Mechanical Engineering - Engineering Mechanics - Discussion

Law of machine gives the relation between effort applied (P) and load lifted (W). By conducting experiments, effort-load graph can be plotted in a graph as effort(P) in y-axis and load(W) in y-axis. A straight inclined line is obtained and the slope this line is a constant called 'm'. m=tan θ\', where θ\' is the angle of line with respect to x-axis. (In some texts 'm' is also referred as the coefficient of friction.) The line touches a point on y-axis. This point is taken as 'C'. From the equation of the line we get,

P = mW+C
When efficiency is maximum (Ideal machines) slope passes through the origin.
That means C=0 or P= mW.
Then we have mechanical advantage, M.A = Velocity Ratio, V.R.
M.A = W/P=W/(mW) =1/m.
Mechanical Efficiency = (1/m)/V.R.
That is Mechanical Efficiency =1/(mV.R).

m is a constant here.

If someone knows the explanation for this question please explain here.

Please mention what these M, V, R indicates?

M means Mechanical advance and VR means Velocity Ratio.

Efficieny = MA/VR.

If MA is Max then Eff is Max.

MA is Max when MA = 1/m we get MA = 1/m from law of machine P = mW+c.

Since MA = W/p and substituting P from law of machine we get MA max = 1/m.

So Eff = 1/m*VR.

MA = W/P,

From law of machine.

P = mW+C.

MA = 1/(m+C/W).

So in limiting case when W tends to infinity, then C/W = 0 and max mechanical advantage equals to 1/m.

So efficiency = MA/VR.

Max efficiency = 1/m*VR.

What is m here?

What is 'm' here?

What is m here? someone please explain.