Newton’s 2nd Law and Air Resistance: Key Concepts and Problems

Is acceleration proportional to net force or does acceleration equal net force?

Acceleration is directly proportional to net force, as stated in Newton's second law of motion, which can be expressed as F = ma, where F is net force, m is mass, and a is acceleration.

Is acceleration directly proportional to mass, or is it inversely proportional to mass? Give an example.

Acceleration is inversely proportional to mass. For example, if a constant force is applied to two objects, a lighter object will accelerate more than a heavier object.

Suppose you exert a horizontal push on a crate that rests on a level floor, and it doesn't move. How much friction acts compared with your push?

The friction force acting on the crate is equal to the horizontal push you exert, but in the opposite direction, resulting in no movement.

As you increase your push, will friction on the crate increase also?

Yes, as you increase your push on the crate, the friction force will also increase until it reaches its maximum static friction limit.

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

Both heavy and light objects accelerate at the same rate due to gravity (approximately 9.81 m/s²) when in free fall, regardless of their mass.

What two principal factors affect the force of air resistance on a falling object?

The two principal factors are the speed of the object and its cross-sectional area.

If two objects of the same size fall through air at different speeds, which encounters the greater air drag?

The object falling at the greater speed encounters the greater air drag.

Calculate the acceleration of a bike that goes from 8 m/s to 20 m/s in 4 s.

The acceleration is calculated using the formula a = (final velocity - initial velocity) / time, which gives a = (20 m/s - 8 m/s) / 4 s = 3 m/s².

Compare from greatest to least: The net forces on boxes of chocolates of various masses on a friction-free level table.

The net force on each box is equal to its mass times acceleration. If all boxes are at rest, the net force on each is zero.

Compare from greatest to least: The acceleration of these skydivers.

The acceleration depends on the net force acting on each skydiver after accounting for air drag. The 1000-N man with 800 N drag has the greatest net force and thus the greatest acceleration.

What is the net force on a bright red Mercedes convertible traveling along a straight road at a steady speed of 100 km/h?

The net force is zero because the car is moving at a constant speed, indicating that all forces acting on it are balanced.

When a junked car is crushed into a compact cube, does its mass change? Its weight? Its volume? Explain.

The mass and weight of the car do not change when it is crushed, but its volume decreases significantly.

What is the acceleration of a ball at the top of its trajectory when thrown straight upward?

The acceleration of the ball at the top of its trajectory is -9.81 m/s² (downward), due to gravity, even though its velocity is zero at that instant.

Two basketballs are dropped from a high building through the air. One ball is hollow and the other filled with rocks. Which accelerates more? Defend your answer.

Both basketballs accelerate at the same rate due to gravity, as air resistance affects them equally regardless of their mass.

How does the terminal speed of a parachutist before opening a parachute compare to terminal speed after? Why is there a difference?

The terminal speed before opening the parachute is higher because the parachutist experiences less air resistance. After opening the parachute, the terminal speed decreases due to increased air resistance.

How does the gravitational force on a falling body compare with the air drag it encounters before it reaches terminal velocity? After?

Before reaching terminal velocity, the gravitational force is greater than air drag. After reaching terminal velocity, the gravitational force equals the air drag, resulting in no further acceleration.