its mass?

It is the mass of the ball, which is responsible for the lower string breaking.

Which is more fundamental: mass or weight? Which varies with location?

Mass is more fundamental than weight. Mass does not vary by location, but weight does vary.

How does the force of friction for a sliding object vary with speed?

Not really at all, the force of friction is not dependent on speed.

If the net force acting on a sliding block is somehow tripled, what happens to the acceleration?

The acceleration is tripled, because of newtons second law.

What is the acceleration of a rock at the top of its trajectory when it has been thrown straight upward? (Is your answer consistent with Newton's second law?)

The acceleration of the rock is equivalent to the gravitational force which is approx. 10 m/s^2 downward. Yes, it is consistent because it states that the acceleration is proportional to the net force acting upon an object.

If the mass of a sliding block is somehow tripled at the same time the net force on it is tripled, how does the resulting acceleration compare with the original acceleration?

The acceleration stays the same. This is because the mass and net force are both equally tripled and per newtons second law, if net force increases acceleration increase the same amount, but if mass increase acceleration does the invers and decreases by the same amount. Thus, both cancel out.

In the absence of air resistance, if a ball is thrown vertically upward with a certain initial speed, on returning to its original level it will have the same speed. When air resistance is a factor, will the ball be moving faster, the same, or more slowly than its throwing speed when it gets back to the same level? Why? (Physicists often use the "principle of exaggeration" to help them analyze a problem. Consider the exaggerated case of a feather, not a ball, because the effect of air resistance on the feather is more pronounced and therefore easier to visualize.)

The ball falls slower because it will eventually have the forces acting on it and its mass cancel out to 0N thus the ball would be in terminal velocity falling at a constant (slower than initially thrown) speed downward.

You exert a force on a ball when you toss it upward. How long does that force last after the ball leaves your hand?

The force I applied will last until it reaches its apex height where the gravity force and the force applied are have a net force equivalent to zero.

Why doesn't a heavy object accelerate more than a light object when both are freely falling?

The heavy object doesn't accelerate more than a light object because the acceleration is the same when the objects are in free fall. Basically, free fall is not dependent on the mass of an object.

What is the net force that acts on a 10-N falling object when it encounters 4 N of air resistance? 10 N of air resistance?

The net force of a 10-N falling object encountering 4 N of air resistance is 6 N. The net force of a 10-N falling object encountering 10-N of air resistance is zero.

What is the net force acting on a 1-kg ball in free fall?

The net force would be approx. 10 N.

The Standard International unit for force is the.

The standard international unit for force is pounds (lb.)

The Standard International unit for mass is the.

The standard international unit for mass is the kilogram (kg)

When a coin is tossed upward, what happens to its velocity while ascending? Its acceleration? (Ignore air resistance.)

The velocity begins to slow down, as it reaches its apex height. The acceleration on the other hand if we ignore air resistance is moving at a constant rate.

What is the weight of a 1-kilogram brick resting on a table?

The weight of a 1-kilogram brick resting on a table is about 10 newtons (more precisely, 9.8 N).

If a motorcycle moves with a constant velocity, can you conclude that there is no net force acting on it? How about if it's moving with constant acceleration?

There is no net force because it is all equalized. If there is no net force by newton's second law of motion, there is no acceleration as they are directly proportional.

What is the acceleration of a falling object that has reached its terminal velocity?

When an object has reached its terminal velocity the acceleration of the falling object is zero.

How does the force of gravity on a raindrop compare with the air drag the drop encounters when it falls at constant velocity?

When an object is moving at constant velocity that means that it has a net force of 0N acting on it. This would mean that the gravitational force is being in a sense canceled out by the force of the air drag.

A discussion partner says that, before the falling ball in the preceding exercise reaches terminal velocity, it gains speed while its acceleration decreases. Do you agree or disagree? Defend your answer.

Yes, I do agree. As the ball increases in speed so does the air resistance to the point that the acting forces on it equalize to 0N. As this happens acceleration being proportional to net force begins to decrease until it terminates.