How Can We Calculate the Distance Traveled by a Coin in a Physics Experiment?

[smslca]

A rough sketch of experiment.

the red dots represent a side view of path traveled, F is downward force and the tool used here is a pen placing parallel to the coinHi. I have newly started to study mechanical physics. based on study, I conduct a simple experiment. But unfortunately i am unable apply the laws in reality.

Experiment:
I placed a coin(2 Indian Rupee coin) with radius "r" positioned flat part of coin parallel to base of my laptop. Also placed at edge of base such that "x mm" of diameter of coin is supported by laptop while 2r-x is free, unsupported with the coin in a balanced position. Now at "x+y mm < r" measured from center of coin toward the free end I applied a random force perpendicular to laptop base.

Now my question is , how can we compute(formulate) distance "z" traveled by coin measured from center of coin at start point to center of coin at the place it stopped in terms of known variables mentioned below.

My attempt:
To me the known values are : r,x,y,density of coin(p),width(or height) of coin(w),time it took to stop(t).
Here for simplicity I have not considered the torque generated, and visualized the traveled path as a simple parabolic path. Now I can measure the distance traveled
z = v₀t+(1/2)gt². where g is acceleration due to gravity.

But how can I find the initial velocity v₀. I know v₀ is not zero, since the situation here is not equivalent to a freely falling scenario.

 

[mikeph]

Is the force acting up or down?

 

[smslca]

Is the force acting up or down?

It's a downward force.

 

[tiny-tim]

hi smslca!

assuming the coin doesn't slip, it will rotate around the edge of the laptop until the reaction force is zero

calculate the velocity (magnitude and direction) of the centre of mass at that instant: that is your v_o and θ

(but it probably will slip, and if the edge is curved not sharp then that makes the maths even more difficult)

 

[PJC01]

Hi there! It's great that you are conducting experiments and trying to apply physics laws to real life situations. In order to calculate the distance traveled by the coin, we need to consider the forces acting on it.

From your experiment, we can see that there are two main forces acting on the coin - the downward force of gravity (represented by F in your sketch) and the perpendicular force applied by you. The force of gravity will cause the coin to accelerate downwards, while the force you applied will cause it to accelerate horizontally.

To find the initial velocity (v0), we need to consider the balance of forces on the coin. At the start, the coin is in a balanced position, meaning the two forces (gravity and the force you applied) are equal in magnitude and opposite in direction. This means that the horizontal component of the force you applied is equal to the weight of the coin (mg), where m is the mass of the coin and g is the acceleration due to gravity.

Using this information, we can calculate the initial velocity using the formula v0 = F/m = (mg)/m = g. This means that the initial velocity is equal to the acceleration due to gravity.

Now, to find the distance traveled (z), we can use the formula z = v0t + (1/2)at^2, where a is the acceleration of the coin. Since we have already found that the initial velocity is equal to the acceleration due to gravity, we can simplify the formula to z = gt^2/2.

I hope this helps! Keep experimenting and applying physics laws to real life situations. Good luck!