Calculate Mass Without Scale - Using Cars & Momentum

[elitespart]

If you were give an uknown mass and told to find it's mass w/out using a scale, how would u go about doing it. You have a meter stick, stopwatch, and 2 cars (which you can mass) w/ flat surfaces so you can put the unknown weight on it. I want to use the conservation of momentum in elastic collisions to figure out the unknown mass, but how would I go about incorprating the friction into it? any other info. would also be very helpful. Thanks.

 

[berkeman]

Since you know weight (and therefore the mass) of the cars, just make your own balance with the meter stick. Use the stopwatch as the fulcrum, and put one car on one side and the unknown mass on the other side. Use the relative distances when balanced to tell you the unknown mass.

That was easy.

 

[kyle8921]

I would approach this problem by first understanding the principles of conservation of momentum and the role of friction in elastic collisions. Conservation of momentum states that the total momentum of a closed system remains constant, meaning that the sum of all the momenta before a collision is equal to the sum of all the momenta after the collision.

In this case, we can use the two cars as a closed system, with one car representing the unknown mass and the other representing a known mass. We can also assume that the collision between these two cars is elastic, meaning that there is no loss of kinetic energy during the collision.

To incorporate friction into this scenario, we need to consider the fact that friction will act on both cars during the collision. This means that the total momentum of the system will not be conserved, as some of the momentum will be lost due to friction. However, we can still use the conservation of momentum principle to calculate the unknown mass by taking into account the frictional forces acting on both cars.

To do this, we can perform several trials with different known masses and measure the time it takes for the two cars to collide and come to a stop. By using the equation for momentum (p=mv) and the conservation of momentum principle, we can then calculate the unknown mass by solving for it in the equation:

m1v1 + m2v2 = (m1+m2)v'

Where m1 and v1 represent the known mass and velocity of one car, m2 and v2 represent the unknown mass and velocity of the other car, and v' represents the velocity of the two cars after the collision.

By rearranging this equation and substituting in values from our trials, we can calculate the unknown mass. However, it's important to note that the calculated mass will be an approximation due to the presence of friction. To improve the accuracy of our results, we can repeat the trials multiple times and take an average of the calculated masses.

In summary, by using the principles of conservation of momentum and taking into account the effects of friction, we can use the given materials and information to calculate the unknown mass without using a scale.