What Does the Y-Intercept and Slope Indicate in an Acceleration vs. Mass Graph?

[L²Cc]

Homework Statement

If in an acceleration vs. mass (kg) graph (where the x-axis reads (1/m1+m2), the inverse of the sum of masses), the best fit does interesect with the origin because if x = zero, or (1/m1+m2) = o, the final solution is unreal since it is mathematically incorrect to divide one by zero.

Likewise, in an acceleration vs. differences of masses, best interesects with origin since when m1-m2=0, acceleration, as as result, equals to zero.

Finally, would it be correct to stay that the y interest of an acceleration vs. mass graph represents the acceleration of the system when 0 masses are involved, or does it repersent the gravitational mass (resistance)?

Also, how would a slope of such a graph hint at the gravitational force acting on the mass, where the units of the slop are m/s²/kg?

Homework Equations

The Attempt at a Solution

 

[andrevdh]

When 1/m -> 0 whe are dealing with a situation where the mass is becoming very large and therefore the force will not be able to accelerate it (or get it to move out of rest and not succeeding). That is we are trying to push a very heavy object.

 

[m2003]

The acceleration vs. mass graph is a representation of the relationship between acceleration and mass in a system. The x-axis represents the inverse of the sum of masses, which means that as the sum of masses increases, the x-values decrease. This is because as the total mass of a system increases, the acceleration decreases due to a greater resistance to motion.

The best fit line intersecting with the origin is a mathematical requirement, as dividing by zero is undefined and unrealistic. This also means that there is no acceleration when the sum of masses is zero, which makes sense since there would be no force acting on the system.

Similarly, when looking at the acceleration vs. differences of masses, the best fit line also intersects with the origin when the difference in masses is zero. This means that when the masses are equal, the acceleration is zero, which again makes sense as there would be no net force acting on the system.

The y-intercept of an acceleration vs. mass graph represents the acceleration of the system when there are no masses involved, which means there is no force acting on the system. It does not represent the gravitational mass or resistance, as those are properties of the masses themselves.

The slope of the graph, with units of m/s²/kg, represents the gravitational force acting on the mass. This can be seen by rearranging the equation F=ma to solve for acceleration (a=F/m) and comparing it to the slope equation (m/s²/kg = F/N/kg). This shows that the slope is directly proportional to the gravitational force acting on the mass, with a greater slope indicating a greater force.