What Do the Slope and Y-Intercept Represent in a Force vs. Acceleration Graph?

In summary, the conversation revolved around the experiment conducted using a cart and a pulley, adding hangers with different masses and measuring forces with a GLX machine. The resulting graph showed a trend line with an equation of y=2.16+0.11, where the slope represented acceleration and the Y intercept represented force. However, the independent and dependent variables on the graph were labeled incorrectly, causing confusion about the meaning of the slope and Y intercept.
  • #1
yeopar
4
0

Homework Statement



we used a cart and a pulley connected, and we added hangers with different masses. masses on hangers were: 0.02, 0.03,0.04, 0.05, 0.06,0.07 (kg) and the forces measured with GLX machine were: 0.19, 0.29, 0.39, 0.49, 0.59, 0.69. then we found out our acceleration and we graphed everything. Force on y-axis and acceleration on x axis. and we got our equation from the trend line which was: y=2.16+0.11

question: what is the value (including units) and the meaning of the slope of your graph?
what is the value (including units) and the meaning of the Y intercept?






Homework Equations


slope of our graph would mean mass since, F/A=M


The Attempt at a Solution


slope of our graph would mean mass, according to the formula we know derived from Newton's second law of motion, but our masses weren't constant. So what would the slope of the graph mean?

and what does Y intercept of the graph mean?
 
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  • #2
yeopar said:

Homework Statement



we used a cart and a pulley connected, and we added hangers with different masses. masses on hangers were: 0.02, 0.03,0.04, 0.05, 0.06,0.07 (kg) and the forces measured with GLX machine were: 0.19, 0.29, 0.39, 0.49, 0.59, 0.69. then we found out our acceleration and we graphed everything. Force on y-axis and acceleration on x axis. and we got our equation from the trend line which was: y=2.16+0.11

question: what is the value (including units) and the meaning of the slope of your graph?
what is the value (including units) and the meaning of the Y intercept?






Homework Equations


slope of our graph would mean mass since, F/A=M


The Attempt at a Solution


slope of our graph would mean mass, according to the formula we know derived from Newton's second law of motion, but our masses weren't constant. So what would the slope of the graph mean?

and what does Y intercept of the graph mean?

It looks to me that your data included Force and mass. You have a bunch of masses written down... 0.02kg, 0.03kg, 0.04kg,... these are masses.

So I can only conclude that you were attempting to determine the acceleration which you basically wrote. You graphed Force against mass so the slope you found was acceleration.
F/m = a
 
  • #3
yeopar said:

Homework Statement



we used a cart and a pulley connected, and we added hangers with different masses. masses on hangers were: 0.02, 0.03,0.04, 0.05, 0.06,0.07 (kg) and the forces measured with GLX machine were: 0.19, 0.29, 0.39, 0.49, 0.59, 0.69. then we found out our acceleration and we graphed everything. Force on y-axis and acceleration on x axis. and we got our equation from the trend line which was: y=2.16+0.11

question: what is the value (including units) and the meaning of the slope of your graph?
what is the value (including units) and the meaning of the Y intercept?






Homework Equations


slope of our graph would mean mass since, F/A=M


The Attempt at a Solution


slope of our graph would mean mass, according to the formula we know derived from Newton's second law of motion, but our masses weren't constant. So what would the slope of the graph mean?

and what does Y intercept of the graph mean?

It looks to me that your data included Force and mass. You have a bunch of masses written down... 0.02kg, 0.03kg, 0.04kg,... these are masses.

So I can only conclude that you were attempting to determine the acceleration which you basically wrote. You graphed Force against mass so the slope you found was acceleration.
F/m = a

I think the part in red I highlighted is where you got a bit off...
 
  • #4
can i send you the copy of our excel sheet so that you can look it over?
 
  • #5
*should i?
 
  • #6
what pgardn is trying to say is that you incorrectly labeled the graph, the independent variable should be the masses you acquired and the dependent variable would be the force.
Now to graph this you'd place mass on the x-axis and force on the y axis. Thus the slope would be f/m=a.
 

Related to What Do the Slope and Y-Intercept Represent in a Force vs. Acceleration Graph?

What is a Force & Acceleration graph?

A Force & Acceleration graph is a visual representation of the relationship between force and acceleration. It shows how changes in force affect the acceleration of an object.

What does the slope of a Force & Acceleration graph represent?

The slope of a Force & Acceleration graph represents the mass of the object. The steeper the slope, the greater the mass of the object.

How is a Force & Acceleration graph related to Newton's Second Law of Motion?

Newton's Second Law of Motion states that the acceleration of an object is directly proportional to the net force acting on it and inversely proportional to its mass. A Force & Acceleration graph visually shows this relationship.

What is the difference between a positive and negative slope on a Force & Acceleration graph?

A positive slope on a Force & Acceleration graph represents a positive acceleration, meaning the object is speeding up. A negative slope represents a negative acceleration, meaning the object is slowing down.

How can a Force & Acceleration graph be used to calculate the net force on an object?

The net force on an object can be calculated by finding the slope of the graph and multiplying it by the mass of the object. The resulting value will be the net force acting on the object.

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