# Motion under variable acceleration experiment

• bubblegumandcameras
In summary, it looks like your data suggests that friction decreases with increasing mass. This is likely due to the fact that the trolley and the mass attached to it are acting as one system.
bubblegumandcameras
Used a mass attached to a dynamic cart via pulley to examine motion under variable acceleration. As the mass was increased, my calculated friction force shows a decrease. I know that friction should increase with larger mass. Any suggestions as to why my calculations show a decrease? Used the equation Fk= mg-Mta where Mt= total mass of system, m=mass added to end of pulley, a=experimental acceleration

Welcome to PF;
It looks like you were examining motion with variable mass - did the acceleration vary during each test run?
Did you change the mass of the cart or the mass on the end of the pulley or both (explain)?
How did you measure the acceleration?
How did you derive the equation you used?
(What assumptions did you use?)

Last edited:
Out of curiosity I took some guesses:
Normally you would model friction as ##f=\mu mg## for the cart ... is there friction in the pulley too?

m=mass of trolley, M=total mass, then hanging mass is M-m > m (##\mu## needs to be measured.)

Free body diagrams for trolley accelerated by hanging mass.
(1) ##T-\mu mg = ma## for the cart
(2) ##(M-m)g - T = (M-m)a## for the hanging mass

Solve for ##a##:
(3) ##a = g - (1+\mu) mg/M##

experiment:
- change mass by taking weights off the trolley and adding them to the hanging mass - so M is a constant.
- measure the acceleration (time T over a fixed distance d ##a=2d/T^2##)
expect the plot of ##a## vs ##m## will be a straight line with slope ##s=-g(1+\mu)/M## and intercept ##g##
(does this sound like what you did?)

This allows us to calculate the friction coefficient from the measured slope.

If ##f## decreases with ##m##, then ##\mu## decreases with ##m## a lot.
This will change the shape of the graph - so: plot your data - is the graph a reasonable straight line?

If not, then what sort of curve is it?
Are there systematic errors in your experiment?
ie. the above calculation neglects friction and mass in the pulley... was this a good idea?

bsheikho

## 1. What is motion under variable acceleration?

Motion under variable acceleration is the movement of an object at different rates, with the acceleration changing at various points during the experiment. This type of motion is typically studied in physics and can be seen in real-world scenarios such as a car accelerating and decelerating on a road.

## 2. How is motion under variable acceleration measured?

Motion under variable acceleration is measured by tracking the position, velocity, and acceleration of an object over time. This can be done using various tools such as motion sensors, stopwatches, and video analysis software.

## 3. What are some examples of experiments that involve motion under variable acceleration?

Some examples of experiments that involve motion under variable acceleration include studying the motion of a pendulum, analyzing the acceleration of a falling object due to gravity, and investigating the motion of a car on an incline.

## 4. What factors can affect motion under variable acceleration?

The factors that can affect motion under variable acceleration include the initial velocity, the magnitude and direction of the applied force, and any external forces such as friction or air resistance. The mass and shape of the object can also play a role in how it accelerates.

## 5. Why is studying motion under variable acceleration important?

Studying motion under variable acceleration is important because it helps us understand the fundamental laws of physics, such as Newton's laws of motion. It also has practical applications, such as predicting the trajectory of a projectile or designing efficient transportation systems.

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