Answer to Question #234852 in Mechanics | Relativity for Kimberly

Question

1. When a force equal to its weight is applied to a body free to move by pushing, pulling, or lifting an object, what is its acceleration? Why? Justify your answer.

2. Can anything ever have a downward acceleration greater than a_g (9.8 m/s²)? If so, how can this be accomplished? Explain your reasoning.

3. When a body is accelerated, a force is invariably acting on it. Does this mean that, when a force is applied to a body, it is invariably accelerated? Why? Explain.

Answer 1

1. There is no acceleration downwards lest it get crushed. The acceleration upward depends on how much additional force you can muster. The applied force acring upward Is equal in magnitude but directly opposite in direction from gravity. The net force is 0. There is no acceleration but you might drift.

Pushing or pulling would be perpendicular to gravity and assuming no friction the acceleration would be I g,. 9.8n/sec² or 32fr/sec² in the direction of the applied force.

2. Yes

Fly a jet to 70,000 feet. Maneuver it to point its nose to the earth.

Acceleration is defined as the rate of change of speed with time, which happens when a force acts on a body. Acceleration due to gravity is due to the force of gravity. So all you need to do is to apply additional force in the direction of gravity, and voila!

So coming back to the jet which has been pointing at the Earth for a while now. Yeah, so turn up those engines, blast those afterburners, etc. Plenty of fighter jets have a thrust to weight ratio (T/W) of more than 1, which means the engines can accelerate the jet against the force of gravity — which means the aircraft can actually climb straight up like a rocket (conditions apply). Working with gravity, you'll be accelerating at ~20 m/s². That’s just an example. Even if T/W is less than 1, you can obviously accelerate faster than 9.81 m/s².

3. In Principia, Newton didn’t use the term “Net Force” in his first law. Upon a deeper read into the rest of Principia it becomes more clear that the term “net force” is what is implied/meant.

So there can be several forces acting on a body. If the vector sum of these forces is zero then a body will not be accelerated.

Accordingly, if a “net force” is acting on a body - then the body will be accelerated. By Newton’s second law:

Fnet=m*a

a=Fnet/m