Question on free fall.

[RoboNerd]

Homework Statement

1. An object is in freefall on Earth. Which of the following statements is true?
   
   1. A) The object is gaining an equal amount of momentum for each second it is in free fall.
      
      
   2. B) The object is gaining an equal amount of momentum for each meter it falls.
      
      
   3. C) The object is gaining an equal amount of kinetic energy for each meter it falls.
      
      
   4. D) The object is gaining an equal amount of kinetic energy for each second it falls.
      
      
   5. E) The object is gaining an equal amount of speed for each meter it falls.
      

Homework Equations

no equations

The Attempt at a Solution

The answers say that the right answer is C. While I understand that there is a constant acceleration of gravity "g," I understand that for each second, there will be an increase in velocity of 9.8. This makes C incorrect, as they say for each meter, and not for a second that the object falls.

Could anyone please explain why each particular answer is wrong, and why C is right?

Thanks!

 

[Paul Colby]

Think about how much you weigh on the ground floor of a building versus how much you weigh on the third floor? What does this say about the force (thinking like Newton) the Earth apples to you? What did Newton say about masses and forces?

 

[Doc Al]

I understand that for each second, there will be an increase in velocity of 9.8.

That's true.

This makes C incorrect, as they say for each meter, and not for a second that the object falls.

How does a statement about each second relate to C, which is about each meter?

Hint: What does conservation of energy tell you?

 

[Doc Al]

The answers say that the right answer is C.

C is correct, but it's not the only correct choice.

 

[RoboNerd]

Think about how much you weigh on the ground floor of a building versus how much you weigh on the third floor? What does this say about the force (thinking like Newton) the Earth apples to you? What did Newton say about masses and forces?

I weigh less on the third floor than on the ground floor. This means that the force of gravity is weaker as according to Newton F = m * acceleration.

How does a statement about each second relate to C, which is about each meter?
Hint: What does conservation of energy tell you?

Conservation of energy shows that my potential energy per meter is converted to kinetic energy per meter.
Namely: mg ( 1 meter ) = (1/2) * m * v^2.

So thus, I now see why C is right. Which other answers are also right, as there is more than one right answer?

 

[CWatters]

Which other answers are also right, as there is more than one right answer?

I note you don't list any relevant equations. Since most of the questions ask about momentum or KE wouldn't it be good to cite the basic equations/definitions for momentum and KE?

Are you also familiar with the equations of motion for constant acceleration?

 

[CWatters]

Are you also familiar with straight line graphs and what they mean? eg If the graph is a straight line it means there is a linear relationship. For example (Question C) a plot of KE vs Displacement would be a straight line.

 

[Doc Al]

Which other answers are also right, as there is more than one right answer?

You tell us!

(Follow CWatters' advice.)

 

[Paul Colby]

I weigh less on the third floor than on the ground floor. This means that the force of gravity is weaker as according to Newton F = m * acceleration.

While what you say is true, I believe the standard physics class assumption is that the gravitational field on the ground is approximated by a constant $9.8m/s^2$. In this limit isn't A true since $\frac{d mv}{dt} = m\frac{dv}{dt} = \text{constant}$

 

[Doc Al]

While what you say is true, I believe the standard physics class assumption is that the gravitational field on the ground is approximated by a constant $9.8m/s^2$. In this limit isn't A true since $\frac{d mv}{dt} = m\frac{dv}{dt} = \text{constant}$

Yes, I think you can safely assume a constant acceleration.

 

[RoboNerd]

Are you also familiar with the equations of motion for constant acceleration?

Yes.

While what you say is true, I believe the standard physics class assumption is that the gravitational field on the ground is approximated by a constant 9.8m/s29.8m/s29.8m/s^2. In this limit isn't A true since dmvdt=mdvdt=constant

Yes. This means that A is true.

B) The object is gaining an equal amount of momentum for each meter it falls.

Let's examine this one. If an object falls, its velocity will vary due to the constant acceleration of gravity. However momentum is p = m * v, so the force of gravity is going to cause an Fg = dp/dt, the change in momentum with respect to time, not with respect to distance dy, so I think this answer is wrong.

We already identified C as the right answer.

D) The object is gaining an equal amount of kinetic energy for each second it falls.

This might be true. For each second, we have a constant acceleration, which leads to the gaining of the same amount of velocity, which is related to kinetic energy. Thus increasing velocity at a constant rate would increase K.E. at a constant rate as well.

1. 1. E) The object is gaining an equal amount of speed for each meter it falls.

Obviously not true. The object is falling down with an increasing speed per second due to increased acceleration, so over time, it will zip through a one meter time frame much quicker and gain less speed through that.

What do you all think about my thoughts?

 

[Doc Al]

Yes. This means that A is true.

Good.

Let's examine this one. If an object falls, its velocity will vary due to the constant acceleration of gravity. However momentum is p = m * v, so the force of gravity is going to cause an Fg = dp/dt, the change in momentum with respect to time, not with respect to distance dy, so I think this answer is wrong.

Good.

This might be true. For each second, we have a constant acceleration, which leads to the gaining of the same amount of velocity, which is related to kinetic energy. Thus increasing velocity at a constant rate would increase K.E. at a constant rate as well.

Careful here. Does an equal increase in speed mean an equal increase in KE? Play with few numbers and test that reasoning. (Try comparing the change in KE in going from 5 m/s to 10 m/s to the change in going from 10 m/s to 15 m/s.)

Obviously not true. The object is falling down with an increasing speed per second due to increased acceleration, so over time, it will zip through a one meter time frame much quicker and gain less speed through that.

Good.

 

[RoboNerd]

Careful here. Does an equal increase in speed mean an equal increase in KE? Play with few numbers and test that reasoning. (Try comparing the change in KE in going from 5 m/s to 10 m/s to the change in going from 10 m/s to 15 m/s.)

Nope, it will not.