IB Physics Uniform Motion
To investigate the relationship between the angle of a slope incline and the acceleration of a model cart moving down it
As the angle of the slope incline increases, the acceleration of the model cart moving down it will also increase.
I have predicted that acceleration is directly linked with the angle of the slope on which the object is moving. When coming up with this hypothesis, I asked myself the following question, “what forces actually act on the model cart as it is going down the slope”. There are in fact three forces acting on the cart. The force of gravity (g), friction (F), and the force of reaction (R) (see diagram 1). If we were to draw a Y and X axis on the object, the X axis showing the movement along and the Y axis being perpendicular to that then we can find out how the forces act.
On the Y axis, there are two forces, the force of reaction and a fraction of the force of gravity. Since there is no movement along the Y axis we know that the forces cancel out. To find out the reaction force, we can use the formula R = mg ∙ cosine α (see diagram).
On the X axis, there is movement, which means that the 2 opposite forces (friction and the other fraction of the gravitational force) do not cancel out. We know that force is equal to mass times acceleration (F = ma) and in this case the force of friction is opposite to the remainder of the force of gravity. F = ma = mg ∙ sine α – Friction
Friction is often defined as a coefficient times the reaction force, (u∙R) and we know previously from our examination of the Y axis what R really is, so we have:
F = ma = mg ∙ sin α - u∙R
= mg ∙ sin α – u ∙ mg ∙ cosine α
take out the mg = mg (sin α – u∙ cosine α)
and that is all equal to ma = mg (sin α – u∙ cosine α)
divide both sides by m a = g (sin α – u∙ cosine α)
In our experiment, the angle (α) will range from 0-90 degrees, and by looking at the formula above I have predicted that as the α increases, so should a (acceleration)