We did an experiment where a cart was being pulled down a track by a mass on a pulley. It looks like this:
http://www.webassign.net/serpse8/8-p-022.gif
where m1 is the cart and m2 is the mass pulling the car.
The purpose of the project was to determine the coefficient of friction. We used sensors to figure out the acceleration of the car and by using a series of equations that have been verified by my teacher and others, we calculated the coefficient of fricion. It was very close to what it was supposed to be.
The problem is that the coefficient of friction keeps changing. If someone increases the mass of m1 (the cart), the coefficient of friction decreases. If someone increases the mass of m2, the coefficient of friction increases.
This makes no freaking sense according to the laws of physics.
Can somone please explain to me why this keeps happening over and over again (100 trials)??
http://www.webassign.net/serpse8/8-p-022.gif
where m1 is the cart and m2 is the mass pulling the car.
The purpose of the project was to determine the coefficient of friction. We used sensors to figure out the acceleration of the car and by using a series of equations that have been verified by my teacher and others, we calculated the coefficient of fricion. It was very close to what it was supposed to be.
The problem is that the coefficient of friction keeps changing. If someone increases the mass of m1 (the cart), the coefficient of friction decreases. If someone increases the mass of m2, the coefficient of friction increases.
This makes no freaking sense according to the laws of physics.
Can somone please explain to me why this keeps happening over and over again (100 trials)??
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You say the coefficient of friction is very close to what it is supposed to be, but you also say it keeps changing. When it changes, is it still close to what it's supposed to be? Do you mean it changes by a small (but consistent) amount?
It could be because your equation is regarding the pulley as massless and frictionless, but that is not really true. If your equations assume the force of the string tension on the cart equals the force of the string tension on the hanging mass, then you are assuming a massless frictionless pulley. In reality the hanging string tension must be slightly higher. The excess goes to overcome friction in the pulley bearing and to accelerate the pulley rotationally.
When you do the experiment, you note that the acceleration is less than it would if the surface was frictionless. You attribute this difference to friction of m1 on the surface, but actually it is also partly the mass and friction of the pulley.
Suppose the coefficient of friction is actually u, and the force needed to overcome the resistance in the pulley is f. When you determine the difference between the no-friction expectation and the experimental result, what you actually get is
um1g + f
but you calculate your experimental result for coefficient of friction as
(um1g + f) / m1g
= u + f/m1g
There is an error of f / m1g. When m1 gets bigger, the error gets smaller, and the coefficient of friction you determine also gets smaller. Also, when m1 gets bigger, f gets smaller, because part of f is for accelerating the pulley, and the acceleration is less. So both factors contribute to a smaller error when m1 is bigger.
Therefore you should conclude that your most accurate result is when you use the largest m1.
Also note that in fact coefficient of friction can change. Surface contact forces are not an exact science, and the rule that frictional force is proportional to normal force is an approximation.
It could be because your equation is regarding the pulley as massless and frictionless, but that is not really true. If your equations assume the force of the string tension on the cart equals the force of the string tension on the hanging mass, then you are assuming a massless frictionless pulley. In reality the hanging string tension must be slightly higher. The excess goes to overcome friction in the pulley bearing and to accelerate the pulley rotationally.
When you do the experiment, you note that the acceleration is less than it would if the surface was frictionless. You attribute this difference to friction of m1 on the surface, but actually it is also partly the mass and friction of the pulley.
Suppose the coefficient of friction is actually u, and the force needed to overcome the resistance in the pulley is f. When you determine the difference between the no-friction expectation and the experimental result, what you actually get is
um1g + f
but you calculate your experimental result for coefficient of friction as
(um1g + f) / m1g
= u + f/m1g
There is an error of f / m1g. When m1 gets bigger, the error gets smaller, and the coefficient of friction you determine also gets smaller. Also, when m1 gets bigger, f gets smaller, because part of f is for accelerating the pulley, and the acceleration is less. So both factors contribute to a smaller error when m1 is bigger.
Therefore you should conclude that your most accurate result is when you use the largest m1.
Also note that in fact coefficient of friction can change. Surface contact forces are not an exact science, and the rule that frictional force is proportional to normal force is an approximation.