Mass vs. Acceleration Graph Proving Newton's Second Law

[erykah722]

Homework Statement

Okay, so here's the question: Does your plot of acceleration versus hanging mass verify the Second Law? Explain your answer.

The experiment involved a cart with weights and a hanging mass on the edge of a table. After each trial, one weight was removed from the cart and put on the hanging mass.

Homework Equations

I know Net force = ma

The Attempt at a Solution

I got the following data and it was all correct when I submitted it:

Hanging Mass: Acceleration:
0.02 0.344
0.03 0.515
0.04 0.692
0.05 0.866
0.06 1.04
0.07 1.20

Okay, I know that as the hanging mass increases and the car weight decreases the acceleration increases. Can someone please explain how the linear graph of acceleration vs. the hanging mass proves Newton's second law?

 

[gneill]

The weights were moved from the cart to the "hanging mass". So no mass was removed from or added to the system. In all cases, the same total mass is being accelerated, right?

What's happening to the force that's doing the acceleration?

 

[erykah722]

So the force is increasing which accounts for the positive linear graph?

 

[erykah722]

Force was held constant throughout the experiment

 

[gneill]

Force was held constant throughout the experiment

How? You said F = ma, and your data says that a is changing. It seems to me that it was total mass that was held constant.

 

[erykah722]

How? You said F = ma, and your data says that a is changing. It seems to me that it was total mass that was held constant.

Here are the "basic principles":

In this experiment you will investigate the acceleration acquired by a body acted on by a constant force.
A cart is accelerated toward the right by the tension force in a string. That tension depends on the value of the hanging mass at the other end of the string.

You will conduct several trials, holding M = m1 + m2 constant (m1 = hanging mass) while varying m1, obtaining a different value of a for each value of m1. By graphing a versus m1 you will be able to fin M, the total mass of the system, which upon examination of a = (m1/M)g you will see is simply related to the slope of our graph.

 

[gneill]

Here are the "basic principles":

In this experiment you will investigate the acceleration acquired by a body acted on by a constant force.
A cart is accelerated toward the right by the tension force in a string. That tension depends on the value of the hanging mass at the other end of the string.

Surely the "constant force" alluded to is the constant force provided by the hanging mass during any given "run" of the experiment. Each run will have a different (but constant) force.

Have you drawn the free-body force diagrams for the setup?

 

[erykah722]

Oh wow, that makes sense. I don't know how I missed that. So back to the graph, since it is increasing, it is showing that force is increasing?

 

[gneill]

Oh wow, that makes sense. I don't know how I missed that. So back to the graph, since it is increasing, it is showing that force is increasing?

It's up to you to interpret the graph! . The data has the hanging mass (which can be translated to force) and the resulting acceleration of the total mass. Draw your conclusions from the plot!

 

[dbakg00]

My question about this setup is if you were to double the mass of the hanging weight, without changing the total mass, would the acceleration double also?

My thoughts are that the acceleration would not double because the total mass in the system would remain constant. This is more of a guess though. Can someone help point me in the right direction? Thanks