Instantaneous velocity of an object with varying mass at the bottom of a slope

[zfa9675]

I conducted an experiment to investigate whether the mass of an object will affect the object speed at the bottom of a slope with a constant gradient. The experiment showed that as the mass of the object (car) increases, the speed of the car at the bottom of the slope increases.

I still do not understand why. So far, I have come up with one proof that shows I am correct:

Assuming that all the potential energy at the top of the track is converted to kinetic energy at the bottom of the track (this is similar to Gallileo's theory)
Ep=mgh
Ek=(mv^2)/2

Ep=Ek
mgh=(mv^2)/2
2mgh=mv^2
2gh=v^2

g=9.81 ms^-2

19.62h=v^2

v=$\sqrt{}19.62h$

Therefore, the laws of indices shows:

The speed of the object at the bottom of the slope is directly proportional to the square root of the height. Therefore, the mass of the object should not affect the speed of the car at any given point.

Can you please tell me why the mass affects the speed

 

[gneill]

I conducted an experiment to investigate whether the mass of an object will affect the object speed at the bottom of a slope with a constant gradient. The experiment showed that as the mass of the object (car) increases, the speed of the car at the bottom of the slope increases.

I still do not understand why. So far, I have come up with one proof that shows I am correct:

Assuming that all the potential energy at the top of the track is converted to kinetic energy at the bottom of the track (this is similar to Gallileo's theory)
Ep=mgh
Ek=(mv^2)/2

Ep=Ek
mgh=(mv^2)/2
2mgh=mv^2
2gh=v^2

g=9.81 ms^-2

19.62h=v^2

v=$\sqrt{}19.62h$

Therefore, the laws of indices shows:

The speed of the object at the bottom of the slope is directly proportional to the square root of the height. Therefore, the mass of the object should not affect the speed of the car at any given point.

Can you please tell me why the mass affects the speed

Can you think of factors that are absent from your ideal mathematical model that might be present in a real-life scenario? How about forces you haven't accounted for?

 

[zfa9675]

The other theory I had which contradicts my first one is that the weight of the car is apart of the unbalanced force which causes its acceleration down the track (Newtons second law of motion)

F(unbalanced)=ma

a=F/m

As the force increases for a constant mass, the acceleration increases. However, the mass will also increase in this cas with the force so I figured the two would even each other out and there would not be a difference in acceleration.