Relationship between mass of cart, mass on a pulley and resulting acceleration

[NeedsHelp1212]

1. So the problem is rather simple. And the descriptive solution is a piece of cake. But I need help finding the mathematical relationship that exists between the mass of the pulley, mass of the cart, and the acceleration. In other words our lab consisted of a cart which had a mass of 500 grams. We had to see what happened to the acceleration when the mass on the pulley increased. Obviously the acceleration increased so when graphed with acceleration on the y-axis and mass of the pulley on the x-axis the line is going in the positive direction. As you can see I can describe what happens when we vary these different variables but I don't know the equation my teacher wants. He said for me to find the slope of each of my graphs. So I did that- for the graph with the cart of 500 grams it has a slope of .00604, for the cart with 600 grams it has a slope of .00572, for the cart of 700 grams it has a slope of .00558. For the cart of 1000 grams it has a slope of .00469. Lastly the cart with 1500 grams has a slope of .00368. As you can see it decreases as the mass of the cart increases. Now how do i incorporate that slope into a mathematical equation to show the relationship. Please help! thanks ( by the way its due tomorrow!)

 

[NeedsHelp1212]

Just to add to what is already stated we are currently learning about Newton's three laws so possibly his second law is involved ( net force = mass times a) I just don't know how. I have been thinking for about an hour with no progress

 

[NeedsHelp1212]

i know your not supposed to bump but this is killing? what could the equation possibly be. Acceleration decreases as mass of cart increases or acceleration increases as mass of pulley increases. How does that translate to an equation

 

[Nikitin]

incase you still haven't figuired it out;

a=F/m

if F (G, the weight of the pulley being pulled down by gravity) stays constant and m increases the a will decrease. You can find G by g*m (9,81 m/s*s times the mass of the pulley).

If you want the ratio between increase in mass and decrease in acceleration: If you increase the mass by factor of k, then the acceleration will "increase" (actually decrease) by a factor of k^(-1).

 

[rwisz]

The relationship between the mass of the cart, mass on the pulley, and resulting acceleration can be described by Newton's Second Law of Motion, which states that the acceleration of an object is directly proportional to the net force acting on it and inversely proportional to its mass. In this scenario, the cart is being pulled by the force of gravity, which is dependent on the mass on the pulley. As the mass on the pulley increases, the net force acting on the cart also increases, resulting in a larger acceleration.

To find the mathematical relationship, we can use the equation F=ma, where F is the net force, m is the mass, and a is the acceleration. By rearranging this equation, we get a=F/m. This means that the acceleration is equal to the net force divided by the mass. In this case, the net force is constant (due to gravity), so the relationship between the mass on the pulley and the acceleration is inverse (as one increases, the other decreases).

To incorporate the slope into the equation, we can use the formula for slope, which is rise over run. In this case, the rise is the change in acceleration and the run is the change in mass on the pulley. Therefore, the slope of the graph represents the change in acceleration per change in mass on the pulley. We can use this information to create a general equation for the relationship: a = k/m, where k is a constant value determined by the slope of the graph.

In conclusion, the mathematical relationship between the mass of the cart, mass on the pulley, and resulting acceleration is described by Newton's Second Law of Motion, with the equation a=F/m. The slope of the graph represents the change in acceleration per change in mass on the pulley, and can be used to create a general equation of a = k/m, where k is a constant value determined by the slope.