Stopping Distance affected by Mass of Cart on Inclined Plane

[Bapple]

Homework Statement

I am doing my IB Physics Individual Investigation on how mass affects the stopping distance of a small cart when colliding with an open box at the bottom of an inclined plane.

I wanted to know the relationship mass has with the stopping distance, similar to how a train colliding with a container is much larger than a car when velocity is uniformly the same. To do this, I have kept as much constant as possible with the inclined plane being at an angle of 13.1 degrees with a constant height and length. The inclined plane allows the same amount of applied force on the cart when multiple tests for a data point is being done. The box is a simple cardboard open box that can easily fit through the constant cart I am testing. I have two motion detectors which detect the position, time, velocity, and acceleration at the same time: one at the bottom, right most on the horizontal table, 99.5 cm from the end of the ramp and one at the top of the ramp, about 61.7 cm from the end of the ramp. The mass is incremented by 0.1kg each time, so the data points would be 0.1, 0.2, 0.3, 0.4, 0.5. I have also attached an illustration of my setup. The only thing missing is the ruler which is positioned from the end of the ramp to the sensor at the bottom. The position at which the cart is released on the ramp is not changed either and is kept constant.

Homework Equations

I have come up with an equation derived from one of the SUVAT equations:
v^2 = u^2 + 2ad
since final velocity is zero, v = 0;
0= u^2 + 2ad
-(u)^2 = 2ad
since a = F/m;
-(u)^2 = 2(F/m)d
m[-(u)^2] / 2F = d

The Attempt at a Solution

When I finished conducting the experiment, I found out that the stopping distance did indeed increase as the mass increased and initial velocity, right before the cart hits the box, is around 1.00 ms^-1 for every mass. When inputing the velocity and stopping distance into the base SUVAT formula, I come up with different negative accelerations, largest being the smaller masses. This supports the hypothesis because the larger negative acceleration results in the cart stopping faster. But when trying to find F in the derived equation, I end up with a larger force as the mass goes up, rather than being constant. This leads to my confusion. If force was found to be constant, then mass would have a direct affect on the acceleration.

I am now very confused as to how I should proceed with my analysis. The data supports the hypothesis but I have no idea as to how this is happening. Is mass affecting this or something else entirely. If someone could please help, I would really appreciate it!

 

[haruspex]

when trying to find F in the derived equation, I end up with a larger force as the mass goes up, rather than being constant.

I'm not quite sure what you are saying. Are you finding that as the mass increases the magnitude of the acceleration decreases, but more slowly? Hence the net force must be increasing somewhat, but more slowly than the mass increases?
What forces do you think contribute to the deceleration?