Incline Planes

1) Purpose: This lab will test our theoretical model of incline planes.

2) Theory: An incline planes is one of three simple machines we will examine this year. The basic scheme in all simple machines is to trade distance for force. The vector relationships can be seen in figure 1:

F_N

m

Fs

Fg

Where: Fg = mg

Fig1

Angle “a”

Fn=Cos(a)*Fg

Fs=Sin(a)*Fg

By definition: F_f = m_s* F_N, therefore: m_s = F_f / F_N

m_s = Sin(a)*Fg / Cos(a)*Fg

m_s = Tan(a) (Eqn #1)

In addition, if the block is in motion with a constant velocity:

SF = 0 (Newton’s 1^st law)

Therefore

F_f + F_E = 0 (F_E = Force exerted on the block)

Therefore:

m_k * Cos(a)*Fg = F_E

if we vary angle “a” and measure F_E , this is in the form y = m*x+b

where m = m_k * Fg and b = 0

2) Procedure:

A) Determine m_s by increasing angle “a” until the object just begins to slide. Make sure you have a statistically valid population of data. Report the average and Relative error.

B) Determine m_k by graphical method

3) Analysis: Make sure you compare the two coefficients of friction. Theory predicts that the kinetic coefficient will be lower than the static. Is this the case? How linear was the plot? How reliable is the data for the static coefficient? Which coefficient do you feel is statiscally more valid, and why?