# Acceleration of a cart being pulled by a falling mass

• jumbogala
In summary, the conversation discusses a physics lab where a cart is attached to a string and is pulled by a falling mass. The goal is to graph the acceleration of the cart against the pulling force, but there is confusion about how to account for the changing mass of the system. Eventually, the correct method of dividing by the total mass is determined and the plot is successfully created.
jumbogala

## Homework Statement

I'm doing a lab and getting very confused.

A cart is on a table. It is attached to a string which goes over a pulley. The pulley is on the edge of the table.

On the end of the string there is a mass. When the mass falls straight down, it pulls on the string and makes the cart accelerate too.

## Homework Equations

Mass of the cart = 1 kg (constant)
Trial 1: mass falling down: 0.1 kg & mass added to cart: 0.4 kg
Trial 2: mass falling down: 0.2 kg & mass added to cart: 0.3 kg
Trial 3: mass falling down: 0.3 kg & mass added to cart: 0.2 kg
Trial 4: mass falling down: 0.4 kg & mass added to cart: 0.1 kg

## The Attempt at a Solution

I am supposed to graph the acceleration of the cart vs. the pulling force. However, I am not sure what this graph should look like.

For trial 1, the pulling force would be (0.1 kg)*(9.81 m/s2)=0.981 N, right? And the theoretical acceleration would be 0.981 N/(0.4 kg+1kg) = 1.962 m/s2.

However, if I graph a vs. F, I don't get a straight line, because the mass of the moving object is always changing. Is this right? In the book they make a big deal about the total mass of the system being constant, so I'm wondering if that has something to do with it.

The big deal is not for nothing: it is not only the cart that accelerates, the pulling mass doesn't stay in the same place either! In fact it accelerates just as fast as the cart. And that requires some force too!
 but I see you correctly take that into consideration.

1 person
Out of curiosity: what is being measured and how do you process the measurements to get a plot? Can you show the plot(s) you have so far ?

Thank you! I'm not sure what I was thinking. It makes much more sense to divide by the total mass. I did take it into consideration but then forgot to include in in my calculation.

Basically I just found the net force for each trial based on the weight of the falling mass. Then, I calculated the acceleration of the cart using a spark timer. I put the net force on the y-axis and the acceleration on the x, which gives a slope of m (total mass).

Unfortunately I did the plot by hand and I don't have a scanner handy, but it seems to be working out now. Thanks a ton for your help, much appreciated!

More than welcome. Good luck further on!

## What is the relationship between the acceleration of a cart and the mass of the falling object?

The acceleration of a cart being pulled by a falling mass is directly proportional to the mass of the falling object. This means that as the mass of the falling object increases, the acceleration of the cart also increases.

## How does the distance between the cart and the falling mass affect the acceleration?

The distance between the cart and the falling mass does not have a direct effect on the acceleration. However, if the distance is too small, the force of gravity acting on the falling mass may not be enough to accelerate the cart at a significant rate.

## What factors can affect the acceleration of the cart?

The acceleration of a cart being pulled by a falling mass is mainly affected by the mass of the falling object and the force of gravity. Other factors such as friction, air resistance, and the surface of the ground can also have an impact on the acceleration.

## Can the acceleration of the cart be greater than the acceleration due to gravity?

Yes, the acceleration of a cart being pulled by a falling mass can be greater than the acceleration due to gravity. This is because the force of gravity is shared between the falling mass and the cart, resulting in a smaller acceleration compared to when the force is applied to only one object.

## How can the acceleration of the cart be calculated?

The acceleration of a cart being pulled by a falling mass can be calculated using the formula a = F/m, where a is the acceleration, F is the force of gravity, and m is the mass of the falling object. The acceleration can also be determined by measuring the change in velocity over time using a velocity-time graph.

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